Quadratic Sequences

A quadratic sequence is an ordered list of n numbers in which the difference in the first difference between consecutive terms, that is the second difference between terms, is constant. Therefore, a quadratic sequence can be described by formula:

The term to term rule of a quadratic sequence describes how to get from one term to the next in the sequence. To find the term to term rule, identify the common second difference term between consecutive terms. From the term to term rule and the first term of the sequence the position to term rule, or general rule, of a quadratic sequence can be worked out with the formula:

The general rule of a quadratic sequence can be used to work out the nth term of the sequence, the term at position n, and is given by the formula:

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