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In order to work with sequences and series, there are formulae that you should memorise. Do you know them? When you think you know, move the mouse over the question mark to check.

Here are some examples of arithmetic series:
0, 2, 4, 6, 8, 10, 12, ...
13, 10, 7, 4, 1, -2, -5, ...
0.7, 1.4, 2.1, 2.8, 3.5, 4.2, ...
In general an arithmetic series has first term a and common difference d.
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Software/Applets used on this page

jsMath
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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

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.

work

Equal to F x s, where F is the force in Newtons and s is the distance travelled and is measured in Joules.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)C2Sequences and seriesArithmetic series-
AQA A2 Maths 2017Pure MathsSequences and SeriesArithmetic Sequences-
AQA AS/A2 Maths 2017Pure MathsSequences and SeriesArithmetic Sequences-
CBSE X (India)AlgebraArithmetic ProgressionsFinding nth term-
CBSE XI (India)AlgebraSequence and SeriesArithmetic progression-
CCEA A-Level (NI)C2Sequences and seriesArithmetic series-
CIE A-Level (UK)P1Sequences and seriesArithmetic series-
Edexcel A-Level (UK - Pre-2017)C1Sequences and seriesArithmetic series-
Edexcel A2 Maths 2017Pure MathsSequences and SeriesArithmetic Sequences-
Edexcel AS/A2 Maths 2017Pure MathsSequences and SeriesArithmetic Sequences-
I.B. Higher Level1Sequences and seriesArithmetic series-
I.B. Standard Level1Sequences and seriesArithmetic series-
Methods (UK)M7Sequences and seriesArithmetic series-
I.B. (MSSL)2Sequences and seriesArithmetic series-
OCR A-Level (UK - Pre-2017)C2Sequences and seriesArithmetic series-
OCR A2 Maths 2017Pure MathsArithmetic and Geometric SequencesArithmetic Sequences-
OCR MEI A2 Maths 2017Pure MathsArithmetic and Geometric SequencesArithmetic Sequences-
OCR-MEI A-Level (UK - Pre-2017)C2Sequences and seriesArithmetic series-
Pre-Calculus (US)E3Sequences and seriesArithmetic series-
Pre-U A-Level (UK)3Sequences and seriesArithmetic series-
Scottish Advanced HighersM2Sequences and seriesArithmetic series-
Scottish (Highers + Advanced)AM2Sequences and seriesArithmetic series-
Universal (all site questions)SSequences and seriesArithmetic series-
WJEC A-Level (Wales)C2Sequences and seriesArithmetic series-