If each term of an infinite G.P. is twice the sum of the terms following it, then find the common ratio of the G.P.

Explanation

Let a be the first term and r the common ratio of the G.P.
Then, `a_(n)=2[a_(n+1)+a_(n+2)+a_(n+3)+..oo]`, for all n`in`N [Given]
`rArrar^(n-1)=2[ar^(n)+ar^(n+1)+..oo]`
or `ar^(n-1)=(2ar^(n))/(1-r)`
or `1=(2r)/(1-r)`
or `r=1/3`