Finding the next term of a quadratic sequence

What is a quadratic sequence?

Look at this sequence:

Quadratic sequence diagram

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 \({2}\). We can state that the second difference is \({2}\).

This means that it is a quadratic sequence.

In fact, whenever the second difference is a constant value it will be a quadratic sequence.

Quadratic sequence diagram

\(+3, +5, +7, +9\) are the first differences,

and \(+2, +2, +2\) are the second differences.

Question

Use this pattern of differences to find the next term of the sequence:

Quadratic sequence diagram
Quadratic sequence diagram