Find wrong number in series: 2, 6, 12, 20, 30, 40, 56
2023
Find wrong number in series: 2, 6, 12, 20, 30, 40, 56
- A.
12
- B.
20
- C.
40
- D.
56
Show answer & explanation
Correct answer: C
Concept: A 'find the wrong number' series problem hides one term that violates the rule linking consecutive terms. Solve it by (1) inferring the rule from the terms that clearly fit, (2) regenerating the correct sequence from that rule, and (3) comparing it term-by-term against the given series - the mismatch is the wrong number.
Application: Here every term fits the rule term(n) = n x (n + 1) - the product of two consecutive integers.
n | Rule: n x (n+1) | Given term |
|---|---|---|
1 | 2 | 2 |
2 | 6 | 6 |
3 | 12 | 12 |
4 | 20 | 20 |
5 | 30 | 30 |
6 | 42 | 40 |
7 | 56 | 56 |
The only row where the rule value and the given term disagree is n = 6: the rule gives 42, but the series shows 40. So 40 is the number that breaks the pattern.
Cross-check: An independent check via first differences (consecutive gaps), which should rise by 2 each step under this rule: 4, 6, 8, 10, 12, 14. The given series' gaps are 4, 6, 8, 10, 10, 16 - the gap breaks exactly at the same point (10 instead of 12, then 16 instead of 14), confirming 40 is the wrong number.