# How do you find the sum of the infinite geometric series given 3+1.8+1.08+...?

Oct 12, 2016

The series has a sum of $7.5$.

#### Explanation:

We use the formula ${s}_{\infty} = \frac{a}{1 - r}$ to determine the sum of an infinite convergent geometric series.

In other words, for us to be able to find the sum, $| r | < 1$.

We can find $r$ by using the formula $r = {t}_{2} / {t}_{1}$.

$r = {t}_{2} / {t}_{1}$

$r = \frac{1.8}{3}$

$r = 0.6$

We now know $a$, which is $3$ and $r$, which is $0.6$.

${s}_{\infty} = \frac{3}{1 - 0.6}$

${s}_{\infty} = \frac{3}{0.4}$

${s}_{\infty} = 7.5$

Hopefully this helps!