Number series – find the next term. Sequence: 10, 5, 13, 10, 16, 20, 19, ( ? )

Introduction / Context:Many number series interleave two independent subsequences at odd and even positions. Isolating each subsequence often reveals simple patterns that make the next term obvious.

Given Data / Assumptions:

• Overall sequence: 10, 5, 13, 10, 16, 20, 19, ( ? )
• We expect two interleaved patterns: one for odd positions, one for even positions.

Concept / Approach:Separate odd-indexed terms and even-indexed terms and analyze each independently. Common rules include constant increments for one and doubling or halving for the other.

Step-by-Step Solution:

Verification / Alternative check:Project forward: if a 9th term were needed (odd position), it would be 19 + 3 = 22, which is consistent, reinforcing the correctness of the extracted rules.

Why Other Options Are Wrong:

• 22: That would be correct for the next odd position, not the 8th term.
• 38 and 23: Do not follow either identified rule from the immediately prior relevant subsequence term.

Common Pitfalls:Trying to force a single-step rule on the entire sequence rather than splitting into interleaved streams.

Final Answer:40