# The sum of an infinite geometric series is 125, and the value of r is 0.4. How do you find the first three terms of the series?

Nov 13, 2016

The first three terms are $75 , 30 , 12$.

#### Explanation:

The formula for sum of an infinite, convergent geometric series is ${s}_{\infty} = \frac{a}{1 - r}$, where ${s}_{\infty}$ is the sum, $a$ is the first term of the series and $r$ is the common ratio.

Hence,

$125 = \frac{a}{1 - 0.4}$

$125 \times 0.6 = a$

$a = 75$

We know that $r = 0.4$, so:

${t}_{2} = 75 \times 0.4 = 30$

${t}_{3} = 30 \times 0.4 = 12$

Hopefully this helps!