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Arithmetic sequences

Arithmetic sequences

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An arithmetic or linear sequence, an, is an ordered list of n numbers where the difference between each consecutive term, d, is constant. An arithmetic sequence can always be described by the general rule:

Basics of arithmetic sequences

The term to term rule of an arithmetic sequence describes how to get from one term to the next in the sequence. To find the term to term rule, subtract the first term from the second term to find the common first difference term. From the common first difference term and the first term the position to term rule, or general rule, can be worked out with the formula:

Generating terms in arithmetic sequences

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

nth term of arithmetic sequences

A series is the sum of the terms of a sequence up to a certain number of terms and it is denoted by Sn. A series for an arithmetic sequence is given by the formula:

Arithmetic series

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