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
$S_{n}=a_{1}\dfrac{r^{n}-1}{r-1}$

Substituting the given numbers, you have
$2730=2\dfrac{4^{n}-1}{4-1}\\\\2730\dfrac{3}{2}=4^{n}-1\\\\4096=4^{n}\\\\\dfrac{\log(4096)}{\log(4)}=n=6$

There are 6 terms in the series.