Two interleaved progressions (+3 and +5): find the next term Sequence: 8, 7, 11, 12, 14, 17, 17, 22, ( ... ). What comes next?

Introduction / Context:
Interleaved series contain two independent subsequences occupying alternating positions. Detecting each subsequence and extending the appropriate one yields the next term correctly.

Given Data / Assumptions:

• Main sequence: 8, 7, 11, 12, 14, 17, 17, 22, ...
• Odd positions: 1st, 3rd, 5th, 7th, ...
• Even positions: 2nd, 4th, 6th, 8th, ...

Concept / Approach:
Separate odd-index and even-index terms and examine the pattern of each. The 9th term will be part of the odd-index subsequence, so extend that one by its rule.

Step-by-Step Solution:
Odd-index subsequence (positions 1,3,5,7,...): 8, 11, 14, 17, ... ⇒ +3 each time ⇒ next odd-index term = 20.Even-index subsequence (positions 2,4,6,8,...): 7, 12, 17, 22, ... ⇒ +5 each time.The 9th term is odd-indexed ⇒ answer = 20.

Verification / Alternative check:
Continuing: after 20 (9th), the 10th would be 27 (even-index subsequence +5 from 22). This confirms both subsequences are consistent.

Why Other Options Are Wrong:
27 would be the 10th term, not the 9th; 22 and 24 do not follow the +3 progression for the odd-index track at this step; 26 also belongs to a different continuation.

Common Pitfalls:
Adding a constant to the entire series without separating the two interwoven patterns. Always split odd and even positions when increments seem to oscillate.

Final Answer:
20