Quadratic sequences
A sequence is a set of numbers that are connected in some way. In this section we will look at quadratic sequences where the difference between the terms changes.
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.
Learn these rules:
If the second difference is 2, you start with n2.
If the second difference is 4, you start with 2n2.
If the second difference is 6, you start with 3n2.
Another definition for Quadratic sequence
A quadratic sequence is a sequence of numbers in which the second difference between each consecutive term is constant. This called a common second difference.