# Sum of the First n Terms of a Geometric Series

If a series is geometric there are ways to find the sum of the first $n$ terms, denoted ${S}_{n}$ , without actually adding all of the terms.

To find the sum of the first $n$ terms of a geometric series use the formula
${S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r},\text{\hspace{0.17em}}\text{\hspace{0.17em}}r\ne 1$ ,
where $n$ is the number of terms, ${a}_{1}$ is the first term and $r$ is the common ratio .