A linear sequence (also known as arithmetic sequence) is a sequence of numbers that have a constant difference, for example 2, 5, 8, 11, ... have a constant difference of 3 are so make a linear sequence. The nth term of any linear sequence with be of the form nth term =an+b, a linear function.

Any sequence that does not have a constant difference is called a non-linear sequence, for example 1, 4, 9, 16... or 1, 3, 6, 10,...

Any sequence that does not have a constant difference is called a non-linear sequence, for example 1, 4, 9, 16... or 1, 3, 6, 10,...

## Software/Applets used on this page

## Glossary

### constant

a value in a formula or equation that cannot change.

### function

A rule that connects one value in one set with one and only one value in another set.

### linear

Straight, not curved. A linear equation is of the first degree, for example y = 2x+1.

### sequence

a number pattern in a definite order following a certain rule

### union

The union of two sets A and B is the set containing all the elements of A and B.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

GCSE Foundation (UK) | Algebra | Sequences | Non-linear sequences | - |

GCSE Higher (UK) | Algebra | Sequences | Non-linear sequences | - |

Universal (all site questions) | S | Sequences | Non-linear sequences | - |

Edexcel GCSE (9-1) Foundation (UK) | A: Sequences | A24: Common Sequences | Recognising Sequences | - |

Edexcel GCSE (9-1) Higher (UK) | A: Sequences | A24: Further Sequences, Including Surds | Non-Linear Sequences | - |

OCR GCSE (9-1) Foundation (UK) | 6: Algebra | 6.06a: Generate Terms of a Sequence | Non-Linear Sequences | - |

AQA GCSE (9-1) Foundation (UK) | A: Sequences | A24: Common Sequences | Recognising Sequences | - |

AQA GCSE (9-1) Higher (UK) | A: Sequences | A24: Further Sequences, Including Surds | Non-Linear Sequences | - |

CIE IGCSE (9-1) Maths (0626 UK) | 2 Algebra and Graphs | B2.7 Sequences | Recognising Sequences | - |