# How do you find the sum of the first 10 terms of the following geometric sequence 5, 10, 20, 40, 80, …….?

Feb 25, 2016

$5115$

#### Explanation:

${a}_{0} = 5$
$r = 2$

We are asked for the sum of the first 10 terms i.e. ${a}_{0} , {a}_{1} , \ldots , {a}_{9}$
so $n = 9$ in the general geometric sum formula:
$\textcolor{w h i t e}{\text{XXX}} {\Sigma}_{i = 0}^{n} = {a}_{0} \cdot \frac{1 - {r}^{n + 1}}{1 - r}$

In this case we have
$\textcolor{w h i t e}{\text{XXX}} {\Sigma}_{i = 0}^{9} = 5 \cdot \frac{1 - {2}^{10}}{1 - 2} = 5 \times 1023 = 5115$