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

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*.## Software/Applets used on this page

## 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.

## This question appears in the following syllabi:

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

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

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

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

CBSE X (India) | Algebra | Arithmetic Progressions | Finding nth term |

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

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

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

D Sequences and Series | D4 Arithmetic Sequences | Arithmetic Sequences | |

Edexcel A-Level (UK - Pre-2017) | C1 | Sequences and series | Arithmetic series |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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