What is the value of X in the sequence 20, 10, 10, 15, 30, 75, X?

Answer: (d) 225

Each term is the previous one multiplied by a factor that grows by 0.5 each time: ×0.5, ×1, ×1.5, ×2, ×2.5. The next factor is ×3, so X = 75 × 3 = 225.

1. Divide each term by the one before it: 10 ÷ 20 = 0.5, 10 ÷ 10 = 1, 15 ÷ 10 = 1.5, 30 ÷ 15 = 2, 75 ÷ 30 = 2.5.
2. The multiplier rises by 0.5 each time, so the next multiplier is 3.
3. X = 75 × 3 = 225.
4. Check: 225 ÷ 75 = 3 continues the pattern 0.5, 1, 1.5, 2, 2.5, 3.

Remember · When differences look irregular, try the ratio of consecutive terms; a steadily growing multiplier is a common pattern.

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