Locate the odd term in alternating increments: 6, 13, 18, 25, 30, 37, 40

Introduction / Context:Alternating-difference series commonly repeat a two-step cycle (e.g., +7, +5, +7, +5, …). One term can violate the cycle, and the break is exposed by inspecting consecutive differences.

Given Data / Assumptions:

• Sequence: 6, 13, 18, 25, 30, 37, 40.
• Hypothesized cycle: +7, +5, +7, +5, +7, +5, …

Concept / Approach:Compute differences to confirm the cycle. If a final step fails to follow the expected +5 after a +7, the last number is suspect.

Step-by-Step Solution:13 − 6 = +718 − 13 = +525 − 18 = +730 − 25 = +537 − 30 = +7Next should be +5 ⇒ 37 + 5 = 42 (but given 40)

Verification / Alternative check:Substituting 42 for 40 reinstates the strict +7, +5 alternation. Earlier steps already fit perfectly, confirming the intended pattern.

Why Other Options Are Wrong:

• 25 / 30 / 37 align with the alternating increments; they are not the anomaly.

Common Pitfalls:

• Smoothing over a two-step cycle with an average increment; the alternation must be respected.

Final Answer:40