in a G.P. of positive numbers, any term is equal to the sum of hte next two terms. the common ratio of the G.P. is-

Let the first term be a and Common ration be r.

Tn = Tn+1 + Tn+2

ar^n-1 = ar^n + ar^n+1

1= r + r ^2

On solving the quadratic equation,

r= (√5 - 1)/2 (The negative answer rejected as the GP is of positive numbers)