Find wrong number in series: 2, 8, 12, 20, 30, 42, 56, 72

Concept:

A ‘wrong number in series’ question is built on a hidden arithmetic rule that generates every term from the one before it — here, a growing sequence of increments (consecutive even numbers) added successively. One inserted term breaks that rule; finding it means reconstructing the rule from the terms that DO fit and checking which term deviates.

Application:

1. Start from the first term, 2.

2. Add the next consecutive even number, 4: 2 + 4 = 6 — this is the expected second term.

3. Add 6 to the expected second term: 6 + 6 = 12 — matches the given third term (12).

4. Add 8: 12 + 8 = 20 — matches the given fourth term (20).

5. Add 10: 20 + 10 = 30 — matches the given fifth term (30).

6. Add 12: 30 + 12 = 42 — matches the given sixth term (42).

7. Add 14: 42 + 14 = 56 — matches the given seventh term (56).

8. Add 16: 56 + 16 = 72 — matches the given eighth term (72).

Cross-check:

Every reconstructed term from the third position onward (12, 20, 30, 42, 56, 72) matches the given series exactly, confirming the consecutive-even-number-addition rule. Only the second position breaks this: the rule predicts 6, but the series shows 8.

Result:

So the number that does not belong to the series is 8; every other term is consistent with adding the next consecutive even number to the previous term.