Hello, sanorita_belle!

I don't know the procedure you were taught, but I can guess . . .Find the solution of the recurrence relation: .

with initial condition

This is a linear non-homogeneous recurrence which has a general solution

of the form: .

I tried solving the , homogeneous part first: .

I got: . , for some constant . . . . Good!

But now i am confused about the particular solution

How do i find that?

You might conjecture that the particular solution is a quadratic ...

. . of the form: .

I was taught a different approach . . . quite long and tedious . . .

. . and came up with: .

. . which cranks out the first few terms: .