# Finding the next term of a quadratic sequence

## What is a quadratic sequence?

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 $${2}$$. 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.

$$+3, +5, +7, +9$$ 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: