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Sum of an infinite GP is 5/4 times the sum all the odd terms the common ratio of the GP is

Sum of an infinite GP is 5/4 times the sum all the odd terms the common ratio of the GP is

Grade:11

2 Answers

Saurabh Singh
20 Points
6 years ago
Sum of a infinite G.P is : a/(1-r)And sum of all terms of a will be:1+3+5+7+9.............(n-1) [ This is A.P]Therefore, Sum of all odd terms will be,S=n/2(2a+(n-1)d) [sum of A.P upto n terms]ThereforeS(odd terms upto n)=(n/2)*(2(1)+(n-1-1)2)=n^2And it is given to us that ,a/(1-r)=5n^2/4=> r=1-(4a/(5n^2))
aashwal dixit
11 Points
5 years ago
let sum of all terms be s1and common retio be rand sum of odd terms be s2now let 1st term be a so 3rd term will be a*r*r and similarly 5th term (which is 3rd odd term also ) will be a*r*r*r*r and so onso that s1 = a/(r-1)s2 = a/(r^2 -1)now according to question s1 = 1/5 s2putting values and solving equation we get r= -4/5

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