The sum of an inf

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,