Complete the two-interleaved sequences (odd and even positions): 10, 5, 13, 10, 16, 20, 19, ( ? )

Introduction / Context:Many series are built from two simpler interleaved sequences: one governing the odd-indexed terms and another governing the even-indexed terms. Separating these streams makes the pattern clear and the missing value easy to compute.

Given Data / Assumptions:

• Total sequence: 10, 5, 13, 10, 16, 20, 19, ( ? )
• Odd positions (1,3,5,7): 10, 13, 16, 19
• Even positions (2,4,6,8): 5, 10, 20, ( ? )

Concept / Approach:Odd-position rule: +3 each step. Even-position rule: ×2 each step. Apply the even-position rule to the last even term to find the 8th term.

Step-by-Step Solution:Odd: 10 → 13 → 16 → 19 (add 3 repeatedly)Even: 5 → 10 → 20 → ( ? ) (double each time)Thus, ( ? ) = 20 * 2 = 40

Verification / Alternative check:Re-merging the two subsequences gives 10,5,13,10,16,20,19,40, which respects both rules.

Why Other Options Are Wrong:22, 38, 23, 35 do not satisfy the ×2 progression on the even-indexed terms.

Common Pitfalls:Trying to force a single-step difference across the whole series instead of splitting into odd/even strands.

Final Answer:40