Answer to Question #336148 in Algebra for habibi

Question #336148

The sum of the first two terms of a geometric progression is 9 and the sum to infinity is 25. If the common ratio is positive, find the common ratio and the first term.   


1
Expert's answer
2022-05-04T12:07:57-0400
a+ar=9a+ar=9

S=a1r=25,r>0S=\dfrac{a}{1-r}=25, r>0

91+r=25(1r)\dfrac{9}{1+r}=25(1-r)

25r2=1625r^2=16

r1=45,r2=45r_1=-\dfrac{4}{5}, r_2=\dfrac{4}{5}

Since r>0,r>0, we take r=45.r=\dfrac{4}{5}.


a=91+45=5a=\dfrac{9}{1+\dfrac{4}{5}}=5

a=5,r=45a=5, r=\dfrac{4}{5}


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