1, 3, 7, 15, 31, ? — Aptitude Question
1, 3, 7, 15, 31, ?: Find the next term: 1, 3, 7, 15, 31, ? Answer and worked solution on CodeKairo.
- Topic: Number & Letter Series
- Section: Logical Reasoning
- Difficulty: Easy
- Time target: 45 seconds
Question
Find the next term:
1, 3, 7, 15, 31, ?
Options
- 47
- 55
- 63
- 64
Show the answer and the worked solution
Correct answer: C. 63
Worked solution
- 1 × 2 + 1 = 3, 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31.
- Next = 31 × 2 + 1 = 63.
- The terms are 2ⁿ − 1. ✓
Answer: 63.
The idea
Roughly doubling means testing 'previous × 2 ± k'. Powers of two offset by one are the commonest form.
Shortcut. The gaps 2, 4, 8, 16 double, so the next gap is 32 and 31 + 32 = 63. Every term is odd, which rules out 64 on sight.
Common trap. 64 — writing the next power of two, 2⁶, and dropping the − 1; each term is one less than a power of two (2 − 1, 4 − 1, …).