In the following question, a number series is given in which one number is…

Concept: In a “find the wrong number” series, each term is built from the previous term by a rule that itself changes step by step — here, multiply by the step number and add the step number squared. To find the wrong term, first uncover this rule from the terms that agree with each other, then test every term against it; the one term that breaks the rule is the answer.

Application:

1. 4 × 1 + 12 = 5 — matches the given second term (5).

2. 5 × 2 + 22 = 14 — matches the given third term (14).

3. 14 × 3 + 32 = 51 — matches the given fourth term (51).

4. 51 × 4 + 42 = 220 — but the series shows 280 here, so 280 does not match the expected value.

5. 220 × 5 + 52 = 1125 — matches the given sixth term (1125).

6. 1125 × 6 + 62 = 6786 — matches the given seventh term (6786).

Cross-check: Continuing the same rule from the corrected value 220 (in place of 280) reproduces every later term in the series exactly (1125, then 6786), confirming the rule is right and that 280 is the sole break in the pattern.

So, 280 is the wrong number in the series.