Second Difference - GCSE Maths Definition

The second difference refers to how numbers change in a sequence. For a sequence of numbers, the first difference would refer to the differences between each pair of terms. Sometimes the first difference will vary, sometimes it will not. When the first difference does vary, the sequence can be investigated further by considering the second differences - these would refer to the differences between each pair of first differences.

In GCSE Mathematics, a constant second difference indicates a quadratic sequence - a sequence of the form , where n is the term number, and a, b and c are constants. Understanding constant second differences and quadratic sequences will then allow us to go on to deduce the values of a, b and c, and thus solve further problems involving the sequence as we will know its full details.