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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}

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## 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:

SyllabusModuleSectionTopic
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
D Sequences and SeriesD5 Geometric SequencesGeometric Sequences
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