Find the nth term of this quadratic sequence
3, 8, 15, 24, 35...

The first difference is +5 +7 +9 +11
The second difference is +2
Half the second difference to get the coefficient of n^2
So it will be n^2
Compare n^2 to original sequence
1 4 9 16 25 36
3 8 15 24 35
The difference between the two is +2 +4 +6 +3
This is a linear sequence with the nth term of 2n
so the nth term is n^2 +2n