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March 5th, 2016, 04:48 AM  #1 
Member Joined: Aug 2015 From: Podgorica Posts: 61 Thanks: 0  Geometric sequence
Here is the problem, that I can not solve: The first term of a geometric series is 6, and the sum of the first 15 terms is 29. Find the common ratio. I have had a weird approach. I used the general formula and from there I found what is r(common ratio) equal to. I got this equation: 0=6r^1529r+23 Can you help me solve this equation? Is there any way of solving this problem, that makes more sense? 
March 5th, 2016, 05:41 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,480 Thanks: 2039 
I don't think you can find exact expressions for the solutions. There are two relevant real roots (r = 1 doesn't count). r = 1.16150319 or 0.80044378 approximately. There are also 6 (conjugate) pairs of complex roots. 
March 5th, 2016, 06:18 AM  #3 
Member Joined: Aug 2015 From: Podgorica Posts: 61 Thanks: 0  Yes, that is the solution. How did you find it?
Last edited by skipjack; March 5th, 2016 at 08:44 AM. 
March 5th, 2016, 08:48 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,480 Thanks: 2039 
I used WolframAlpha.


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