S(n) = 6*2^n + 3^n Construct the recursive form of S(n).

Using "The Cheap Method" S(n)-S(n-1) 6 S(n) = S(n-1) + (2 S(0) = Using the linear homogeneous method: Construct the characteristic equation: (x - 2) (x Put it in canonical form: x2 + Mult. by a * xn-2 on both sides, and then sub in S(n) = a xn S(n-1) = a xn-1 S(n-2) = a xn-2 and solve for S(n): S(n) = Basis S(0) = S(1) = S(n-1) S(n-2)