Find the wrong term in the number series: 1, 5, 13, 31, 61, 125, 253. Exactly one entry breaks the “add powers of two” rule; identify it.

Introduction / Context:
A classic construction uses differences that double each time (powers of two). We locate the single term that disrupts this pattern.

Given Data / Assumptions:

• Series: 1, 5, 13, 31, 61, 125, 253.
• Hypothesis: add 2^2, 2^3, 2^4, … in order.

Concept / Approach:
Compute the intended running totals using powers of two and compare with the given terms.

Step-by-Step Solution:

Verification / Alternative check:
If the third increment is +16, the sequence is 1, 5, 13, 29, 61, 125, 253, which is perfectly consistent.

Why Other Options Are Wrong:
1, 5, 61 match the expected cumulative sums under the power-of-two differences.

Common Pitfalls:
Assuming differences grow arbitrarily; check for powers-of-two first in such progressions.

Final Answer:
31 is the wrong term (should be 29).