Find the missing term: 7, 9, 16, 25, 41, ?, 107, 173. Hint: look at the pattern in successive differences.

Introduction / Context:
Sometimes the series itself is not Fibonacci-like, but the differences follow a Fibonacci rule (each term equals the sum of the two immediately preceding differences).

Given Data / Assumptions:

• Terms: 7, 9, 16, 25, 41, ?, 107, 173.
• Let d_i be successive differences.

Concept / Approach:
Compute differences and test whether d_i = d_{i-1} + d_{i-2}.

Step-by-Step Solution:

Verification / Alternative check:
Both forward and backward checks preserve the same additive rule in differences.

Why Other Options Are Wrong:
70, 68, 74 break the Fibonacci-like property of the difference sequence.

Common Pitfalls:
Looking for multiplication or powers; sometimes the “action” is in the first-difference layer.

Final Answer:
66.