#
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

${S}_{n}=\frac{{a}_{1}(1-{r}^{n})}{1-r},\text{\hspace{0.17em}}\text{\hspace{0.17em}}r\ne 1$
,

where
$n$
is the number of terms,
${a}_{1}$
is the first term and
$r$
is the
common ratio
.