Number series (two interleaved sequences): 3, 7, 6, 5, 9, 3, 12, 1, 15, (…) Find the next term by separating the odd and even positions into their own progressions.

Introduction / Context:
Many series are constructed by interleaving two simpler sequences (one occupying the odd positions, the other the even). Identifying and separating them is key to determining the correct next term.

Given Data / Assumptions:

• Total sequence: 3, 7, 6, 5, 9, 3, 12, 1, 15, (…)
• Odd positions: 1st, 3rd, 5th, 7th, 9th → 3, 6, 9, 12, 15.
• Even positions: 2nd, 4th, 6th, 8th → 7, 5, 3, 1.

Concept / Approach:
Treat each subsequence independently. The odd-position terms increase by +3 each step. The even-position terms decrease by −2 each step. The next term to produce is the 10th term (even position), so continue the even subsequence.

Step-by-Step Solution:

Verification / Alternative check:
Extend both subsequences further and interleave them to confirm the original pattern is preserved.

Why Other Options Are Wrong:

• 18: Would be the next odd-position term (after 15), not appropriate here.
• 13 and 3: Do not follow the even-position decrement rule from 1.

Common Pitfalls:
Forgetting to track whether the next required term is from the odd or even subsequence leads to choosing the wrong branch.

Final Answer:
-1