Question

Find the sum of the geometric sequence. 4 divided by 3, 16 divided by 3, 64 divided by 3, 256 divided by 3, 1024 divided by 3

Answer 1

Sum =
`(1364)/(3)`

Explanation:

The given geometric sequence is:

`(4)/(3), (16)/(3), (64)/(3), (256)/(3),(1024)/(3)`

The first term of the sequence is
`a_(1)=(4)/(3)`

The common ratio of the sequence is:

`r=((16)/(3) )/((4)/(3) )=4`

There are 5 terms in total in the given sequence so n = 5

The formula to calculate the sum of finite geometric sequence is:

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

Using the given values, we get:

`S_(5)=((4)/(3) (1-4^(5)) )/(1-5) = (1364)/(3)`

Therefore, the sum of given geometric sequence is
`(1364)/(3)`