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

Given data

• Series: 2, 1, (1/2), (1/4), ...

Concept/ApproachThe terms are halved each time (multiply by (1/2)).

Step-by-Step calculation2 → 1 (multiply by (1/2))1 → (1/2) (multiply by (1/2))(1/2) → (1/4) (multiply by (1/2))Next: (1/4) × (1/2) = (1/8)

Verification/AlternativeGeneral term a_n = 2 × (1/2)^n-1. For n = 4, a₄ = 2×(1/8) = (1/4); for n = 5, a₅ = (1/8).

Common pitfalls

• Using subtraction instead of a ratio pattern.

Final Answer(1/8)