Question

What is the sum of the first five terms of a geometric series with ay = 6 and r= 1/3?

Answer 1

`(242)/(27)`

Explanation:

Given:

a = 6

r = 1/3

n= 5

since r < 1, then

`\boxed{S_n=(a(1-r^n))/(1-r)}`

`S_n=(6(1-((1)/(3)) ^5))/(1-(1)/(3) )`

`=6(1-(1)/(243) )/(2)/(3)`

`=6*(242)/(243) *(3)/(2)`

`=(242)/(27)`