# Geometric Sequence Calculator

## Solve geometric progressions step by step

The calculator will find the terms, common ratio, sum of the first $n$ terms and, if possible, the infinite sum of the geometric sequence from the given data, with steps shown.

Related calculator: Arithmetic Sequence Calculator

$a($
$)=$
$a($
$)=$
$a($
$)=$
$S($
$)=$
$S($
$)=$
$S($
$)=$
$S_{n}$ is the sum of the first $n$ terms.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

### Your Input

Find $a_{4}$, $S_{3}$, $S_{\infty}$, given $a_{1} = 3$, $r = 5$.

### Solution

We have that $a_{1} = 3$.

We have that $r = 5$.

$a_{4} = a_{1} r^{4 - 1} = 3 \cdot 5^{4 - 1} = 375$

$S_{3} = \frac{a_{1} \left(1 - r^{3}\right)}{1 - r} = \frac{3 \left(1 - 5^{3}\right)}{1 - 5} = 93$

Since $\left|{r}\right| = 5 \geq 1$, the infinite sum is infinite.

### Answer

$a_{4} = 375$A

$S_{3} = 93$A