S(0) = 3 S(1) = 14 S(n) = 4S(n-l) - 4S(n-2) Give S(n) in closed form and prove correct by induction. Find the values for the characteristic equation, x_1, c_2 and c_2 Characteristic Equation: x^2 + ____ x + _____ = 0 x_1 = x_2 = _____ Given: S(n) = X_1^n(c_1 + c_2n) S(0) = 3 = x_1^0(c_l + c_2*0) S(l) = 14 = x_1^1(c_1 + c_2*l) c1 = S(n) = Basis: S(0) = 3 = x_1^0(c_1 + c_2*0) = _______ Does it equal 3? (y) ________ S(1) = 14 = x_1^1(c_1 + c_2*l) = ________ Does it equal 14? (y) ________ Assume: S(n - l) = S(n - 2) = Prove S(n) = Enter the rest of your proof in the box below. No points are awarded for this question until it has been graded by a TA. ________