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# What are arithmetic series and sequences?

An arithmetic series—also called arithmetic progression—is one of the simpler types of series in mathematics. In such a series, each new term is the previous number plus a given number; it is usually seen in the form of a + (a + d) + (a + 2d) + (a + 3d) + , …, a + (n - 1)d. An example of an arithmetic series would be 2 + 6 + 10 + 14 + …, and so on, in which d is equal to 4. The initial term is the first one in the series; the difference between each term (d, or 4 in this case) is called the common difference.

An arithmetic sequence is usually in the form of a, a + d, a + 2d, a + 3d, …, and so on, in which a is the first term and d is the constant difference between the two successive terms throughout. An example of an arithmetic sequence is (1, 4, 7, 10, 13 …), in which the difference is always a constant of 3. The notation for arithmetic sequences is:

an+1 = an + d.

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