2, 6, 12, 20, 30, ? — Aptitude Question
2, 6, 12, 20, 30, ?: Find the next term: 2, 6, 12, 20, 30, ? Answer and worked solution on CodeKairo.
- Topic: Number & Letter Series
- Section: Logical Reasoning
- Difficulty: Easy
- Time target: 45 seconds
Question
Find the next term:
2, 6, 12, 20, 30, ?
Options
- 36
- 40
- 42
- 46
Show the answer and the worked solution
Correct answer: C. 42
Worked solution
- Differences: 4, 6, 8, 10, rising by 2 each time.
- Next difference = 12, so the term is 30 + 12 = 42.
- The terms are n(n + 1): 1×2, 2×3, 3×4, 4×5, 5×6, 6×7 = 42. ✓
Answer: 42.
The idea
First differences that rise steadily point to a quadratic. Recognising n(n + 1) confirms the pattern instantly.
Shortcut. Spot 30 = 5 × 6 and jump straight to 6 × 7 = 42. Of the options only 42 is a product of two consecutive whole numbers, so no differences are needed.
Common trap. 40 — adding the last difference, 10, a second time (30 + 10); the gaps grow by 2, so the next one is 12.