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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:

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