# How do you find the sum of the infinite geometric series given 16+12+9+...?

Feb 9, 2017

Sum of the infinite geometric series is $64$

#### Explanation:

Sum of the infinite geometric series converges to $\frac{{a}_{1}}{1 - r}$, where ${a}_{1}$ is the first term and $r$ is the common ratio and $| r | < 1$.

Here, we have ${a}_{1} = 16$ and $r = \frac{12}{16} = \frac{9}{12} = \frac{3}{4}$ and $| r | < 1$,

Hence, sum of the infinite geometric series is

$\frac{16}{1 - \frac{3}{4}} = \frac{16}{\frac{1}{4}} = 16 \times 4 = 64$