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## 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} You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

## 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.

Full Glossary List

## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AP Calculus BC (USA)5Sequences and seriesGeometric series-
AQA A-Level (UK - Pre-2017)C2Sequences and seriesGeometric series-
AQA A2 Maths 2017Pure MathsSequences and SeriesGeometric Sequences-
AQA AS/A2 Maths 2017Pure MathsSequences and SeriesGeometric Sequences-
CBSE XI (India)AlgebraSequence and SeriesGeometric progression-
CCEA A-Level (NI)C2Sequences and seriesGeometric series-
CIE A-Level (UK)P1Sequences and seriesGeometric series-
Edexcel A-Level (UK - Pre-2017)C2Sequences and seriesGeometric series-
Edexcel A2 Maths 2017Pure MathsSequences and SeriesGeometric Sequences-
Edexcel AS/A2 Maths 2017Pure MathsSequences and SeriesGeometric Sequences-
I.B. Higher Level1Sequences and seriesGeometric series-
I.B. Standard Level1Sequences and seriesGeometric series-
Methods (UK)M7Sequences and seriesGeometric series-
I.B. (MSSL)2Sequences and seriesGeometric series-
OCR A-Level (UK - Pre-2017)C2Sequences and seriesGeometric series-
OCR A2 Maths 2017Pure MathsArithmetic and Geometric SequencesGeometric Sequences-
OCR MEI A2 Maths 2017Pure MathsArithmetic and Geometric SequencesGeometric Sequences-
OCR-MEI A-Level (UK - Pre-2017)C2Sequences and seriesGeometric series-
Pre-Calculus (US)E3Sequences and seriesGeometric series-
Pre-U A-Level (UK)3Sequences and seriesGeometric series-
Scottish Advanced HighersM2Sequences and seriesGeometric series-
Scottish (Highers + Advanced)AM2Sequences and seriesGeometric series-
Universal (all site questions)SSequences and seriesGeometric series-
WJEC A-Level (Wales)C2Sequences and seriesGeometric series-