Help me out of this

Le {a,} be a sequence of positive real numbers such that a, = 1, a "n+1 -2a,a,-a, =0 for all n 21. Then the sum of the series lies in the interval (a) (1, 2] (c) 3, 4] n=l 3" (b) (2, 3] (d) (4, 5]