Question

Find the seventh term of the geometric sequence 1, 2, 4, ... and the sum of the first seven terms. t7= S7=

Answer 1

Seventh term is 64

Sum of the first seven terms is 127

Explanation:

The common ratio is 2

`a_(n) = a_(1) r^(n - 1)`

n = 7 and the first term is 1. So,

`a_(7) = 1(2^(7 - 1) ) = 2^(6) = 64`

Seventh term is 64

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

`S_(7) = (1(2^(7) -1))/(2 - 1)`

`= (128 - 1)/(1) = 127`

Sum of the first seven terms is 127