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.
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.