# Understand Linear Sequences (term-to-term rules)

In this worksheet, students will find term-to-term rules for linear sequences and apply these to find next or specified terms.

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Algebra

Curriculum subtopic:   Sequences

Difficulty level:

#### Worksheet Overview

A linear sequence has a difference between the terms that is the same each time, so it increases or decreases by equal steps.

This means we can continue such a sequence using a term-to-term rule.

e.g. Find the 10th number in this sequence:

2, 6, 10, 14, ...

If we look at the differences between the terms, each term is 4 more than the previous.

So the term-to-term rule is + 4.

If we continue this sequence, it would become:

2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, etc...

The tenth term is 38.

In this activity, we will find term-to-term rules for linear sequences and apply these to find next or specified terms.

You should not use a calculator for this activity, but rather practise your mental arithmetic skills.

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