\displaystyle 3 +2	\displaystyle =	\displaystyle 5	Add 2 to 3
\displaystyle 5+2	\displaystyle =	\displaystyle 7	Add 2 to 5
\displaystyle 7+2	\displaystyle =	\displaystyle 9	Add 2 to 7
\displaystyle 9+2	\displaystyle =	\displaystyle 11	Add 2 to 9

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.

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Examples

Example 2

Complete the pattern:

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.

\displaystyle 7-5

\displaystyle =

\displaystyle 2

Subtract two numbers

Add 2 to each number to complete the pattern.

\displaystyle 9+2	\displaystyle =	\displaystyle 11	Add 2 to 9
\displaystyle 11+2	\displaystyle =	\displaystyle 13	Add 2 to 11
\displaystyle 13+2	\displaystyle =	\displaystyle 15	Add 2 to 13

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

What is the rule for filling in the pattern?

Add 2

Add 3

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?

Outcomes

AC9M3N07

follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns

8.04 Find the rule

Ideas

Are you ready?

Examples

Example 1

Find the rule

Examples

Example 2

Outcomes

AC9M3N07

What is Mathspace

About Mathspace