Consider the quadratic function y=x^2+2x-3.
Now we shall calculate some y-values by substituting x-values from -5 to +5.
The first differences between the terms are all different.(Got by subtracting the consecutive y-values)
However, if you look at the differences between these first differences they go up in steps of 2.
We can state that the second difference is 2.
This means that it is a quadratic sequence.
A quadratic sequence is a sequence of numbers in which the second difference between any two consecutive terms is constant.