### Home > PC > Chapter 8 > Lesson 8.2.6 > Problem8-150

8-150.

Given the infinite sum $5 + 5x + 5x^{2} + 5x^{3} + ... = 10$, what is the value of $x$

Use the infinite geometric series formula(shown below) and set it equal to $10$. Then solve for $x$.

$S_{n}=\frac{a_{1}}{1-x}$

$a_{1} = 5$

$\:\:\:5 = 10\left(1 − x\right)$
$\:\:\:5 = 10 − 10x$
$−5 = −10x$