Geometric Sequence Calculator

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

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

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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