# 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... 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit the n-th term an sum Sn
 $\normal Geometric\ progression\\\vspace{5}(1)\ a_n=ar^{n-1}\\(2)\ Sn={\large \sum_{\small k=1}^{\small n}}ar^{k-1}\\\hspace{45} =a+ar+ar^2+ar^3+\cdots +ar^{n-1}\\\vspace{5}\hspace{45} =\left\{\begin{array}{1}{\large\frac{a(1-r^n)}{1-r}\hspace{40}r\neq 1}\\\hspace{10} {\normal na\hspace{70}r=1}\end{array}\right.\\$

Geometric progression
 [1-3] /3 Disp-Num5103050100200
[1]  2019/02/15 08:04   Male / Under 20 years old / Elementary school/ Junior high-school student / Useful /
Purpose of use
math problem
Comment/Request
cool
[2]  2018/03/17 07:43   Female / Under 20 years old / High-school/ University/ Grad student / Not at All /
Purpose of use
I was looking for a calculator to find the common ratio of a sequence when given the first 3 numbers of that sequence. I can''t seem to find one of those...
[3]  2013/03/23 03:56   Male / 50 years old level / Others / A little /
Purpose of use
Von Neumann probe estimate. 400 billion stars in the galaxy, how many iterations before a reproducing probe produces a number equivalent to one probe per star. Assume original probe produces 1 per month until T is reached. Every probe after that does the same once its arrived. Average travel time between stars assume 50 years.

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