Find the wrong term in the number series: 2, 8, 32, 148, 765, 4626, 32431. Exactly one term violates a consistent pattern; identify the incorrect term.

Introduction / Context:
This is a wrong-term detection problem in a number series. We must discover a single, clean rule that fits all positions except one, and then mark the violating term.

Given Data / Assumptions:

• Series: 2, 8, 32, 148, 765, 4626, 32431.
• Index n starts at 1 for the first step (from 2 to 8).
• Look for multiplicative growth with a small additive adjustment.

Concept / Approach:
A compact pattern that nearly fits is: a(n+1) = a(n) * (n+1) + (n+1)^2. We verify each transition and isolate any mismatch.

Step-by-Step Solution:

Verification / Alternative check:
If the 3rd term were 33 instead of 32, then 33*4 + 16 = 148 (exact). Thus a single earlier slip (32 vs 33) explains both mismatches and restores a perfect rule for the tail.

Why Other Options Are Wrong:
Terms 8, 148, 765 all become consistent once the 3rd term is corrected from 32→33; they are not the primary error.

Common Pitfalls:
Blaming a later term when an earlier off-by-one causes downstream wobble. Always check if fixing one term repairs later transitions.

Final Answer:
32 is the lone wrong term under a(n+1) = a(n)*(n+1) + (n+1)^2.