Two interleaved arithmetic sequences (+3, −2) Complete: 3, 7, 6, 5, 9, 3, 12, 1, 15, ( ... ).

Introduction / Context:
In interleaved series, odd and even positions follow different linear rules. Recognizing each subsequence allows you to extend the correct one to find the next term in the main sequence.

Given Data / Assumptions:

• Main sequence: 3, 7, 6, 5, 9, 3, 12, 1, 15, ...
• Odd-index positions: 1st, 3rd, 5th, 7th, 9th (values 3, 6, 9, 12, 15).
• Even-index positions: 2nd, 4th, 6th, 8th (values 7, 5, 3, 1).

Concept / Approach:
Observe that odd-index terms increase by +3, while even-index terms decrease by −2. The 10th term is even-indexed, so apply the even rule (−2 from the previous even term).

Step-by-Step Solution:
Odd-index subsequence: 3 → 6 → 9 → 12 → 15 (add 3 each time).Even-index subsequence: 7 → 5 → 3 → 1 (subtract 2 each time).Next (10th) term = previous even term (1) − 2 = −1.

Verification / Alternative check:
If continued, the 11th term (odd-index) would be 18 (15 + 3), confirming both patterns remain consistent beyond the provided segment.

Why Other Options Are Wrong:
18 is the 11th term, not the 10th; 13 and 3 belong to the odd-index progression; 0 breaks the −2 pattern from 1.

Common Pitfalls:
Failing to separate the sequence into two tracks and trying to force a single constant difference across all terms.

Final Answer:
-1