Patterns and Sequences
Quadratic Sequences
In a quadratic sequence, the differences between consecutive terms are not constant, but the second differences (the differences of the differences) are constant. This constant second difference is always 2a, where a is the coefficient of n² in the nth term formula.
Worked Example
Sequence: 3, 6, 11, 18, ... First differences: 3, 5, 7. Second difference: 2 (constant). The next first difference is 9, so the next term is 18 + 9 = 27.
Practice: Quadratic Sequences
Find the next term using second differences, or evaluate a quadratic nth term formula.