What will come in place of in the sequence 3, 14, 39, 84, , 258?

Answer: (b) 155

The terms are n³ + n² + n for n = 1, 2, 3, …: 3, 14, 39, 84, 155, 258. So the missing term is 125 + 25 + 5 = 155.

1. First differences: 11, 25, 45. Second differences: 14, 20, rising by 6, so the next second difference is 26.
2. Next first difference = 45 + 26 = 71, so the missing term = 84 + 71 = 155.
3. Check the last term: next second difference 32, so the next first difference is 71 + 32 = 103, and 155 + 103 = 258.
4. Formula view: n³ + n² + n gives 3, 14, 39, 84, 155, 258.

Remember · If first differences don’t settle a series, take second differences; a steady rise in them points to a cubic pattern.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error