Look at this series: 2, 1, 1/2, 1/4, … What number should come next?

Question

Look at this series: 2, 1, 1/2, 1/4, … What number should come next?

1. A. 1/3
2. B. 1/8 (Correct answer)
3. C. 1/4
4. D. 1/16

Correct Answer

Option B — 1/8

Detailed Solution & Explanation

The correct answer is 1/8.

Key Points

• Each term is half the one before: 2 → 1 → 1/2 → 1/4.
• The next term is therefore 1/4 ÷ 2 = 1/8.
• This is a geometric progression with first term 2 and common ratio 1/2.

Additional Information

• In a GP the ratio between consecutive terms is constant, while in an AP the difference is. Checking both is the first step in any series question.
• The nth term of a GP is arⁿ⁻¹; here 2 × (1/2)ⁿ⁻¹.
• Because the ratio lies between 0 and 1, this series converges; its infinite sum is a/(1 − r) = 2/(1 − ½) = 4.