Sequences are sets of numbers that are connected in some way. In a quadratic sequence, the difference between each term increases, or decreases, at a constant rate.

Part of

Look again at the sequence of square numbers:

The diagram shows that:

- the first term is ( )
- the second term is ( )
- the third term is ( )
- the fourth term is ( )

So the term is .

Whenever a sequence has a second difference of , it will be connected to the sequence of square numbers and the term will have something to do with .

- Question
What is the term of the sequence , , , , ... ?

The second difference is , so the term has something to do with .

The sequence of square numbers is: , , , , ...

Our sequence is: , , , , ...

**Can you see what the difference is?**Each term is higher than the corresponding term in the sequence of square numbers, so the rule for the term is .

- Question
What is the term of the sequence , , , , ...?

The second differences are , so the formula has something to do with .

The sequence of square numbers is: , , , , ...

Our sequence is: , , , , ...

Each term in this sequence is less than the corresponding term in the sequence of square numbers, so the rule for the term is .