How to solve: T(n) = T(n - 1) + n

Question

I have the following worked out:

T(n) = T(n - 1) + n = O(n^2)

Now when I work this out I find that the bound is very loose. Have I done so

Answer 1

Looks about right, but will depend on the base case T(1). Assuming you will do n steps to get T(n) to T(0) and each time the n term is anywhere between 0 and n for an average of n/2 so n * n/2 = (n^2)/2 = O(n^2).