What an arithmetic sequence is
An arithmetic sequence is a list of numbers where each term is found by adding the same fixed amount, called the common difference, to the term before it. For example, 3, 8, 13, 18 is arithmetic with a common difference of 5.
The formula used
The nth term of an arithmetic sequence is found with a_n = a1 + (n – 1)d, where a1 is the first term and d is the common difference. The sum of the first n terms is found with S_n = (n/2) × (2a1 + (n – 1)d).
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Last reviewed August 2026