Q. 133.6( 5 Votes )

The sum of an infinite GP is 57, and the sum of their cubes is 9747. Find the GP.

Answer :

Let the first term Of G.P. be a, and common ratio be r.



On cubing each term will become,


a3, a3r3, ….


This sum


a=57(1-r) put this in equation 2 we get





19(1-2r+r2)=1+r+r2


19r2-r2-38r-r+19-1=0


18r2-39r+18=0


6r2-13r+6=0


(2r-3)(3r-2)=0


r= 2/3, 3/2


But -1<r<1


r=2/3


Substitute this value of r in equation 1 we get



Thus the first term of G.P. is 19, and the common ratio is 2/3


G.P=19,


19,


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