1, 5, 14, 30, 55, ? — Aptitude Question
1, 5, 14, 30, 55, ?: Find the next term: 1, 5, 14, 30, 55, ? Answer and worked solution on CodeKairo.
- Topic: Number & Letter Series
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 90 seconds
Question
Find the next term:
1, 5, 14, 30, 55, ?
Options
- 80
- 85
- 91
- 95
Show the answer and the worked solution
Correct answer: C. 91
Worked solution
- Differences: 4, 9, 16, 25 = 2², 3², 4², 5².
- Next difference = 6² = 36, so the term is 55 + 36 = 91.
- The terms are the running sums of squares. ✓
Answer: 91.
The idea
When the differences themselves are squares or cubes, the series is a running total. Extend the differences and add.
Shortcut. Use the sum-of-squares formula n(n + 1)(2n + 1)/6 with n = 6: 6 × 7 × 13 ÷ 6 = 91.
Common trap. 80 — adding the last gap, 25, again (55 + 25); the gaps are the squares 4, 9, 16, 25, so the next is 36.