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.

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) (Show Source): You can put this solution on YOUR website!
a, ar, ar^2, ar^3 are the terms.

and

Note that and or ;
Also

One task might be solve for a, and solve for r; and then you can get an expression for the term ar and you can also get a value for .

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.
RELATED QUESTIONS
A geometric progression has 6 terms. The first term is 192 and the common ratio is 1.5.... (answered by greenestamps)

A geometric progression has six terms. The first term is 486 and the common ratio is ;.... (answered by greenestamps)

The arithmetic progression consists of 15 terms. If the sum of the 3 terms in the middle (answered by ikleyn)

find the sum of the first 5 terms of the geometric progression for which the first and... (answered by richwmiller)

the sum of first 4 terms of Geometric progression is 7.5 if the sum of middle two terms... (answered by reviewermath)

In a geometric progression,the 6th term is 96 and the common ratio is -2. Find the sum of (answered by ikleyn)

find the first 3 terms of a geometric progression whose sum is 42 and whose product is... (answered by htmentor)

First question: A geometric sequence consisting of four terms in which ratio is... (answered by robertb)

In a geometric progression of positive terms, the 5th term is 9 times the 3rd term and... (answered by richwmiller)