{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0001","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-12)+(-3)n，n∈N={0,1,2,…}。求索引 n=0 的項。","answer":{"kind":"short_text","value":"-12","explanation_zh":"把明示索引代入通項，a_0=-12+(-3)×0=-12；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305001,"parameters":{"operation":"explicit_term","u":-12,"d":-3,"n":0,"semantic_template":"qf-sequence-explicit-term/{\"d\":-3,\"n\":0,\"operation\":\"explicit_term\",\"u\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0002","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-11)+(-2)n，n∈N={0,1,2,…}。求索引 n=1 的項。","answer":{"kind":"short_text","value":"-13","explanation_zh":"把明示索引代入通項，a_1=-11+(-2)×1=-13；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305002,"parameters":{"operation":"explicit_term","u":-11,"d":-2,"n":1,"semantic_template":"qf-sequence-explicit-term/{\"d\":-2,\"n\":1,\"operation\":\"explicit_term\",\"u\":-11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0003","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-10)+(-1)n，n∈N={0,1,2,…}。求索引 n=2 的項。","answer":{"kind":"short_text","value":"-12","explanation_zh":"把明示索引代入通項，a_2=-10+(-1)×2=-12；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305003,"parameters":{"operation":"explicit_term","u":-10,"d":-1,"n":2,"semantic_template":"qf-sequence-explicit-term/{\"d\":-1,\"n\":2,\"operation\":\"explicit_term\",\"u\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0004","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-9)+(0)n，n∈N={0,1,2,…}。求索引 n=3 的項。","answer":{"kind":"short_text","value":"-9","explanation_zh":"把明示索引代入通項，a_3=-9+(0)×3=-9；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305004,"parameters":{"operation":"explicit_term","u":-9,"d":0,"n":3,"semantic_template":"qf-sequence-explicit-term/{\"d\":0,\"n\":3,\"operation\":\"explicit_term\",\"u\":-9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0005","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-8)+(1)n，n∈N={0,1,2,…}。求索引 n=4 的項。","answer":{"kind":"short_text","value":"-4","explanation_zh":"把明示索引代入通項，a_4=-8+(1)×4=-4；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305005,"parameters":{"operation":"explicit_term","u":-8,"d":1,"n":4,"semantic_template":"qf-sequence-explicit-term/{\"d\":1,\"n\":4,\"operation\":\"explicit_term\",\"u\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0006","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-7)+(2)n，n∈N={0,1,2,…}。求索引 n=5 的項。","answer":{"kind":"short_text","value":"3","explanation_zh":"把明示索引代入通項，a_5=-7+(2)×5=3；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305006,"parameters":{"operation":"explicit_term","u":-7,"d":2,"n":5,"semantic_template":"qf-sequence-explicit-term/{\"d\":2,\"n\":5,\"operation\":\"explicit_term\",\"u\":-7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0007","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-6)+(3)n，n∈N={0,1,2,…}。求索引 n=6 的項。","answer":{"kind":"short_text","value":"12","explanation_zh":"把明示索引代入通項，a_6=-6+(3)×6=12；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305007,"parameters":{"operation":"explicit_term","u":-6,"d":3,"n":6,"semantic_template":"qf-sequence-explicit-term/{\"d\":3,\"n\":6,\"operation\":\"explicit_term\",\"u\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0008","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-5)+(-3)n，n∈N={0,1,2,…}。求索引 n=7 的項。","answer":{"kind":"short_text","value":"-26","explanation_zh":"把明示索引代入通項，a_7=-5+(-3)×7=-26；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305008,"parameters":{"operation":"explicit_term","u":-5,"d":-3,"n":7,"semantic_template":"qf-sequence-explicit-term/{\"d\":-3,\"n\":7,\"operation\":\"explicit_term\",\"u\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0009","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-4)+(-2)n，n∈N={0,1,2,…}。求索引 n=8 的項。","answer":{"kind":"short_text","value":"-20","explanation_zh":"把明示索引代入通項，a_8=-4+(-2)×8=-20；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305009,"parameters":{"operation":"explicit_term","u":-4,"d":-2,"n":8,"semantic_template":"qf-sequence-explicit-term/{\"d\":-2,\"n\":8,\"operation\":\"explicit_term\",\"u\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0010","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-3)+(-1)n，n∈N={0,1,2,…}。求索引 n=9 的項。","answer":{"kind":"short_text","value":"-12","explanation_zh":"把明示索引代入通項，a_9=-3+(-1)×9=-12；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305010,"parameters":{"operation":"explicit_term","u":-3,"d":-1,"n":9,"semantic_template":"qf-sequence-explicit-term/{\"d\":-1,\"n\":9,\"operation\":\"explicit_term\",\"u\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0011","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-2)+(0)n，n∈N={0,1,2,…}。求索引 n=0 的項。","answer":{"kind":"short_text","value":"-2","explanation_zh":"把明示索引代入通項，a_0=-2+(0)×0=-2；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305011,"parameters":{"operation":"explicit_term","u":-2,"d":0,"n":0,"semantic_template":"qf-sequence-explicit-term/{\"d\":0,\"n\":0,\"operation\":\"explicit_term\",\"u\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0012","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(-1)+(1)n，n∈N={0,1,2,…}。求索引 n=1 的項。","answer":{"kind":"short_text","value":"0","explanation_zh":"把明示索引代入通項，a_1=-1+(1)×1=0；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305012,"parameters":{"operation":"explicit_term","u":-1,"d":1,"n":1,"semantic_template":"qf-sequence-explicit-term/{\"d\":1,\"n\":1,\"operation\":\"explicit_term\",\"u\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0013","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(0)+(2)n，n∈N={0,1,2,…}。求索引 n=2 的項。","answer":{"kind":"short_text","value":"4","explanation_zh":"把明示索引代入通項，a_2=0+(2)×2=4；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305013,"parameters":{"operation":"explicit_term","u":0,"d":2,"n":2,"semantic_template":"qf-sequence-explicit-term/{\"d\":2,\"n\":2,\"operation\":\"explicit_term\",\"u\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0014","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(1)+(3)n，n∈N={0,1,2,…}。求索引 n=3 的項。","answer":{"kind":"short_text","value":"10","explanation_zh":"把明示索引代入通項，a_3=1+(3)×3=10；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305014,"parameters":{"operation":"explicit_term","u":1,"d":3,"n":3,"semantic_template":"qf-sequence-explicit-term/{\"d\":3,\"n\":3,\"operation\":\"explicit_term\",\"u\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0015","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(2)+(-3)n，n∈N={0,1,2,…}。求索引 n=4 的項。","answer":{"kind":"short_text","value":"-10","explanation_zh":"把明示索引代入通項，a_4=2+(-3)×4=-10；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305015,"parameters":{"operation":"explicit_term","u":2,"d":-3,"n":4,"semantic_template":"qf-sequence-explicit-term/{\"d\":-3,\"n\":4,\"operation\":\"explicit_term\",\"u\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0016","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(3)+(-2)n，n∈N={0,1,2,…}。求索引 n=5 的項。","answer":{"kind":"short_text","value":"-7","explanation_zh":"把明示索引代入通項，a_5=3+(-2)×5=-7；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305016,"parameters":{"operation":"explicit_term","u":3,"d":-2,"n":5,"semantic_template":"qf-sequence-explicit-term/{\"d\":-2,\"n\":5,\"operation\":\"explicit_term\",\"u\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0017","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(4)+(-1)n，n∈N={0,1,2,…}。求索引 n=6 的項。","answer":{"kind":"short_text","value":"-2","explanation_zh":"把明示索引代入通項，a_6=4+(-1)×6=-2；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305017,"parameters":{"operation":"explicit_term","u":4,"d":-1,"n":6,"semantic_template":"qf-sequence-explicit-term/{\"d\":-1,\"n\":6,\"operation\":\"explicit_term\",\"u\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0018","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(5)+(0)n，n∈N={0,1,2,…}。求索引 n=7 的項。","answer":{"kind":"short_text","value":"5","explanation_zh":"把明示索引代入通項，a_7=5+(0)×7=5；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305018,"parameters":{"operation":"explicit_term","u":5,"d":0,"n":7,"semantic_template":"qf-sequence-explicit-term/{\"d\":0,\"n\":7,\"operation\":\"explicit_term\",\"u\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0019","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(6)+(1)n，n∈N={0,1,2,…}。求索引 n=8 的項。","answer":{"kind":"short_text","value":"14","explanation_zh":"把明示索引代入通項，a_8=6+(1)×8=14；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305019,"parameters":{"operation":"explicit_term","u":6,"d":1,"n":8,"semantic_template":"qf-sequence-explicit-term/{\"d\":1,\"n\":8,\"operation\":\"explicit_term\",\"u\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0020","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(7)+(2)n，n∈N={0,1,2,…}。求索引 n=9 的項。","answer":{"kind":"short_text","value":"25","explanation_zh":"把明示索引代入通項，a_9=7+(2)×9=25；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305020,"parameters":{"operation":"explicit_term","u":7,"d":2,"n":9,"semantic_template":"qf-sequence-explicit-term/{\"d\":2,\"n\":9,\"operation\":\"explicit_term\",\"u\":7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0021","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(8)+(3)n，n∈N={0,1,2,…}。求索引 n=0 的項。","answer":{"kind":"short_text","value":"8","explanation_zh":"把明示索引代入通項，a_0=8+(3)×0=8；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305021,"parameters":{"operation":"explicit_term","u":8,"d":3,"n":0,"semantic_template":"qf-sequence-explicit-term/{\"d\":3,\"n\":0,\"operation\":\"explicit_term\",\"u\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0022","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(9)+(-3)n，n∈N={0,1,2,…}。求索引 n=1 的項。","answer":{"kind":"short_text","value":"6","explanation_zh":"把明示索引代入通項，a_1=9+(-3)×1=6；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305022,"parameters":{"operation":"explicit_term","u":9,"d":-3,"n":1,"semantic_template":"qf-sequence-explicit-term/{\"d\":-3,\"n\":1,\"operation\":\"explicit_term\",\"u\":9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0023","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(10)+(-2)n，n∈N={0,1,2,…}。求索引 n=2 的項。","answer":{"kind":"short_text","value":"6","explanation_zh":"把明示索引代入通項，a_2=10+(-2)×2=6；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305023,"parameters":{"operation":"explicit_term","u":10,"d":-2,"n":2,"semantic_template":"qf-sequence-explicit-term/{\"d\":-2,\"n\":2,\"operation\":\"explicit_term\",\"u\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0024","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(11)+(-1)n，n∈N={0,1,2,…}。求索引 n=3 的項。","answer":{"kind":"short_text","value":"8","explanation_zh":"把明示索引代入通項，a_3=11+(-1)×3=8；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305024,"parameters":{"operation":"explicit_term","u":11,"d":-1,"n":3,"semantic_template":"qf-sequence-explicit-term/{\"d\":-1,\"n\":3,\"operation\":\"explicit_term\",\"u\":11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-explicit-term-0025","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"零起始通項計算","stem_zh":"實數數列索引從 0，明示 a_n=(12)+(0)n，n∈N={0,1,2,…}。求索引 n=4 的項。","answer":{"kind":"short_text","value":"12","explanation_zh":"把明示索引代入通項，a_4=12+(0)×4=12；不涉及數列極限。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","明示通項"]},"variant":{"family_id":"qf-sequence-explicit-term","seed":202609305025,"parameters":{"operation":"explicit_term","u":12,"d":0,"n":4,"semantic_template":"qf-sequence-explicit-term/{\"d\":0,\"n\":4,\"operation\":\"explicit_term\",\"u\":12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0001","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=12，遞迴 a_(j+1)=a_j+(-3) 對所有 j≥0。求索引 n=0 的項。","answer":{"kind":"short_text","value":"12","explanation_zh":"由 a_0 出發做 0 次明示遞迴更新，得到 a_0=12；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305101,"parameters":{"operation":"recursive_term","u":12,"d":-3,"n":0,"semantic_template":"qf-sequence-recursive-term/{\"d\":-3,\"n\":0,\"operation\":\"recursive_term\",\"u\":12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0002","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=11，遞迴 a_(j+1)=a_j+(-2) 對所有 j≥0。求索引 n=3 的項。","answer":{"kind":"short_text","value":"5","explanation_zh":"由 a_0 出發做 3 次明示遞迴更新，得到 a_3=5；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305102,"parameters":{"operation":"recursive_term","u":11,"d":-2,"n":3,"semantic_template":"qf-sequence-recursive-term/{\"d\":-2,\"n\":3,\"operation\":\"recursive_term\",\"u\":11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0003","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=10，遞迴 a_(j+1)=a_j+(-1) 對所有 j≥0。求索引 n=6 的項。","answer":{"kind":"short_text","value":"4","explanation_zh":"由 a_0 出發做 6 次明示遞迴更新，得到 a_6=4；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305103,"parameters":{"operation":"recursive_term","u":10,"d":-1,"n":6,"semantic_template":"qf-sequence-recursive-term/{\"d\":-1,\"n\":6,\"operation\":\"recursive_term\",\"u\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0004","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=9，遞迴 a_(j+1)=a_j+(0) 對所有 j≥0。求索引 n=9 的項。","answer":{"kind":"short_text","value":"9","explanation_zh":"由 a_0 出發做 9 次明示遞迴更新，得到 a_9=9；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305104,"parameters":{"operation":"recursive_term","u":9,"d":0,"n":9,"semantic_template":"qf-sequence-recursive-term/{\"d\":0,\"n\":9,\"operation\":\"recursive_term\",\"u\":9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0005","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=8，遞迴 a_(j+1)=a_j+(1) 對所有 j≥0。求索引 n=12 的項。","answer":{"kind":"short_text","value":"20","explanation_zh":"由 a_0 出發做 12 次明示遞迴更新，得到 a_12=20；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305105,"parameters":{"operation":"recursive_term","u":8,"d":1,"n":12,"semantic_template":"qf-sequence-recursive-term/{\"d\":1,\"n\":12,\"operation\":\"recursive_term\",\"u\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0006","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=7，遞迴 a_(j+1)=a_j+(2) 對所有 j≥0。求索引 n=2 的項。","answer":{"kind":"short_text","value":"11","explanation_zh":"由 a_0 出發做 2 次明示遞迴更新，得到 a_2=11；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305106,"parameters":{"operation":"recursive_term","u":7,"d":2,"n":2,"semantic_template":"qf-sequence-recursive-term/{\"d\":2,\"n\":2,\"operation\":\"recursive_term\",\"u\":7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0007","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=6，遞迴 a_(j+1)=a_j+(3) 對所有 j≥0。求索引 n=5 的項。","answer":{"kind":"short_text","value":"21","explanation_zh":"由 a_0 出發做 5 次明示遞迴更新，得到 a_5=21；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305107,"parameters":{"operation":"recursive_term","u":6,"d":3,"n":5,"semantic_template":"qf-sequence-recursive-term/{\"d\":3,\"n\":5,\"operation\":\"recursive_term\",\"u\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0008","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=5，遞迴 a_(j+1)=a_j+(-3) 對所有 j≥0。求索引 n=8 的項。","answer":{"kind":"short_text","value":"-19","explanation_zh":"由 a_0 出發做 8 次明示遞迴更新，得到 a_8=-19；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305108,"parameters":{"operation":"recursive_term","u":5,"d":-3,"n":8,"semantic_template":"qf-sequence-recursive-term/{\"d\":-3,\"n\":8,\"operation\":\"recursive_term\",\"u\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0009","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=4，遞迴 a_(j+1)=a_j+(-2) 對所有 j≥0。求索引 n=11 的項。","answer":{"kind":"short_text","value":"-18","explanation_zh":"由 a_0 出發做 11 次明示遞迴更新，得到 a_11=-18；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305109,"parameters":{"operation":"recursive_term","u":4,"d":-2,"n":11,"semantic_template":"qf-sequence-recursive-term/{\"d\":-2,\"n\":11,\"operation\":\"recursive_term\",\"u\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0010","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=3，遞迴 a_(j+1)=a_j+(-1) 對所有 j≥0。求索引 n=1 的項。","answer":{"kind":"short_text","value":"2","explanation_zh":"由 a_0 出發做 1 次明示遞迴更新，得到 a_1=2；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305110,"parameters":{"operation":"recursive_term","u":3,"d":-1,"n":1,"semantic_template":"qf-sequence-recursive-term/{\"d\":-1,\"n\":1,\"operation\":\"recursive_term\",\"u\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0011","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=2，遞迴 a_(j+1)=a_j+(0) 對所有 j≥0。求索引 n=4 的項。","answer":{"kind":"short_text","value":"2","explanation_zh":"由 a_0 出發做 4 次明示遞迴更新，得到 a_4=2；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305111,"parameters":{"operation":"recursive_term","u":2,"d":0,"n":4,"semantic_template":"qf-sequence-recursive-term/{\"d\":0,\"n\":4,\"operation\":\"recursive_term\",\"u\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0012","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=1，遞迴 a_(j+1)=a_j+(1) 對所有 j≥0。求索引 n=7 的項。","answer":{"kind":"short_text","value":"8","explanation_zh":"由 a_0 出發做 7 次明示遞迴更新，得到 a_7=8；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305112,"parameters":{"operation":"recursive_term","u":1,"d":1,"n":7,"semantic_template":"qf-sequence-recursive-term/{\"d\":1,\"n\":7,\"operation\":\"recursive_term\",\"u\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0013","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=0，遞迴 a_(j+1)=a_j+(2) 對所有 j≥0。求索引 n=10 的項。","answer":{"kind":"short_text","value":"20","explanation_zh":"由 a_0 出發做 10 次明示遞迴更新，得到 a_10=20；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305113,"parameters":{"operation":"recursive_term","u":0,"d":2,"n":10,"semantic_template":"qf-sequence-recursive-term/{\"d\":2,\"n\":10,\"operation\":\"recursive_term\",\"u\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0014","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-1，遞迴 a_(j+1)=a_j+(3) 對所有 j≥0。求索引 n=0 的項。","answer":{"kind":"short_text","value":"-1","explanation_zh":"由 a_0 出發做 0 次明示遞迴更新，得到 a_0=-1；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305114,"parameters":{"operation":"recursive_term","u":-1,"d":3,"n":0,"semantic_template":"qf-sequence-recursive-term/{\"d\":3,\"n\":0,\"operation\":\"recursive_term\",\"u\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0015","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-2，遞迴 a_(j+1)=a_j+(-3) 對所有 j≥0。求索引 n=3 的項。","answer":{"kind":"short_text","value":"-11","explanation_zh":"由 a_0 出發做 3 次明示遞迴更新，得到 a_3=-11；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305115,"parameters":{"operation":"recursive_term","u":-2,"d":-3,"n":3,"semantic_template":"qf-sequence-recursive-term/{\"d\":-3,\"n\":3,\"operation\":\"recursive_term\",\"u\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0016","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-3，遞迴 a_(j+1)=a_j+(-2) 對所有 j≥0。求索引 n=6 的項。","answer":{"kind":"short_text","value":"-15","explanation_zh":"由 a_0 出發做 6 次明示遞迴更新，得到 a_6=-15；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305116,"parameters":{"operation":"recursive_term","u":-3,"d":-2,"n":6,"semantic_template":"qf-sequence-recursive-term/{\"d\":-2,\"n\":6,\"operation\":\"recursive_term\",\"u\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0017","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-4，遞迴 a_(j+1)=a_j+(-1) 對所有 j≥0。求索引 n=9 的項。","answer":{"kind":"short_text","value":"-13","explanation_zh":"由 a_0 出發做 9 次明示遞迴更新，得到 a_9=-13；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305117,"parameters":{"operation":"recursive_term","u":-4,"d":-1,"n":9,"semantic_template":"qf-sequence-recursive-term/{\"d\":-1,\"n\":9,\"operation\":\"recursive_term\",\"u\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0018","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-5，遞迴 a_(j+1)=a_j+(0) 對所有 j≥0。求索引 n=12 的項。","answer":{"kind":"short_text","value":"-5","explanation_zh":"由 a_0 出發做 12 次明示遞迴更新，得到 a_12=-5；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305118,"parameters":{"operation":"recursive_term","u":-5,"d":0,"n":12,"semantic_template":"qf-sequence-recursive-term/{\"d\":0,\"n\":12,\"operation\":\"recursive_term\",\"u\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0019","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-6，遞迴 a_(j+1)=a_j+(1) 對所有 j≥0。求索引 n=2 的項。","answer":{"kind":"short_text","value":"-4","explanation_zh":"由 a_0 出發做 2 次明示遞迴更新，得到 a_2=-4；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305119,"parameters":{"operation":"recursive_term","u":-6,"d":1,"n":2,"semantic_template":"qf-sequence-recursive-term/{\"d\":1,\"n\":2,\"operation\":\"recursive_term\",\"u\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0020","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-7，遞迴 a_(j+1)=a_j+(2) 對所有 j≥0。求索引 n=5 的項。","answer":{"kind":"short_text","value":"3","explanation_zh":"由 a_0 出發做 5 次明示遞迴更新，得到 a_5=3；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305120,"parameters":{"operation":"recursive_term","u":-7,"d":2,"n":5,"semantic_template":"qf-sequence-recursive-term/{\"d\":2,\"n\":5,\"operation\":\"recursive_term\",\"u\":-7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0021","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-8，遞迴 a_(j+1)=a_j+(3) 對所有 j≥0。求索引 n=8 的項。","answer":{"kind":"short_text","value":"16","explanation_zh":"由 a_0 出發做 8 次明示遞迴更新，得到 a_8=16；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305121,"parameters":{"operation":"recursive_term","u":-8,"d":3,"n":8,"semantic_template":"qf-sequence-recursive-term/{\"d\":3,\"n\":8,\"operation\":\"recursive_term\",\"u\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0022","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-9，遞迴 a_(j+1)=a_j+(-3) 對所有 j≥0。求索引 n=11 的項。","answer":{"kind":"short_text","value":"-42","explanation_zh":"由 a_0 出發做 11 次明示遞迴更新，得到 a_11=-42；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305122,"parameters":{"operation":"recursive_term","u":-9,"d":-3,"n":11,"semantic_template":"qf-sequence-recursive-term/{\"d\":-3,\"n\":11,\"operation\":\"recursive_term\",\"u\":-9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0023","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-10，遞迴 a_(j+1)=a_j+(-2) 對所有 j≥0。求索引 n=1 的項。","answer":{"kind":"short_text","value":"-12","explanation_zh":"由 a_0 出發做 1 次明示遞迴更新，得到 a_1=-12；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305123,"parameters":{"operation":"recursive_term","u":-10,"d":-2,"n":1,"semantic_template":"qf-sequence-recursive-term/{\"d\":-2,\"n\":1,\"operation\":\"recursive_term\",\"u\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0024","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-11，遞迴 a_(j+1)=a_j+(-1) 對所有 j≥0。求索引 n=4 的項。","answer":{"kind":"short_text","value":"-15","explanation_zh":"由 a_0 出發做 4 次明示遞迴更新，得到 a_4=-15；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305124,"parameters":{"operation":"recursive_term","u":-11,"d":-1,"n":4,"semantic_template":"qf-sequence-recursive-term/{\"d\":-1,\"n\":4,\"operation\":\"recursive_term\",\"u\":-11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-recursive-term-0025","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"附初值的遞迴項","stem_zh":"實數數列索引從 0，明示初值 a_0=-12，遞迴 a_(j+1)=a_j+(0) 對所有 j≥0。求索引 n=7 的項。","answer":{"kind":"short_text","value":"-12","explanation_zh":"由 a_0 出發做 7 次明示遞迴更新，得到 a_7=-12；沒有使用未給定的後續規則。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["初始條件","有限遞迴"]},"variant":{"family_id":"qf-sequence-recursive-term","seed":202609305125,"parameters":{"operation":"recursive_term","u":-12,"d":0,"n":7,"semantic_template":"qf-sequence-recursive-term/{\"d\":0,\"n\":7,\"operation\":\"recursive_term\",\"u\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0001","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-12)+(-3)n，n∈N。列出長度 L=0 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[]","explanation_zh":"依索引次序從 0 取恰好 0 項，得到 []；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305201,"parameters":{"operation":"prefix","u":-12,"d":-3,"L":0,"semantic_template":"qf-sequence-prefix/{\"L\":0,\"d\":-3,\"operation\":\"prefix\",\"u\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0002","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-11)+(-2)n，n∈N。列出長度 L=2 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-11, -13]","explanation_zh":"依索引次序從 0 取恰好 2 項，得到 [-11, -13]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305202,"parameters":{"operation":"prefix","u":-11,"d":-2,"L":2,"semantic_template":"qf-sequence-prefix/{\"L\":2,\"d\":-2,\"operation\":\"prefix\",\"u\":-11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0003","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-10)+(-1)n，n∈N。列出長度 L=3 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-10, -11, -12]","explanation_zh":"依索引次序從 0 取恰好 3 項，得到 [-10, -11, -12]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305203,"parameters":{"operation":"prefix","u":-10,"d":-1,"L":3,"semantic_template":"qf-sequence-prefix/{\"L\":3,\"d\":-1,\"operation\":\"prefix\",\"u\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0004","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-9)+(0)n，n∈N。列出長度 L=4 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-9, -9, -9, -9]","explanation_zh":"依索引次序從 0 取恰好 4 項，得到 [-9, -9, -9, -9]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305204,"parameters":{"operation":"prefix","u":-9,"d":0,"L":4,"semantic_template":"qf-sequence-prefix/{\"L\":4,\"d\":0,\"operation\":\"prefix\",\"u\":-9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0005","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-8)+(1)n，n∈N。列出長度 L=5 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-8, -7, -6, -5, -4]","explanation_zh":"依索引次序從 0 取恰好 5 項，得到 [-8, -7, -6, -5, -4]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305205,"parameters":{"operation":"prefix","u":-8,"d":1,"L":5,"semantic_template":"qf-sequence-prefix/{\"L\":5,\"d\":1,\"operation\":\"prefix\",\"u\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0006","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-7)+(2)n，n∈N。列出長度 L=6 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-7, -5, -3, -1, 1, 3]","explanation_zh":"依索引次序從 0 取恰好 6 項，得到 [-7, -5, -3, -1, 1, 3]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305206,"parameters":{"operation":"prefix","u":-7,"d":2,"L":6,"semantic_template":"qf-sequence-prefix/{\"L\":6,\"d\":2,\"operation\":\"prefix\",\"u\":-7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0007","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-6)+(3)n，n∈N。列出長度 L=7 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-6, -3, 0, 3, 6, 9, 12]","explanation_zh":"依索引次序從 0 取恰好 7 項，得到 [-6, -3, 0, 3, 6, 9, 12]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305207,"parameters":{"operation":"prefix","u":-6,"d":3,"L":7,"semantic_template":"qf-sequence-prefix/{\"L\":7,\"d\":3,\"operation\":\"prefix\",\"u\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0008","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-5)+(-3)n，n∈N。列出長度 L=8 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-5, -8, -11, -14, -17, -20, -23, -26]","explanation_zh":"依索引次序從 0 取恰好 8 項，得到 [-5, -8, -11, -14, -17, -20, -23, -26]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305208,"parameters":{"operation":"prefix","u":-5,"d":-3,"L":8,"semantic_template":"qf-sequence-prefix/{\"L\":8,\"d\":-3,\"operation\":\"prefix\",\"u\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0009","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-4)+(-2)n，n∈N。列出長度 L=1 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-4]","explanation_zh":"依索引次序從 0 取恰好 1 項，得到 [-4]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305209,"parameters":{"operation":"prefix","u":-4,"d":-2,"L":1,"semantic_template":"qf-sequence-prefix/{\"L\":1,\"d\":-2,\"operation\":\"prefix\",\"u\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0010","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-3)+(-1)n，n∈N。列出長度 L=2 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-3, -4]","explanation_zh":"依索引次序從 0 取恰好 2 項，得到 [-3, -4]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305210,"parameters":{"operation":"prefix","u":-3,"d":-1,"L":2,"semantic_template":"qf-sequence-prefix/{\"L\":2,\"d\":-1,\"operation\":\"prefix\",\"u\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0011","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-2)+(0)n，n∈N。列出長度 L=3 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-2, -2, -2]","explanation_zh":"依索引次序從 0 取恰好 3 項，得到 [-2, -2, -2]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305211,"parameters":{"operation":"prefix","u":-2,"d":0,"L":3,"semantic_template":"qf-sequence-prefix/{\"L\":3,\"d\":0,\"operation\":\"prefix\",\"u\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0012","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(-1)+(1)n，n∈N。列出長度 L=4 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[-1, 0, 1, 2]","explanation_zh":"依索引次序從 0 取恰好 4 項，得到 [-1, 0, 1, 2]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305212,"parameters":{"operation":"prefix","u":-1,"d":1,"L":4,"semantic_template":"qf-sequence-prefix/{\"L\":4,\"d\":1,\"operation\":\"prefix\",\"u\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0013","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(0)+(2)n，n∈N。列出長度 L=5 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[0, 2, 4, 6, 8]","explanation_zh":"依索引次序從 0 取恰好 5 項，得到 [0, 2, 4, 6, 8]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305213,"parameters":{"operation":"prefix","u":0,"d":2,"L":5,"semantic_template":"qf-sequence-prefix/{\"L\":5,\"d\":2,\"operation\":\"prefix\",\"u\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0014","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(1)+(3)n，n∈N。列出長度 L=6 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[1, 4, 7, 10, 13, 16]","explanation_zh":"依索引次序從 0 取恰好 6 項，得到 [1, 4, 7, 10, 13, 16]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305214,"parameters":{"operation":"prefix","u":1,"d":3,"L":6,"semantic_template":"qf-sequence-prefix/{\"L\":6,\"d\":3,\"operation\":\"prefix\",\"u\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0015","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(2)+(-3)n，n∈N。列出長度 L=7 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[2, -1, -4, -7, -10, -13, -16]","explanation_zh":"依索引次序從 0 取恰好 7 項，得到 [2, -1, -4, -7, -10, -13, -16]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305215,"parameters":{"operation":"prefix","u":2,"d":-3,"L":7,"semantic_template":"qf-sequence-prefix/{\"L\":7,\"d\":-3,\"operation\":\"prefix\",\"u\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0016","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(3)+(-2)n，n∈N。列出長度 L=8 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[3, 1, -1, -3, -5, -7, -9, -11]","explanation_zh":"依索引次序從 0 取恰好 8 項，得到 [3, 1, -1, -3, -5, -7, -9, -11]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305216,"parameters":{"operation":"prefix","u":3,"d":-2,"L":8,"semantic_template":"qf-sequence-prefix/{\"L\":8,\"d\":-2,\"operation\":\"prefix\",\"u\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0017","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(4)+(-1)n，n∈N。列出長度 L=1 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[4]","explanation_zh":"依索引次序從 0 取恰好 1 項，得到 [4]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305217,"parameters":{"operation":"prefix","u":4,"d":-1,"L":1,"semantic_template":"qf-sequence-prefix/{\"L\":1,\"d\":-1,\"operation\":\"prefix\",\"u\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0018","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(5)+(0)n，n∈N。列出長度 L=2 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[5, 5]","explanation_zh":"依索引次序從 0 取恰好 2 項，得到 [5, 5]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305218,"parameters":{"operation":"prefix","u":5,"d":0,"L":2,"semantic_template":"qf-sequence-prefix/{\"L\":2,\"d\":0,\"operation\":\"prefix\",\"u\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0019","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(6)+(1)n，n∈N。列出長度 L=3 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[6, 7, 8]","explanation_zh":"依索引次序從 0 取恰好 3 項，得到 [6, 7, 8]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305219,"parameters":{"operation":"prefix","u":6,"d":1,"L":3,"semantic_template":"qf-sequence-prefix/{\"L\":3,\"d\":1,\"operation\":\"prefix\",\"u\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0020","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(7)+(2)n，n∈N。列出長度 L=4 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[7, 9, 11, 13]","explanation_zh":"依索引次序從 0 取恰好 4 項，得到 [7, 9, 11, 13]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305220,"parameters":{"operation":"prefix","u":7,"d":2,"L":4,"semantic_template":"qf-sequence-prefix/{\"L\":4,\"d\":2,\"operation\":\"prefix\",\"u\":7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0021","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(8)+(3)n，n∈N。列出長度 L=5 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[8, 11, 14, 17, 20]","explanation_zh":"依索引次序從 0 取恰好 5 項，得到 [8, 11, 14, 17, 20]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305221,"parameters":{"operation":"prefix","u":8,"d":3,"L":5,"semantic_template":"qf-sequence-prefix/{\"L\":5,\"d\":3,\"operation\":\"prefix\",\"u\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0022","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(9)+(-3)n，n∈N。列出長度 L=6 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[9, 6, 3, 0, -3, -6]","explanation_zh":"依索引次序從 0 取恰好 6 項，得到 [9, 6, 3, 0, -3, -6]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305222,"parameters":{"operation":"prefix","u":9,"d":-3,"L":6,"semantic_template":"qf-sequence-prefix/{\"L\":6,\"d\":-3,\"operation\":\"prefix\",\"u\":9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0023","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(10)+(-2)n，n∈N。列出長度 L=7 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[10, 8, 6, 4, 2, 0, -2]","explanation_zh":"依索引次序從 0 取恰好 7 項，得到 [10, 8, 6, 4, 2, 0, -2]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305223,"parameters":{"operation":"prefix","u":10,"d":-2,"L":7,"semantic_template":"qf-sequence-prefix/{\"L\":7,\"d\":-2,\"operation\":\"prefix\",\"u\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0024","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(11)+(-1)n，n∈N。列出長度 L=8 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[11, 10, 9, 8, 7, 6, 5, 4]","explanation_zh":"依索引次序從 0 取恰好 8 項，得到 [11, 10, 9, 8, 7, 6, 5, 4]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305224,"parameters":{"operation":"prefix","u":11,"d":-1,"L":8,"semantic_template":"qf-sequence-prefix/{\"L\":8,\"d\":-1,\"operation\":\"prefix\",\"u\":11}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-prefix-0025","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"明示數列的有限前綴","stem_zh":"實數數列索引從 0，明示 a_n=(12)+(0)n，n∈N。列出長度 L=1 的前綴 [a_0,…,a_(L-1)]；L=0 時用 []。","answer":{"kind":"short_text","value":"[12]","explanation_zh":"依索引次序從 0 取恰好 1 項，得到 [12]；這是明示公式的前綴，不是猜測規律。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["前綴長度","索引次序"]},"variant":{"family_id":"qf-sequence-prefix","seed":202609305225,"parameters":{"operation":"prefix","u":12,"d":0,"L":1,"semantic_template":"qf-sequence-prefix/{\"L\":1,\"d\":0,\"operation\":\"prefix\",\"u\":12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0001","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=0，索引從 0，可用索引須滿足 0≤n<L。n=-1 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 -1, 0；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305301,"parameters":{"operation":"finite_index","L":0,"n":-1,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":0,\"n\":-1,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0002","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=0，索引從 0，可用索引須滿足 0≤n<L。n=0 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 0, 0；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305302,"parameters":{"operation":"finite_index","L":0,"n":0,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":0,\"n\":0,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0003","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=0，索引從 0，可用索引須滿足 0≤n<L。n=1 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 1, 0；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305303,"parameters":{"operation":"finite_index","L":0,"n":1,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":0,\"n\":1,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0004","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=1，索引從 0，可用索引須滿足 0≤n<L。n=-1 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 -1, 1；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305304,"parameters":{"operation":"finite_index","L":1,"n":-1,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":1,\"n\":-1,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0005","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=1，索引從 0，可用索引須滿足 0≤n<L。n=0 是可用索引嗎？","answer":{"kind":"short_text","value":"是","explanation_zh":"待判定索引與長度為 0, 1；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305305,"parameters":{"operation":"finite_index","L":1,"n":0,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":1,\"n\":0,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0006","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=1，索引從 0，可用索引須滿足 0≤n<L。n=1 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 1, 1；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305306,"parameters":{"operation":"finite_index","L":1,"n":1,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":1,\"n\":1,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0007","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=1，索引從 0，可用索引須滿足 0≤n<L。n=2 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 2, 1；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305307,"parameters":{"operation":"finite_index","L":1,"n":2,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":1,\"n\":2,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0008","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=2，索引從 0，可用索引須滿足 0≤n<L。n=0 是可用索引嗎？","answer":{"kind":"short_text","value":"是","explanation_zh":"待判定索引與長度為 0, 2；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305308,"parameters":{"operation":"finite_index","L":2,"n":0,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":2,\"n\":0,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0009","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=2，索引從 0，可用索引須滿足 0≤n<L。n=1 是可用索引嗎？","answer":{"kind":"short_text","value":"是","explanation_zh":"待判定索引與長度為 1, 2；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305309,"parameters":{"operation":"finite_index","L":2,"n":1,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":2,\"n\":1,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0010","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=2，索引從 0，可用索引須滿足 0≤n<L。n=2 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 2, 2；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305310,"parameters":{"operation":"finite_index","L":2,"n":2,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":2,\"n\":2,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0011","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=2，索引從 0，可用索引須滿足 0≤n<L。n=-2 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 -2, 2；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305311,"parameters":{"operation":"finite_index","L":2,"n":-2,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":2,\"n\":-2,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0012","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=3，索引從 0，可用索引須滿足 0≤n<L。n=2 是可用索引嗎？","answer":{"kind":"short_text","value":"是","explanation_zh":"待判定索引與長度為 2, 3；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305312,"parameters":{"operation":"finite_index","L":3,"n":2,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":3,\"n\":2,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0013","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=3，索引從 0，可用索引須滿足 0≤n<L。n=3 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 3, 3；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305313,"parameters":{"operation":"finite_index","L":3,"n":3,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":3,\"n\":3,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0014","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=3，索引從 0，可用索引須滿足 0≤n<L。n=4 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 4, 3；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305314,"parameters":{"operation":"finite_index","L":3,"n":4,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":3,\"n\":4,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0015","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=3，索引從 0，可用索引須滿足 0≤n<L。n=-1 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 -1, 3；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305315,"parameters":{"operation":"finite_index","L":3,"n":-1,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":3,\"n\":-1,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0016","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=5，索引從 0，可用索引須滿足 0≤n<L。n=0 是可用索引嗎？","answer":{"kind":"short_text","value":"是","explanation_zh":"待判定索引與長度為 0, 5；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305316,"parameters":{"operation":"finite_index","L":5,"n":0,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":5,\"n\":0,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0017","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=5，索引從 0，可用索引須滿足 0≤n<L。n=4 是可用索引嗎？","answer":{"kind":"short_text","value":"是","explanation_zh":"待判定索引與長度為 4, 5；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305317,"parameters":{"operation":"finite_index","L":5,"n":4,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":5,\"n\":4,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0018","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=5，索引從 0，可用索引須滿足 0≤n<L。n=5 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 5, 5；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305318,"parameters":{"operation":"finite_index","L":5,"n":5,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":5,\"n\":5,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0019","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=5，索引從 0，可用索引須滿足 0≤n<L。n=6 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 6, 5；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305319,"parameters":{"operation":"finite_index","L":5,"n":6,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":5,\"n\":6,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0020","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=10，索引從 0，可用索引須滿足 0≤n<L。n=-1 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 -1, 10；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305320,"parameters":{"operation":"finite_index","L":10,"n":-1,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":10,\"n\":-1,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0021","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=10，索引從 0，可用索引須滿足 0≤n<L。n=0 是可用索引嗎？","answer":{"kind":"short_text","value":"是","explanation_zh":"待判定索引與長度為 0, 10；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305321,"parameters":{"operation":"finite_index","L":10,"n":0,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":10,\"n\":0,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0022","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=10，索引從 0，可用索引須滿足 0≤n<L。n=9 是可用索引嗎？","answer":{"kind":"short_text","value":"是","explanation_zh":"待判定索引與長度為 9, 10；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305322,"parameters":{"operation":"finite_index","L":10,"n":9,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":10,\"n\":9,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0023","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=10，索引從 0，可用索引須滿足 0≤n<L。n=10 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 10, 10；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305323,"parameters":{"operation":"finite_index","L":10,"n":10,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":10,\"n\":10,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0024","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=10，索引從 0，可用索引須滿足 0≤n<L。n=11 是可用索引嗎？","answer":{"kind":"short_text","value":"否","explanation_zh":"待判定索引與長度為 11, 10；檢查 0≤n<L 後答案為否。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305324,"parameters":{"operation":"finite_index","L":10,"n":11,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":10,\"n\":11,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r05-sequence-finite-index-validity-0025","batch_id":"batch-20260930-r05-sequence-foundations","language":"zh-Hant","source_mko_ids":["mko-sequence"],"title_zh":"有限数列的索引邊界","stem_zh":"有限實數數列長度 L=100，索引從 0，可用索引須滿足 0≤n<L。n=99 是可用索引嗎？","answer":{"kind":"short_text","value":"是","explanation_zh":"待判定索引與長度為 99, 100；檢查 0≤n<L 後答案為是。長度 0 時沒有可用索引。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["零起始索引","有限長度"]},"variant":{"family_id":"qf-sequence-finite-index-validity","seed":202609305325,"parameters":{"operation":"finite_index","L":100,"n":99,"semantic_template":"qf-sequence-finite-index-validity/{\"L\":100,\"n\":99,\"operation\":\"finite_index\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}