# If r = 3 and the sum of 6 terms of the geometric series is 3640, what is the first term?

May 7, 2016

First term is $10$

#### Explanation:

In a geometric series, if $a$ is the first term and ratio between a term and its preceding term is $r$, then sum of first $n$ terms ia given by

$a \frac{{r}^{n} - 1}{r - 1}$

As $r = 3$ and sum of first $6$ terms is $3640$, we have

$a \frac{{3}^{6} - 1}{3 - 1} = 3640$

hence $a \frac{729 - 1}{3 - 1} = \frac{a \times 728}{2} = 3640$

or $364 a = 3640$ and hence

$a = 10$.