Question 35126: Finite Prefix of an Explicit Sequence

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Original question and givens
Definition and scope
Step-by-step derivation
Reverse checks
Result
This question review and source binding

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R0069-35126 · q-20260930-r05-sequence-prefix-0001

Original question and givens

The real sequence is indexed from 0 with a_n=(-12)+(-3)n. List the prefix [a_0,…,a_(L-1)] of length L=0; use [] when L=0.

G001 — The real sequence is indexed from 0 with a_n=(-12)+(-3)n. List the prefix [a_0,…,a_(L-1)] of length L=0; use [] when L=0.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

mko-sequence

Step-by-step derivation

S001 · implies

Before

source roles = [qf-sequence-prefix, [L, d, operation, u]]

After

derived = [prefix, no-invented-domain]

Conditions: none

Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract.

Step identifiers and dependencies

Rule: R69_SOURCE_specific_keys_operation_domain_AND_binary_contract · Uses: G001

S002 · implies

Before

source roles = [-12, -3, 0, prefix]

After

derived = [a_0=u, a_n=u+n*d, zero based]

Conditions: none

Type ALL RAW u/d/count fields EVEN for prefix L=0.Indices start at0 and the formula/recurrence is GIVEN;do not infer a general rule from finite samples.

Step identifiers and dependencies

Rule: Sequence_ALL_RAW_initial_step_and_count_EVEN_empty_prefix · Uses: G001, S001

S003 · implies

Before

source roles = [-12, -3, 0]

After

derived = [[], []]

Conditions: none

Take EXACTLY L terms in index order from a0 through a_(L−1),NOT through aL.L=0 displays[].The GIVEN formula determines these terms;the prefix alone need not determine an unknown rule.

Step identifiers and dependencies

Rule: Sequence_PREFIX_EXACT_length_L_indices0_to_Lminus1 · Uses: G001, S002

Reverse checks

S003 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
S002 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
S001 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.

Result

[]

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts

input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
original question SHA-256: 62244b6dbf9f8c494f56eae9c11735c7eef3be820ba39bf05ae5e61bbf65b108
candidate record SHA-256: 01b1d7c8895f200df62028d9766a6dde81434e6cd81aaa6a2e8be864fc5eb91c
semantic review receipt SHA-256: ccf93c72638d6abf6a412514da5838d55ecb09b71d0e4fdec2b559dc9fdee14b
question-first witness SHA-256: 11af9a338b5a610342b2cfb2ee295683131b3139ac402dd19b1ba1725976d518
Lean: NOT_RUN · human review: NOT_PERFORMED

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