2, 5, 10, 17, 26, ? — Aptitude Question
2, 5, 10, 17, 26, ?: Find the next term: 2, 5, 10, 17, 26, ? 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, 5, 10, 17, 26, ?
Options
- 35
- 36
- 37
- 38
Show the answer and the worked solution
Correct answer: C. 37
Worked solution
- Differences: 5 − 2 = 3, 10 − 5 = 5, 17 − 10 = 7, 26 − 17 = 9. They grow by 2.
- Next difference = 11, so the term is 26 + 11 = 37.
- Equivalently the terms are n² + 1: 1+1, 4+1, 9+1, 16+1, 25+1, 36+1 = 37.
Answer: 37.
The idea
Take first differences; if they are not constant, take second differences. A constant second difference means the terms follow a quadratic, usually n² plus a shift.
Shortcut. Parity alternates even, odd, even, odd, even, so the next term is odd (35 or 37); the gaps 3, 5, 7, 9 call for 11, not 9.
Common trap. 35 — repeating the last gap of 9 instead of letting the odd gaps grow to 11.