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March 5th, 2016, 04:48 AM   #1
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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?
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March 5th, 2016, 05:41 AM   #2
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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.
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March 5th, 2016, 06:18 AM   #3
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Quote:
Originally Posted by skipjack View Post

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.
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March 5th, 2016, 08:48 AM   #4
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I used WolframAlpha.
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