Question

What is the sum of the geometric sequence 4, 16, 64, ... if there are 8 terms? (6 points)

Answer 1

87380

Explanation:

The sum to n terms of a geometric sequence is

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

where a is the first term and r the common ratio

r =
`(16)/(4)` = 4 and a = 4, hence

`S_(8)` =
`(4(4^8-1))/(4-1)` =
`(4(65535))/(4)` = 87380