a) Consider the following linear homogeneous recurrence relation: Rn = 4Rn-1 - 3Rn-2. It is known that: R₀ = 1, R₂ = 5. Find R₃.
b) Determine the general solution of the recurrence equation if its characteristic equation has the following roots: 1, -2, -2, 2, 7, 7.
c) Determine the general solution of the recurrence equation An = 256A,-4.
d) Find the general form of the particular solution of the recurrence Bn = 3Bn-2 - 2Bn-3 + 2.