# 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= 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. ## 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.