Question

What is the sum of the first five terms of s geometric series with a1=6 and r=1/3

Answer 1

`S_(5)` =
`(242)/(27)` = 8
`(26)/(27)`

The sum of n terms in a geometric series is

`S_(n)` =
`(a(1-r^n))/(1-r)`, hence

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

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

= 9 (
`(242)/(243)`) =
`(242)/(27)`