# How do you find the sum of the finite geometric sequence of Sigma 500(1.04)^n from n=0 to 6?

Dec 16, 2017

See below.

#### Explanation:

The sum of a geometric series is given by:

$a \left(\frac{1 - {r}^{n}}{1 - r}\right)$

Where $a$ is the first term, $r$ is the common ratio and $n$ is the nth term.

From example:

$a = 500$ , $r = 1 , 04$ and $n = 7$ ( since we start at 0 )

$\therefore$

$500 \left(\frac{1 - {\left(1.04\right)}^{7}}{1 - 1.04}\right) \approx 3949.147$

${\sum}_{n = 0}^{6} 500 {\left(1.04\right)}^{n} \approx 3949.147$