Number series – find the next term. Sequence: 8, 7, 11, 12, 14, 17, 17, 22, ( ? )

Introduction / Context:This sequence is formed by interleaving two simpler subsequences. Identifying and separating them is the key step to determining the next number.

Given Data / Assumptions:

• Main sequence: 8, 7, 11, 12, 14, 17, 17, 22, ( ? )
• Terms at odd positions and even positions likely follow different rules.

Concept / Approach:Extract the odd-position subsequence and the even-position subsequence. Analyze each for a consistent add pattern.

Step-by-Step Solution:

Verification / Alternative check:Project the even sequence further: after 22 would come 27, which matches option 27 but would be the 10th term, not the 9th. This cross-check supports 20 as the correct immediate next value.

Why Other Options Are Wrong:

• 27: Correct for the 10th term (even position), not for the 9th.
• 22 and 24: Do not match the +3 increment needed at odd positions after 17.

Common Pitfalls:Forcing a single rule on the entire list. Always consider interleaving when differences appear inconsistent.

Final Answer:20