Let the G.P. is ,
`a,ar,ar^2,...oo`
Then, `a/(1-r) = 57`
` a = 57(1-r)->(1)`
Now, if we take cubes of the terms, then G.P. will be,
`a^3,a^3r^3,a^3r^6,...oo`
Now, sum of the cubes of this G.P.. will be,
`a^3/(1-r^3) = 9457`
`=>(57(1-r))^3/(1-r^3) = 9457`
`=>(1-r)^3/(1-r^3) = 9457/(57)^3`
`=>((1-r)(1+r^2-2r))/((1-r)(1+r^2+r)) = 1/19`
`=>(1+r^2-2r)/(1+r^2+r) = 1/19`
`=>19+19r^2-38r = 1+r^2+r`
`=>18r^2-39r+18 =0`
`=>6r^2-13r+6 = 0`
`=>6r^2-9r-4r+6 = 0`
`=>(3r-2)(2r-3) = 0`
`=>r = 2/3 or r = 3/2`
When `r = 2/3`,
`a = 57(1-2/3) = 57(1/3) = 19`
So, the required G.P. will be,
`19,38/3,76/9...oo.`
