Here are some suggestions:
Find f(n) such that b_n=a_n-f(n) has a nice property.
I think we can find f(n) as a polynomial of n.
a) f(n)-f(n-1)=3(n-1). Let f(n)=pn^2+qn.
By substituting, we see that p=3/2 and q=-3/2 works.
e) I am not sure what you mean by "2n2",
but the same method should work if this is "2n^2".
a-c) It is also common to consider the sequence obtained by
I hope it helps.