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.

`a`()`=`

`a`()`=`

`a`()`=`

Common ratio `q=`

Sum of the first terms `S`()`=`

Sum of the first terms `S`()`=`

Sum of the first terms `S`()`=`

Infinite sum `S=`

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Solution

Your input: find $$$a_{4}$$$, the sum of the first $$$3$$$ terms, the infinite sum $$$S$$$, given $$$a_{1}=3$$$, the common ratio $$$q=5$$$.

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

We have that $$$q=5$$$.

Finally,

$$$a_{4}=a_1 \cdot q^{4 - 1}=3\cdot\left(5\right)^{4 - 1}=375$$$.

$$$S_{3}=a_1\frac{1 - q^{3 - 1}}{1-q}=\left(3\right)\frac{1-\left(5\right)^{3 - 1}}{1-\left(5\right)}=93$$$.

Since the common ratio $$$|q| = 5 > 1$$$, then the infinite sum is infinite.

Answer

$$$a_{1}=3$$$.

$$$a_{4}=375$$$.

The common ratio is $$$q=5$$$.

$$$S\left(3\right)=93$$$.

The infinite sum is infinite.