SOLUTION: find a geometric progression of four terms in which the sum of the first and last terms is 27 and the sum of the middle terms is 18.

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Question 818503: find a geometric progression of four terms in which the sum of the first and last terms is 27 and the sum of the middle terms is 18.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
a, ar, ar^2, ar^3 are the terms.

a%2Bar%5E3=27 and ar%2Bar%5E2=18

Note that a%281%2Br%5E2%29=27 and %28ar%2Br%29%281%2Br%29=18 or r%28a%2B1%29%281%2Br%29=18;
Also a%2Bar%2Bar%5E2%2Bar%5E3=39

One task might be solve a%281%2Br%5E2%29=27 for a, and solve r%28a%2B1%29%281%2Br%29=18 for r; and then you can get an expression for the term ar and you can also get a value for ar.

Ordinarily, I would solve a help-requested problem at least partially or give a more complete strategy. I won't this time. Can what I gave so far help with this problem? What I'm doing here is not the best way, but might be enough for you to make progress with the question.