What is a Quadratic sequence?

Consider the quadratic function y=x^2+2x-3.

Now we shall calculate some y-values by substituting x-values from -5 to +5.

x-5-4-3-2-1012345
x^2251694101491625
2x-10-8-6-4-20246810
-3-3-3-3-3-3-3-3-3-3-3-3
y1250-3-4-305122132
Now take the y-values
y1250-3-4-305122132
1st difference7531-1-3-5-7-9-11
2nd difference2222222222

The first differences between the terms are all different.(Got by subtracting the consecutive y-values)

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.

A quadratic sequence is a sequence of numbers in which the second difference between any two consecutive terms is constant.

Leave a Comment

Your email address will not be published. Required fields are marked *