Finding the common ratio of a geometric series from the sum and first term

Question

If the sum of a geometric series is 80, and the first term is 5, and the number of terms is 5, how can I determine the common ratio?

You end up with a quintic equation, I'm not sure if this one is solvable but Solvable quintics might be of some help. — kintoki, Nov 30 '13 at 18:58

snowfall512 · Accepted Answer · 2013-12-10T21:08:34.540

1

This is pretty much brute-force.

Let r be the common ratio. Then $5+5r+5r^2+5r^3+5r^4=80$, so $r+r^2+r^3+r^4=15$. Now just use the series formula!

edited Dec 10 '13 at 21:08

answered Nov 29 '13 at 00:51

snowfall512

For $r+r2+r3+r4=15$, r doesn't equal 5. If r=2, $r+r2+r3+r4=16$, and if r=1, $r+r2+r3+r4=6$. The answer is somewhere in between 1 and 2. I would need to use brute force to find the correct number, by trying them until I find the right one. – Orkwad Nov 29 '13 at 02:25
Hm, I'm not sure where I put the 5. I'll edit it. – snowfall512 Dec 10 '13 at 21:08

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