What are arithmetic series and sequences?

Sequences and Series Read more from
Chapter Mathematical Analysis

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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