Fill in the missing term to continue the alternating +3, −1 pattern: 9, 12, 11, 14, 13, ( ? ), 15

Introduction / Context:
This is a completion-type number series. Many aptitude sequences alternate between two simple operations. Here the differences appear to repeat in a short cycle, which allows us to fill in the gap accurately.

Given Data / Assumptions:

• Observed sequence: 9, 12, 11, 14, 13, ( ? ), 15
• We assume a short repeating pattern of operations.

Concept / Approach:
Check consecutive differences and see if they alternate: +3, −1, +3, −1, … If so, apply the next +3 step to the known preceding term to obtain the missing value, then confirm by the subsequent −1 step reaching the final given term.

Step-by-Step Solution:
9 → 12: +312 → 11: −111 → 14: +314 → 13: −113 → ( ? ): +3 ⇒ 1616 → 15: −1 (matches the last term)

Verification / Alternative check:
Rewriting the pattern: start at 9, then apply (+3, −1) repeatedly to reconstruct the full sequence, which uniquely yields 16 as the middle term.

Why Other Options Are Wrong:
12, 10, 17, and 14 do not satisfy the alternating +3 then −1 steps while still landing on 15 afterwards.

Common Pitfalls:
Trying to force a single arithmetic progression; many test items rely on alternating micro-patterns.

Final Answer:
16