# Formulas and properties of geometric sequence

Definition

**Geometric sequence**(

**geometric progression**) — a sequence of numbers b

_{1}, b

_{2}, b

_{3}, ..., in which each member, starting with the second, equal to the product of the previous member and a constant number q (

*common ratio*), where b

_{1}≠ 0, q ≠ 0.

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

b_{n}= b

_{1}· q

^{n - 1}

b

_{n}= b

_{n - 1}· q

## Common ratio

q = | b_{n} |

b_{n - 1} |

A

**geometric series**is the*sum*of the numbers in a geometric sequence.## Formulas of geometric series

S_{n} = |
b_{1} - b_{n + 1} |

1 - q |

S_{n} = b_{1} · |
1 - q^{n} |

1 - q |

## Properties of geometric sequence

b_{n}

^{2}= b

_{n + 1}· b

_{n - 1}

## An infinite geometric series

If |q| < 1 and n → ∞S = | b_{1} |

1 - q |

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

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