# Generate patterns from rules

Lesson

## Following a rule

A rule for a number pattern sets out what we need to do to move from one number to the next. Once we have a starting point, we are able to do what the rule says, and work out the next number. From there, we can continue to follow the rule to create our pattern of numbers.

Here's what the end result might look like for a particular pattern:

3 10 17 24

Can you work out what rule is being used above?

In Video 1, we're about to make a pattern, using a rule that tells us what we need to do.

## Two steps

If our rule has more than one operator, we need to use two steps to work out the next number in our pattern. It's similar to solving two -step problems but we don't have to work out what to solve first! Let's see how we break this into two parts to continue the pattern in Video 2.

## Decimals

In Video 3, we use a written pattern to follow a rule, with some tips to add at each step. We also look at how to follow a rule when decimals are involved. It's short and sharp, take a look!

#### Worked examples

##### Question 1

Create a pattern using the rule of adding $7$7 to the previous number.

1.  $+$+$7$7 $+$+$7$7 $\nearrow$↗ $\searrow$↘ $\nearrow$↗ $\searrow$↘ $4$4 $\editable{}$ $\editable{}$

##### Question 2

Create a pattern using the rule of multiplying the previous number by $3$3, and then adding $2$2 to the result.

1.  multiply by $3$3 and then add $2$2 multiply by $3$3 and then add $2$2 $\nearrow$↗ $\searrow$↘ $\nearrow$↗ $\searrow$↘ $7$7 $\editable{}$ $\editable{}$

##### Question 3

A rule is used to generate a pattern. The rule is to add $8$8 to the previous number.

Write the next three numbers in the sequence if the starting number is:

1. $1,\editable{},\editable{},\editable{}$1,,, $\dots$

2. $9,\editable{},\editable{},\editable{}$9,,, $\ldots$

3. $2.6,\editable{},\editable{},\editable{}$2.6,,, $\ldots$