# How do you find the sum of the finite geometric sequence of Sigma 10(1/5)^n from n=0 to 20?

Oct 13, 2017

$12.45$ (2 .d.p)

#### Explanation:

First calculate the first three terms:

$10 {\left(\frac{1}{5}\right)}^{0} = \textcolor{b l u e}{10} , 10 {\left(\frac{1}{5}\right)}^{1} = \textcolor{b l u e}{2} , 10 {\left(\frac{1}{5}\right)}^{2} = \textcolor{b l u e}{\frac{2}{5}}$

Find the common ratio:

$\frac{2}{10} = \frac{\frac{2}{5}}{2} = \frac{1}{5}$

The sum of a geometric sequence is:

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

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

So:

$10 \left(\frac{1 - {\left(\frac{1}{5}\right)}^{20}}{1 - \left(\frac{1}{5}\right)}\right) = 12.4999999999999737856$