## Summary/Background

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3 and 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.

The sum of the terms of a geometric progression is known as a geometric series.

\displaystyle \sum_{k=1}^n ar^{k-1} = ar^0 + ar^1 + ar^2 + ... + ar^{n-1}

The sum of the terms of a geometric progression is known as a geometric series.

\displaystyle \sum_{k=1}^n ar^{k-1} = ar^0 + ar^1 + ar^2 + ... + ar^{n-1}

## Software/Applets used on this page

## Glossary

### geometric

A sequence where each term is obtained by multiplying the previous one by a constant.

### sequence

a number pattern in a definite order following a certain rule

### series

the sum of terms in a sequence

### union

The union of two sets A and B is the set containing all the elements of A and B.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AP Calculus BC (USA) | 5 | Sequences and series | Geometric series |

AQA A-Level (UK - Pre-2017) | C2 | Sequences and series | Geometric series |

AQA A2 Maths 2017 | Pure Maths | Sequences and Series | Geometric Sequences |

AQA AS/A2 Maths 2017 | Pure Maths | Sequences and Series | Geometric Sequences |

CBSE XI (India) | Algebra | Sequence and Series | Geometric progression |

CCEA A-Level (NI) | C2 | Sequences and series | Geometric series |

CIE A-Level (UK) | P1 | Sequences and series | Geometric series |

D Sequences and Series | D5 Geometric Sequences | Geometric Sequences | |

Edexcel A-Level (UK - Pre-2017) | C2 | Sequences and series | Geometric series |

Edexcel A2 Maths 2017 | Pure Maths | Sequences and Series | Geometric Sequences |

Edexcel AS/A2 Maths 2017 | Pure Maths | Sequences and Series | Geometric Sequences |

I.B. Higher Level | 1 | Sequences and series | Geometric series |

I.B. Standard Level | 1 | Sequences and series | Geometric series |

Methods (UK) | M7 | Sequences and series | Geometric series |

I.B. (MSSL) | 2 | Sequences and series | Geometric series |

OCR A-Level (UK - Pre-2017) | C2 | Sequences and series | Geometric series |

OCR A2 Maths 2017 | Pure Maths | Arithmetic and Geometric Sequences | Geometric Sequences |

OCR MEI A2 Maths 2017 | Pure Maths | Arithmetic and Geometric Sequences | Geometric Sequences |

OCR-MEI A-Level (UK - Pre-2017) | C2 | Sequences and series | Geometric series |

Pre-Calculus (US) | E3 | Sequences and series | Geometric series |

Pre-U A-Level (UK) | 3 | Sequences and series | Geometric series |

Scottish Advanced Highers | M2 | Sequences and series | Geometric series |

Scottish (Highers + Advanced) | AM2 | Sequences and series | Geometric series |

Universal (all site questions) | S | Sequences and series | Geometric series |

WJEC A-Level (Wales) | C2 | Sequences and series | Geometric series |