I have two questions don't know how to solve and need helpThank you so much

Questions are on the pictures.

(a) Solve the recurrence relation an = 12 am 16 an_3 + 9 . 2'n+1 + 25m, n \\V \"co where a0 = 20, a1 = 31 and a2 = 62. (b) Write down the generating function of the sequence an in part (a) in a closed form. 2. Recall that the Fibonacci and Lucas sequences FT, and L,1 are (0, l, 1,2,. . .) and (2, 1,3, 4,. . .), respectively. (a) Derive closed formulas for the generating functions F(z) and L(z). (b) Use your answers in part (a) to prove the relation Lnl Lin2 L0 F\" = - n o _ 2 + 22 + + 2\" for all n 2 1. (c) Find and prove a formula expressing L1, as a linear combination of the Fi bonacci numbers