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.

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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) About Me  (Show Source):
You can put this solution on YOUR website!
a, ar, ar^2, ar^3, are the terms.
a%2Bar%2Bar%5E2%2Bar%5E3=5
a%28r%5E3%2Br%5E2%2Br%2B1%29=5
and
a%281%2Br%29=1

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:
%28a%28r%5E3%2Br%5E2%2Br%2B1%29%29%2F%28a%281%2Br%29%29=5%2F1
highlight_green%28%28r%5E3%2Br%5E2%2Br%2B1%29%2F%28r%2B1%29=5%29 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...