## Mathematical Analysis## Sequences and Series |

## 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:

^{a}_{n+1} = *a*_{n} + *d*.