# 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 |

Factoring: Some special cases
Formulas and properties of exponents
Formulas and properties of nth root
Formulas and properties of logarithms
Formulas and properties of arithmetic sequence
Formulas and properties of geometrical sequence
Trigonometry formulasDerivative formulas
Integrals table

Try the online calculators to calculate progressionsn-th term of an arithmetic progressionSum of an arithmetic progressionShow all online calculators

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