Question

Which expression could be used to find the sum of the first n terms of the geometric sequence that begins 11,22,44,…?

Answer 1

`S_(n)` = 11(
`2^(n)` - 1)

Explanation:

The sum to n terms of a geometric sequence is

`S_{1n` =
`(a_(1)(r^(n)-1) )/(r-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 11 and r =
`(a_(2) )/(a_(1) )` =
`(22)/(11)` = 2 , then

`S_(n)` =
`(11(2^(n)-1) )/(2-1)` = 11 (
`2^(n)` - 1)