# How do you find the sum of the infinite geometric series 72 + 12 + 2 + +… ?

Jan 10, 2016

$\frac{432}{5} = 84 \frac{2}{5}$

#### Explanation:

The formula for the sum of an infinite series is $S = \frac{a}{1 - r}$
where r is the common ratio and a is the first term.

Therefore, $S = \frac{72}{1 - \frac{1}{6}} = \frac{72}{\frac{5}{6}} = \frac{432}{5}$

Jan 10, 2016

First, you must find the common ratio, r, of the series.

#### Explanation:

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

r = $\frac{12}{72}$

r = $\frac{1}{6}$

S_∞ = $\frac{a}{1 - r}$

S_∞ = $\frac{72}{1 - \frac{1}{6}}$

S_∞ = $\frac{72}{\frac{5}{6}}$

S_∞=  (72 • 6)/ 5

S_∞ = $\frac{432}{5}$ or 146.4

The sum is $\frac{432}{5}$ or 146.4. Hopefully you understand now!

Below I have posted one problem for your practice.

1. Find the wanted information.

a) An infinite geometric series has a third term of 18 and a common ratio of $\frac{1}{2}$. Find it's sum.

b) A pendulum has a first swing of 186 centimeters and a second swing of 124 centimetres. Assuming the pendulum swings forever, find the total distance travelled, rounded to the closest hundredth when necessary.