Question

what is the sum of the first five terms of geometry series with A1 is equal to 20 and R is equal to 1/4 express your answer as an improper fraction in the lowest term without using spaces

Answer 1

You have:

a1 = 20

r = 1/4

The general expression for the sum of the first n terms of a geometric series is given by:

Sn = a1(r^n - 1)/(r - 1)

For the first five terms of the summation is:

S5 = 20((1/4)⁵ - 1)/(1/4 - 1)

S5 = 20(-0.999)/(-0.75)

S5 = 14.985

Hence, the sum of the first five terms is S5 = 14.985