Question

If the sum of first n terms of a G.P. is s and the sum of its first 2n terms is 5S, then show that the sum of its first 3n terms is 21S .

Answer 1

`S=[((a)(1-r^n))/(1-r)]`
`S_5=[((a)(1-r^(2n)))/(1-r)]`
`S_5/S=(1-r^(2n))/(1-r^n)`
`5=1+r^n`
`r^n=4`
`S=a/(1-r)*(1-4)`
`a/(1-r)=-S/3`
`S_(3n)=a/(1-r)[1-r^(3n)]`
`=a/(1-r)[1-(r^n)^3]`
`=-S/3[1-4^3]`
`S_(3n)=21s`.