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

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

∴

On cubing each term will become,

a^3, 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,