0, 2, 6, 12, 20, ? — Aptitude Question
0, 2, 6, 12, 20, ?: Find the next term: 0, 2, 6, 12, 20, ? Answer and worked solution on CodeKairo.
- Topic: Number & Letter Series
- Section: Logical Reasoning
- Difficulty: Easy
- Time target: 45 seconds
Question
Find the next term:
0, 2, 6, 12, 20, ?
Options
- 26
- 28
- 30
- 32
Show the answer and the worked solution
Correct answer: C. 30
Worked solution
- Differences: 2, 4, 6, 8 — the even numbers.
- Next = 20 + 10 = 30.
- The terms are n² − n. ✓
Answer: 30.
The idea
Even differences point to n² − n or a shift of it. Extending the differences is quicker than finding the formula.
Shortcut. Halve the terms: 0, 1, 3, 6, 10 are the triangular numbers, whose next member is 15, so the answer is 2 × 15 = 30.
Common trap. 28 — adding the last gap, 8, again (20 + 8); the gaps rise by 2, so the next is 10.