Question

How many terms are there in a geometric series if the first terms is 2, the common ratio is 4, and the sum of the series is 2,730 ?

Answer 1

The sum of n terms of a geometric series is given by

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

Substituting the given numbers, you have

`2730=2(4^(n)-1)/(4-1)\\\\2730(3)/(2)=4^(n)-1\\\\4096=4^(n)\\\\(\log(4096))/(\log(4))=n=6`

There are 6 terms in the series.