3, 7, 15, 31, 63, ? — Aptitude Question
3, 7, 15, 31, 63, ?: Find the next term: 3, 7, 15, 31, 63, ? Answer and worked solution on CodeKairo.
- Topic: Number & Letter Series
- Section: Logical Reasoning
- Difficulty: Easy
- Time target: 45 seconds
Question
Find the next term:
3, 7, 15, 31, 63, ?
Options
- 95
- 119
- 127
- 131
Show the answer and the worked solution
Correct answer: C. 127
Worked solution
- 3 × 2 + 1 = 7; 7 × 2 + 1 = 15; 15 × 2 + 1 = 31; 31 × 2 + 1 = 63.
- Next = 63 × 2 + 1 = 127.
- The terms are 2ⁿ − 1: 4−1, 8−1, 16−1, 32−1, 64−1, 128−1.
Answer: 127.
The idea
When terms roughly double, test 'previous × 2 ± k'. Powers of 2 offset by a constant are the most common disguise.
Shortcut. The gaps 4, 8, 16, 32 double each time, so the next gap is 64: 63 + 64 = 127.
Common trap. 95 — repeating the last gap of 32 instead of doubling it to 64.