Sequences that increase in increasing steps
When the second row of differences forms the constant number of a sequence, this is called a quadratic sequence. In the following example, the sequence increases in unequal steps:
4, 5, 7, 10, 14, 19………..
the differences in between the terms are as follows:
1, 2, 3, 4, 5…… (this is the differences between the differences or the second row of differences)
The differences between the terms is what forms the linear sequence. Therefore in this circumstance, it is easier to work out the second row of differences.
In a quadratic sequence, the nth term of the sequence is expressed in the following form:
Un = an² + bn + c (a, b and c are constants and a ≠ 0)