# How to find r for the sum of GP series?

• Apr 15th 2013, 07:16 AM
Apple1
How to find r for the sum of GP series?
Hi

Given such an equation, how do I find r? Thank you

(1-r^m)/ (1-r)= s
where m can be any positive whole number
s can also be any positive number

The equation is actually the summation for a GP series with a=1, so basically I want to know how to find r (ratio factor) for the sum of a GP .
• Apr 15th 2013, 12:03 PM
HallsofIvy
Re: How to find r for the sum of GP series?
So you are basically just asking how to solve $\frac{1- r^m}{1- r}= s$ for r? You can multiply on both sides by 1- r to get $1- r^m= s-rs$ which can be reduced $r^m- sr+ (s-1)= 0$. That is an 'm-degree' polynomial. However, there are no formulas, using elementary functions, for solving polynomials of degree greater than 5.
• Apr 16th 2013, 06:02 AM
Apple1
Re: How to find r for the sum of GP series?
Hi

Thanks for the reply.

Then how do u solve if m greater than 5? Is there an Excel function to do it?

Thanks