Question

In a G.P. of positive terms if any terms is equal to the sum of next tow terms, find the common ratio of the G.P.

Answer 1

Let the G.P. is,
`a, ar,ar^2,ar^3...`
Here, `a` is the first term and `r` is the common ratio.
Then, it is given that ,
`ar+ar^2 = a`
`=>r+r^2 = 1`
`=>r^2+r-1 = 0`
`=> r = (-1+-(sqrt(1-4(-1)(1))))/2 =+- (sqrt5-1)/2`
Here, we will take only positive value as it is given that G.P. is of positive terms.
So, common ratio of this G.P. is `(sqrt5-1)/2.`