# Formulas and properties of arithmetic sequence

Definition

**Arithmetic sequence**(

**arithmetic progression**) — a sequence of numbers a

_{1}, a

_{2}, a

_{3}, ..., in which each member, starting with the second, equal to the sum of the previous member and a constant number d, called the

*common difference*.

## n -th term of the sequence is given by

a_{n}= a

_{1}+ (n - 1)d

a

_{n}= a

_{n - 1}+ d

## Common difference

d = a_{n}- a

_{n - 1}

The

*sum*of a finite arithmetic progression is called an**arithmetic series**.## Formulas of arithmetic series

S_{n} = |
(a_{1} + a_{n}) · n |

2 |

S_{n} = |
2a_{1} + (n - 1) d |
· n |

2 |

## Properties of arithmetic sequence

a_{n} = |
a_{n + 1} + a_{n - 1} |

2 |

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