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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^15-29r+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
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Quote:
 Originally Posted by skipjack There are two relevant real roots (r = 1 doesn't count). r = -1.16150319 or 0.80044378 approximately.
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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