Number series — fill in the next term. Sequence: 0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ?

Introduction / Context:
This sequence mixes two alternating increment patterns: a constant small jump and a steadily increasing odd-number jump. Detecting the alternation allows you to continue the series with confidence.

Given Data / Assumptions:

• Sequence: 0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ?
• We analyze consecutive differences.
• We expect an alternating motif.

Concept / Approach:
Compute term-to-term differences: +2, +1, +2, +3, +2, +5, +2, +7, +2, ?. The pattern alternates +2 with ascending odd numbers: +1, +3, +5, +7, +9, ... Therefore, after the last +2, the next jump should be +9.

Step-by-Step Solution:
List differences: 0→2 (+2), 2→3 (+1), 3→5 (+2), 5→8 (+3), 8→10 (+2), 10→15 (+5), 15→17 (+2), 17→24 (+7), 24→26 (+2). Following the rule, next increase = +9. Compute next term: 26 + 9 = 35.

Verification / Alternative check:
The odd increments form a clear sequence 1, 3, 5, 7, 9. Interleaving with +2 confirms the structure holds throughout.

Why Other Options Are Wrong:
28/30/32: Correspond to +2, +4, +6 changes, which would break the established alternating +2, +(odd growing) scheme.

Common Pitfalls:
Assuming a single constant difference or missing the interleaving of two separate incremental rules.

Final Answer:
35