Solve the following recurrences exactly

(a) T(1) = 8, and for all n ≥ 2, T(n) = 3T(n − 1) − 15
(b) T(1) = 3, and for all n ≥ 2, T(n) = T(n − 1) + 2n − 3
(c) T(1) = 1, and for all n ≥ 2 such that n is a power of 2, T(n) = 2T(n2) + 6n − 1
(d) T(1) = 1, and for all n ≥ 2 such that n is a power of 3, T(n) = 4T (n3) + n 2 − 7n + 5