Question

Write the explicit formula for the geometric sequence.

2, 8, 32, 128, ...


A)
an = 2n-1


B)
an = 2 · 6n-1


C)
an = 2 · 2n-1


D)
an = 2 · 4n-1

Answer 1

Uₙ = 2(4)ⁿ⁻¹

Explanation:

General Formula: Uₙ = a(r)ⁿ⁻¹

a = first term = 2

r = common ratio

r = (Uₙ₊₁)/Uₙ:

r = U₂/U₁

r = 8/2 = 4

∴ formula is: Uₙ = 2(4)ⁿ⁻¹

Answer 2

I believe the answer is D