# Geometric progression Calculator

## Calculates the n-th term and sum of the geometric progression with the common ratio.

 $\normal Sn=a+ar+ar^2+ar^3+\cdots +ar^{n-1}\\$
initial term a
common ratio r
number of terms n
 n＝1,2,3...

the n-th term an
sum Sn
 $\normal Geometric\ progression\\\vspace{5}(1)\ a_n=ar^{n-1}\\(2)\ Sn={\large \sum_{\small k=1}^{\small n}}ar^{k-1}\\\hspace{45} =a+ar+ar^2+ar^3+\cdots +ar^{n-1}\\\vspace{5}\hspace{45} =\left\{\begin{array}{1}{\large\frac{a(1-r^n)}{1-r}\hspace{40}r\neq 1}\\\hspace{10} {\normal na\hspace{70}r=1}\end{array}\right.\\$

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