Solve the following recurrence relations.

a. x (n) = x (n 1) + 3 for n > 1 and x (1) = 9.

b. x (n) = 3x (n 1) + 4 for n > 0 and x (0) = 9.

c. x (n) = x (n 1) + n 2 for n > 0 and x (0) = 5.

d. x (n) = x n 8 + n for n > 1 and x (1) = 2. Solve for n = 8k .

e. x (n) = x n 6 + 6 for n > 1 and x (1) = 3. Solve for n = 6k .