Quadratic sequences

If the difference between the terms changes, this is called a quadratic sequence.

If you use the formula n² + n to make a sequence, it means that:

• When n = 1 you get 1² + 1 = 2
• When n = 2 you get 2² + 2 = 6
• When n = 3 you get 3² + 3 = 12
• When n = 4 you get 4² + 4 = 20

- giving the sequence 2, 6, 12, 20.

Here, the differences between terms are not constant, but there is still a pattern.

• - the first differences increase by 2 each time
• - the second increases by 2

When the second difference is constant, you have a quadratic sequence - ie, there is an n² term.

Now practise recognising quadratic sequences in the activity below.

Now try a Test Bite