Home > Subjects > Mathematics > Level 1 > 1.3 Tables, equations and graphs (AS91028) > Subject content > Linear patterns

- Subject: Mathematics
- AS: 91028
- Level: 1
- Credits: 4
- External

## Mathematics 1.3 Investigate relationships between tables, equations and graphs

### Linear patterns

In a sequence of numbers, each number is called a term.

For the sequence 2, 5, 8, 11, …

The first term is 2, the second term is 5, etc.

The gap between the numbers is called the difference.

In this example the difference is 3, because 5 – 2 = 8 – 5 = 11 - 8 = 3.

Linear patterns have the same difference between the terms.

To find the rule, look for a relationship between the number of the term and the term itself. The rule is the same for each term.

In this example: 2 = 3 x 1 – 1, 5 = 3 x 2 – 1 and 8 = 3 x 3 – 1,

so the rule is t = 3 x n – 1 or t = 3n - 1

#### Problem

For the sequence of diagrams below, find the rule for the number of white tiles (w) in terms of the number of black tiles (b).

#### Answer

Number of black tiles (b) | Number of white tiles (w) | Difference |
---|---|---|

1 | 8 | |

3 | 13 | 5 |

4 | 18 | 5 |

4 |

The difference between each term is 5. (13 - 8 = 5, 18 - 13 = 5, etc)

The difference (5) is the multiplier, so the rule must be w = 5b + ?.

To work out the ?, substitute in b = 1 and w = 8 from the first line of the table

8 = 5 x 1 + ?.

The constant term must be 3.

Giving the rule as w = 5b + 3.

For more information see:

Constructing a formula

Finding the next number in a sequence

Recognising sequences

Sequences - Finding a Rule