# Finite Sequence Windows, Extensions, and Ordered Differences

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261011-advance-20261015-r05-sequence-foundations · 2026-10-11 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=0; only 0≤n<L is allowed for a_n=1+(2)n. Ordered candidate indices=[-1, 0, 1]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(0, [No, No, No], [invalid-index, invalid-index, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (0, [No, No, No], [invalid-index, invalid-index, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0001/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 2. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=1; only 0≤n<L is allowed for a_n=0+(0)n. Ordered candidate indices=[0, 1, -1]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(1, [Yes, No, No], [0, invalid-index, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (1, [Yes, No, No], [0, invalid-index, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0002/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 3. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-10+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-10, -7, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-10, -7, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0003/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 4. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-9+(-1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-9, -12, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-9, -12, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0004/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 5. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-8+(0)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-8, -8, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-8, -8, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0005/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 6. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-7+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-7, -4, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-7, -4, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0006/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 7. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-6+(-1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-6, -9, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-6, -9, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0007/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 8. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-5+(0)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-5, -5, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-5, -5, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0008/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 9. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-4+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-4, -1, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-4, -1, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0009/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 10. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-3+(-1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-3, -6, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-3, -6, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0010/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 11. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-2+(0)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-2, -2, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-2, -2, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0011/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 12. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=-1+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [-1, 2, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [-1, 2, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0012/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 13. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=0+(-1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [0, -3, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [0, -3, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0013/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 14. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=1+(0)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [1, 1, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [1, 1, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0014/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 15. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=2+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [2, 5, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [2, 5, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0015/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 16. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=3+(-1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [3, 0, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [3, 0, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0016/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 17. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=4+(0)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [4, 4, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [4, 4, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0017/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 18. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=5+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [5, 8, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [5, 8, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0018/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 19. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=6+(-1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [6, 3, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [6, 3, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0019/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 20. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=7+(0)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [7, 7, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [7, 7, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0020/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 21. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=8+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [8, 11, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [8, 11, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0021/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 22. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=9+(-1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [9, 6, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [9, 6, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0022/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 23. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=10+(0)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [10, 10, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [10, 10, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0023/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 24. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=11+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [11, 14, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [11, 14, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0024/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 25. Finite Sequence Query Bounds before Evaluation

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=12+(-1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

View answer and explanation(4, [Yes, Yes, No], [12, 9, invalid-index])

Check the finite index bound before substitution; an outside index does not acquire a term merely because the affine expression could be evaluated there. The exact result, retaining the requested order, is (4, [Yes, Yes, No], [12, 9, invalid-index]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0025/)

Sequence · qf-density15-sequence-window-boundary-queries · candidate





## 26. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=0, a_(n+1)=a_n+(1), start=0, length=0. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([], [], [])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([], [], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0026/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 27. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=0, a_(n+1)=a_n+(7), start=0, length=1. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([0], [0], [])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([0], [0], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0027/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 28. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-10, a_(n+1)=a_n+(1), start=0, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([0, 1, 2], [-10, -9, -8], [1, 1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([0, 1, 2], [-10, -9, -8], [1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0028/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 29. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-9, a_(n+1)=a_n+(-1), start=1, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([1, 2, 3], [-10, -11, -12], [-1, -1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([1, 2, 3], [-10, -11, -12], [-1, -1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0029/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 30. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-8, a_(n+1)=a_n+(0), start=2, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([2, 3, 4], [-8, -8, -8], [0, 0])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([2, 3, 4], [-8, -8, -8], [0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0030/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 31. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-7, a_(n+1)=a_n+(1), start=3, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([3, 4, 5], [-4, -3, -2], [1, 1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([3, 4, 5], [-4, -3, -2], [1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0031/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 32. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-6, a_(n+1)=a_n+(-1), start=4, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([4, 5, 6], [-10, -11, -12], [-1, -1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([4, 5, 6], [-10, -11, -12], [-1, -1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0032/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 33. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-5, a_(n+1)=a_n+(0), start=5, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([5, 6, 7], [-5, -5, -5], [0, 0])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([5, 6, 7], [-5, -5, -5], [0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0033/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 34. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-4, a_(n+1)=a_n+(1), start=6, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([6, 7, 8], [2, 3, 4], [1, 1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([6, 7, 8], [2, 3, 4], [1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0034/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 35. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-3, a_(n+1)=a_n+(-1), start=7, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([7, 8, 9], [-10, -11, -12], [-1, -1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([7, 8, 9], [-10, -11, -12], [-1, -1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0035/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 36. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-2, a_(n+1)=a_n+(0), start=8, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([8, 9, 10], [-2, -2, -2], [0, 0])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([8, 9, 10], [-2, -2, -2], [0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0036/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 37. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=-1, a_(n+1)=a_n+(1), start=9, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([9, 10, 11], [8, 9, 10], [1, 1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([9, 10, 11], [8, 9, 10], [1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0037/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 38. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=0, a_(n+1)=a_n+(-1), start=10, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([10, 11, 12], [-10, -11, -12], [-1, -1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([10, 11, 12], [-10, -11, -12], [-1, -1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0038/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 39. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=1, a_(n+1)=a_n+(0), start=11, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([11, 12, 13], [1, 1, 1], [0, 0])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([11, 12, 13], [1, 1, 1], [0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0039/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 40. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=2, a_(n+1)=a_n+(1), start=12, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([12, 13, 14], [14, 15, 16], [1, 1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([12, 13, 14], [14, 15, 16], [1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0040/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 41. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=3, a_(n+1)=a_n+(-1), start=13, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([13, 14, 15], [-10, -11, -12], [-1, -1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([13, 14, 15], [-10, -11, -12], [-1, -1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0041/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 42. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=4, a_(n+1)=a_n+(0), start=14, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([14, 15, 16], [4, 4, 4], [0, 0])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([14, 15, 16], [4, 4, 4], [0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0042/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 43. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=5, a_(n+1)=a_n+(1), start=15, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([15, 16, 17], [20, 21, 22], [1, 1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([15, 16, 17], [20, 21, 22], [1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0043/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 44. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=6, a_(n+1)=a_n+(-1), start=16, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([16, 17, 18], [-10, -11, -12], [-1, -1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([16, 17, 18], [-10, -11, -12], [-1, -1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0044/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 45. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=7, a_(n+1)=a_n+(0), start=17, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([17, 18, 19], [7, 7, 7], [0, 0])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([17, 18, 19], [7, 7, 7], [0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0045/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 46. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=8, a_(n+1)=a_n+(1), start=18, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([18, 19, 20], [26, 27, 28], [1, 1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([18, 19, 20], [26, 27, 28], [1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0046/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 47. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=9, a_(n+1)=a_n+(-1), start=19, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([19, 20, 21], [-10, -11, -12], [-1, -1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([19, 20, 21], [-10, -11, -12], [-1, -1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0047/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 48. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=10, a_(n+1)=a_n+(0), start=20, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([20, 21, 22], [10, 10, 10], [0, 0])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([20, 21, 22], [10, 10, 10], [0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0048/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 49. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=11, a_(n+1)=a_n+(1), start=21, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([21, 22, 23], [32, 33, 34], [1, 1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([21, 22, 23], [32, 33, 34], [1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0049/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 50. Ordered Recurrence Window and Adjacent Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=12, a_(n+1)=a_n+(-1), start=22, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

View answer and explanation([22, 23, 24], [-10, -11, -12], [-1, -1])

Apply the declared recurrence from its given initial term and record the ordered window; the index list and repetitions remain meaningful. The exact result, retaining the requested order, is ([22, 23, 24], [-10, -11, -12], [-1, -1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0050/)

Sequence · qf-density15-sequence-affine-recurrence-window · candidate





## 51. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[0, 0, 0, 0] and candidate nexts=[0, 0]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([0, 0, 0, 0, 0], [0, 0, 0, 0, 0], Yes, Yes)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([0, 0, 0, 0, 0], [0, 0, 0, 0, 0], Yes, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0051/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 52. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[1, 1, 2, 2] and candidate nexts=[3, 4]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([1, 1, 2, 2, 3], [1, 1, 2, 2, 4], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([1, 1, 2, 2, 3], [1, 1, 2, 2, 4], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0052/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 53. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-10, 0, -10, 1] and candidate nexts=[2, -1]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-10, 0, -10, 1, 2], [-10, 0, -10, 1, -1], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-10, 0, -10, 1, 2], [-10, 0, -10, 1, -1], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0053/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 54. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-9, 0, -9, 1] and candidate nexts=[3, -2]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-9, 0, -9, 1, 3], [-9, 0, -9, 1, -2], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-9, 0, -9, 1, 3], [-9, 0, -9, 1, -2], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0054/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 55. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-8, 0, -8, 1] and candidate nexts=[4, -3]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-8, 0, -8, 1, 4], [-8, 0, -8, 1, -3], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-8, 0, -8, 1, 4], [-8, 0, -8, 1, -3], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0055/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 56. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-7, 0, -7, 1] and candidate nexts=[5, -4]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-7, 0, -7, 1, 5], [-7, 0, -7, 1, -4], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-7, 0, -7, 1, 5], [-7, 0, -7, 1, -4], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0056/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 57. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-6, 0, -6, 1] and candidate nexts=[6, -5]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-6, 0, -6, 1, 6], [-6, 0, -6, 1, -5], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-6, 0, -6, 1, 6], [-6, 0, -6, 1, -5], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0057/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 58. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-5, 0, -5, 1] and candidate nexts=[7, -6]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-5, 0, -5, 1, 7], [-5, 0, -5, 1, -6], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-5, 0, -5, 1, 7], [-5, 0, -5, 1, -6], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0058/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 59. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-4, 0, -4, 1] and candidate nexts=[8, -7]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-4, 0, -4, 1, 8], [-4, 0, -4, 1, -7], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-4, 0, -4, 1, 8], [-4, 0, -4, 1, -7], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0059/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 60. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-3, 0, -3, 1] and candidate nexts=[9, -8]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-3, 0, -3, 1, 9], [-3, 0, -3, 1, -8], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-3, 0, -3, 1, 9], [-3, 0, -3, 1, -8], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0060/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 61. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-2, 0, -2, 1] and candidate nexts=[10, -9]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-2, 0, -2, 1, 10], [-2, 0, -2, 1, -9], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-2, 0, -2, 1, 10], [-2, 0, -2, 1, -9], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0061/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 62. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[-1, 0, -1, 1] and candidate nexts=[11, -10]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([-1, 0, -1, 1, 11], [-1, 0, -1, 1, -10], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([-1, 0, -1, 1, 11], [-1, 0, -1, 1, -10], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0062/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 63. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[0, 0, 0, 1] and candidate nexts=[12, -11]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([0, 0, 0, 1, 12], [0, 0, 0, 1, -11], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([0, 0, 0, 1, 12], [0, 0, 0, 1, -11], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0063/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 64. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[1, 0, 1, 1] and candidate nexts=[13, -12]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([1, 0, 1, 1, 13], [1, 0, 1, 1, -12], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([1, 0, 1, 1, 13], [1, 0, 1, 1, -12], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0064/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 65. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[2, 0, 2, 1] and candidate nexts=[14, -13]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([2, 0, 2, 1, 14], [2, 0, 2, 1, -13], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([2, 0, 2, 1, 14], [2, 0, 2, 1, -13], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0065/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 66. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[3, 0, 3, 1] and candidate nexts=[15, -14]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([3, 0, 3, 1, 15], [3, 0, 3, 1, -14], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([3, 0, 3, 1, 15], [3, 0, 3, 1, -14], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0066/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 67. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[4, 0, 4, 1] and candidate nexts=[16, -15]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([4, 0, 4, 1, 16], [4, 0, 4, 1, -15], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([4, 0, 4, 1, 16], [4, 0, 4, 1, -15], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0067/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 68. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[5, 0, 5, 1] and candidate nexts=[17, -16]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([5, 0, 5, 1, 17], [5, 0, 5, 1, -16], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([5, 0, 5, 1, 17], [5, 0, 5, 1, -16], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0068/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 69. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[6, 0, 6, 1] and candidate nexts=[18, -17]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([6, 0, 6, 1, 18], [6, 0, 6, 1, -17], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([6, 0, 6, 1, 18], [6, 0, 6, 1, -17], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0069/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 70. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[7, 0, 7, 1] and candidate nexts=[19, -18]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([7, 0, 7, 1, 19], [7, 0, 7, 1, -18], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([7, 0, 7, 1, 19], [7, 0, 7, 1, -18], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0070/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 71. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[8, 0, 8, 1] and candidate nexts=[20, -19]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([8, 0, 8, 1, 20], [8, 0, 8, 1, -19], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([8, 0, 8, 1, 20], [8, 0, 8, 1, -19], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0071/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 72. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[9, 0, 9, 1] and candidate nexts=[21, -20]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([9, 0, 9, 1, 21], [9, 0, 9, 1, -20], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([9, 0, 9, 1, 21], [9, 0, 9, 1, -20], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0072/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 73. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[10, 0, 10, 1] and candidate nexts=[22, -21]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([10, 0, 10, 1, 22], [10, 0, 10, 1, -21], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([10, 0, 10, 1, 22], [10, 0, 10, 1, -21], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0073/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 74. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[11, 0, 11, 1] and candidate nexts=[23, -22]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([11, 0, 11, 1, 23], [11, 0, 11, 1, -22], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([11, 0, 11, 1, 23], [11, 0, 11, 1, -22], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0074/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 75. Two Fifth-Term Extensions of a Given Four-Term Prefix

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[12, 0, 12, 1] and candidate nexts=[24, -23]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.

View answer and explanation([12, 0, 12, 1, 24], [12, 0, 12, 1, -23], Yes, No)

Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([12, 0, 12, 1, 24], [12, 0, 12, 1, -23], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0075/)

Sequence · qf-density15-sequence-two-finite-extensions · candidate





## 76. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[0, 0, 0, 0, 0]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([0, 0, 0, 0, 0], [0, 0, 0, 0], Yes)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([0, 0, 0, 0, 0], [0, 0, 0, 0], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0076/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 77. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[2, 2, 2, 2, 2]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([2, 4, 6, 8, 10], [0, 0, 0, 0], Yes)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([2, 4, 6, 8, 10], [0, 0, 0, 0], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0077/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 78. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-2, -1, 0, 1, 2]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-2, -3, -3, -2, 0], [1, 1, 1, 1], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-2, -3, -3, -2, 0], [1, 1, 1, 1], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0078/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 79. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-9, 0, -9, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-9, -9, -18, -19, -18], [9, -9, 8, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-9, -9, -18, -19, -18], [9, -9, 8, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0079/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 80. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-8, 0, -8, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-8, -8, -16, -17, -16], [8, -8, 7, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-8, -8, -16, -17, -16], [8, -8, 7, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0080/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 81. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-7, 0, -7, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-7, -7, -14, -15, -14], [7, -7, 6, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-7, -7, -14, -15, -14], [7, -7, 6, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0081/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 82. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-6, 0, -6, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-6, -6, -12, -13, -12], [6, -6, 5, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-6, -6, -12, -13, -12], [6, -6, 5, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0082/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 83. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-5, 0, -5, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-5, -5, -10, -11, -10], [5, -5, 4, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-5, -5, -10, -11, -10], [5, -5, 4, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0083/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 84. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-4, 0, -4, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-4, -4, -8, -9, -8], [4, -4, 3, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-4, -4, -8, -9, -8], [4, -4, 3, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0084/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 85. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-3, 0, -3, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-3, -3, -6, -7, -6], [3, -3, 2, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-3, -3, -6, -7, -6], [3, -3, 2, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0085/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 86. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-2, 0, -2, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-2, -2, -4, -5, -4], [2, -2, 1, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-2, -2, -4, -5, -4], [2, -2, 1, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0086/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 87. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[-1, 0, -1, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([-1, -1, -2, -3, -2], [1, -1, 0, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([-1, -1, -2, -3, -2], [1, -1, 0, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0087/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 88. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[0, 0, 0, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([0, 0, 0, -1, 0], [0, 0, -1, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([0, 0, 0, -1, 0], [0, 0, -1, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0088/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 89. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[1, 0, 1, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([1, 1, 2, 1, 2], [-1, 1, -2, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([1, 1, 2, 1, 2], [-1, 1, -2, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0089/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 90. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[2, 0, 2, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([2, 2, 4, 3, 4], [-2, 2, -3, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([2, 2, 4, 3, 4], [-2, 2, -3, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0090/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 91. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[3, 0, 3, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([3, 3, 6, 5, 6], [-3, 3, -4, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([3, 3, 6, 5, 6], [-3, 3, -4, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0091/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 92. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[4, 0, 4, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([4, 4, 8, 7, 8], [-4, 4, -5, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([4, 4, 8, 7, 8], [-4, 4, -5, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0092/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 93. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[5, 0, 5, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([5, 5, 10, 9, 10], [-5, 5, -6, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([5, 5, 10, 9, 10], [-5, 5, -6, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0093/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 94. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[6, 0, 6, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([6, 6, 12, 11, 12], [-6, 6, -7, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([6, 6, 12, 11, 12], [-6, 6, -7, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0094/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 95. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[7, 0, 7, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([7, 7, 14, 13, 14], [-7, 7, -8, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([7, 7, 14, 13, 14], [-7, 7, -8, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0095/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 96. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[8, 0, 8, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([8, 8, 16, 15, 16], [-8, 8, -9, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([8, 8, 16, 15, 16], [-8, 8, -9, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0096/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 97. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[9, 0, 9, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([9, 9, 18, 17, 18], [-9, 9, -10, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([9, 9, 18, 17, 18], [-9, 9, -10, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0097/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 98. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[10, 0, 10, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([10, 10, 20, 19, 20], [-10, 10, -11, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([10, 10, 20, 19, 20], [-10, 10, -11, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0098/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 99. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[11, 0, 11, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([11, 11, 22, 21, 22], [-11, 11, -12, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([11, 11, 22, 21, 22], [-11, 11, -12, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0099/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate





## 100. Five Prefix Sums and Four Ordered Differences

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Five ordered values=[12, 0, 12, -1, 1]. Give (five inclusive prefix sums, four following-minus-previous differences, are all five values equal?).

View answer and explanation([12, 12, 24, 23, 24], [-12, 12, -13, 2], No)

Accumulate in order and subtract adjacent values, without sorting or deduplicating; finite sums are not an infinite series or limit. The exact result, retaining the requested order, is ([12, 12, 24, 23, 24], [-12, 12, -13, 2], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r05-sequence-0100/)

Sequence · qf-density15-sequence-five-term-prefix-deltas · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261011-advance-20261015-r05-sequence-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261011-advance-20261015-r05-sequence-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261011-advance-20261015-r05-sequence-foundations/validation-report.json)