SOLUTION: the sum of the first two terms of a geometric series is 1 and the sum of its first four terms is 5. if all of its terms are positive, find the first term and the common ratio.

Question 817320: the sum of the first two terms of a geometric series is 1 and the sum of its first four terms is 5. if all of its terms are positive, find the first term and the common ratio.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
a, ar, ar^2, ar^3, are the terms.

and

You might try multiplying the "1" equation by 5:
5a(r+1)=5*1
5a(r+1)=5
Not useful...

BETTER: You might try dividing the "5" equation's members by the "1" equation's members:

and this equation should be useful. From this, try to simplify and use whatever polynomial handling skills you have, like rational roots theorem, remainder, factor theorems...
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