I think I might be spoiling you because in this format it's hard to read and not likely to get accepted.
(a) ck = 3ck-1 + 1 for all integers (INDUCTION STATEMENT P)
c1 = 1
ck-1 = 3ck-2 + 1, so
ck = 3 (3ck-2 + 1) + 1 = (3^2)ck-2 + 2 (MODIFIED INDUCTION STATEMENT P)
((Proceed inductively by replacing ck-m term until you reach c1 = 1 ))
= 3^(k-1)c1 + k
= 3^(k-1) + k
Prove this statement by general induction if needed.