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arithmetic progression Sequence of numbers in which each term is produced by adding a constant term (the common difference d) to the preceding one. It has the form a, a + d, a + 2d, and so on. An example is the sequence 1, 3, 5, …. The sum of such a progression, a + (a + d) + (a + 2d) + … is an arithmetic series. For n terms, it has a value sn [2a + 0.5(n − 1) d].