5, 9, 17, 29, 45, ? — Aptitude Question
5, 9, 17, 29, 45, ?: Find the next term: 5, 9, 17, 29, 45, ? Answer and worked solution on CodeKairo.
- Topic: Number & Letter Series
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 50 seconds
Question
Find the next term:
5, 9, 17, 29, 45, ?
Options
- 61
- 63
- 65
- 67
Show the answer and the worked solution
Correct answer: C. 65
Worked solution
- Differences: 4, 8, 12, 16 — multiples of 4.
- Next = 45 + 20 = 65.
Answer: 65.
The idea
Differences in arithmetic progression again, this time stepping by 4. The method does not change with the step size.
Shortcut. The gaps are 4 × 1, 4 × 2, 4 × 3 …, so term n = 5 + 2n(n − 1); for the sixth term that is 5 + 2 × 6 × 5 = 65.
Common trap. 61 — adding the last gap, 16, again (45 + 16); the gaps step up by 4, so the next is 20.