What is the value of X in the sequence 2, 12, 36, 80, 150, X?

Answer: (b) 252

The terms are n² × (n + 1) — that is, n³ + n² — for n = 1, 2, 3, 4, 5: 2, 12, 36, 80, 150. The next term is 6² × 7 = 252.

1. Test n²(n + 1): 1 × 2 = 2, 4 × 3 = 12, 9 × 4 = 36, 16 × 5 = 80, 25 × 6 = 150.
2. Next term: 36 × 7 = 252.
3. Check with differences: 10, 24, 44, 70, 102; second differences 14, 20, 26, 32 rise steadily by 6, as they should for a cubic pattern.

Remember · If terms grow roughly like cubes, test n³ ± n² or n³ ± n before trying differences.

Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error