Question

Find the sum of the geometric series. 0.25 + 0.5 + 1 + 2 + . . . .256

A) 511.75

B) 512.25

C) 256.125

D) 515.5

Answer 1

511.75

Explanation:

S_n = a_1(1 - r^n)/(1 - r)

We need to find n, the number of terms.

a_n = 256

a_1 = 0.25

r = 2

a_n = a_1 × r^(n - 1)

256 = 0.25 × 2^(n - 1)

1024 = 2^(n - 1)

2^10 = 2^(n - 1)

n - 1 = 10

n = 11

S_n = a_1(1 - r^n)/(1 - r)

S_11 = 0.25 × (1 - 2^11)/(1 - 2)

S_11 = 0.25 × (1 - 2048)/(-1)

S_11 = 0.25 × 2047

S_11 = 511.75