N th term of quadratic sequence 3, 11, 25, 45

The first differences are 8, 14, 20.

The second differences are 6.

Half of 6 is 3, so the first term of the sequence is 3n^2.

If you subtract 3n^2 from the sequence you get 0,-1,-2,-3 which has the nth term of - n + 1.

Therefore your final answer will be 3n^2 - n + 1