# The sum of an infinite geometric series is 81, and its common ratio is 2/3, how do you find the first three terms of the series?

Jan 7, 2017

${a}_{1} = 27 , {a}_{2} = 18 , {a}_{3} = 12$

#### Explanation:

We use the formula ${s}_{\infty} = \frac{a}{1 - r}$ to find the sum of an infinite geometric series, where $- 1 < r < 1$. We know the sum and the common ratio, so we'll be solving for $a$.

${s}_{\infty} = \frac{a}{1 - r}$

$81 = \frac{a}{1 - \frac{2}{3}}$

$81 = \frac{a}{\frac{1}{3}}$

$81 = 3 a$

$a = 27$

Since our common ratio is $\frac{2}{3}$, we multiply the first term by a factor of $\frac{2}{3}$ to get our second term, and our second term by $\frac{2}{3}$ to get our third term.

Hence,

${a}_{2} = 18$
${a}_{3} = 12$

Hopefully this helps!