Which of the following recursive formulas represents the same geometric sequence as the formula an = 2x 1/2 (n-1)?

Question

A. { a₁ = 1/2

{a_n = a_n-1 > 2.5

B. {a₁=2

{a_n =a_n-1(1/2)

C. {a₁ = 1/2

{a_n = a_n-1 > 2

D. { a₁=2

{a_n =a_n-1 x2

Answer 1

Assuming that you mean a_n = 2(1/2)^n-1,

a₁ = 2(1/2)⁰ = 2

a₂ = 2(1/2)¹ = 1 = a₁(1/2)

a₃ = 2(1/2)² = 1/2 = a₂(1/2)...

a_n = a_n-1(1/2)

Answer: B