 # 12.01 Finding rules

Lesson

## Ideas

Can you continue a pattern?

### Examples

#### Example 1

Create a pattern by adding 2 each time.

3, \,⬚, \, ⬚, \,⬚, \,⬚

Worked Solution
Create a strategy

Add 2 to the last given value to complete the pattern.

Apply the idea

Add 2 to the last number to complete the pattern.

The complete pattern is 3,\, 5,\, 7,\, 9,\,11 .

## Find the rule

You may not have realised but patterns have a rule that you follow to work out the next number, Let's look at how to write rules to describe patterns.

### Examples

#### Example 2

Complete the pattern:

a

5,\,7,\,9,\,⬚,\,⬚,\,⬚

Worked Solution
Create a strategy

Find how much the numbers are increasing by each time and add that to the last given value to complete the pattern.

Apply the idea

To work out how much the numbers are increasing by each time, you can count up or find the difference between two numbers.

Add 2 to each number to complete the pattern.

The complete pattern is 5,\,7,\,9,\,11,\,13,\,15.

b

What is the rule for filling in the pattern?

A
B
Worked Solution
Create a strategy

What number did we add by in part (a)?

Apply the idea

The numbers are increasing by 2\,, this means that the rule of filling in the pattern is add 2.

So, the correct option is A.

Idea summary

Think about how the numbers are changing to work out the rule. Are the numbers getting bigger or smaller, and by how many?