Look at this sequence:
The first differences between the terms are all different.
However, if you look at the differences between these first differences they go up in steps of . We can state that the second difference is .
This means that it is a quadratic sequence.
In fact, whenever the second difference is a constant value it will be a quadratic sequence.
are the first differences,
and are the second differences.
Use this pattern of differences to find the next term of the sequence: