Patterns are everywhere in the world.

### Architecture

### Indigenous artwork

### Nature

Did you know that mathematics is often described as the study of patterns!

Well the patterns we have studied already include the ways that numbers are written, the digits that are used and the order they are used, place value columns, decimals, fractions, patterns of the four operations and now we will look at some more formal patterns involving the sequence of numbers.

## Additive and Subtractive Sequences

Number sequences can use addition like this one 2, 4, 6, 8, 10. All terms have the same (constant) amount added each time.

Sequences like 20, 15, 10... and 64, 57, 50, 43 are subtractive sequences, all terms decrease by a constant amount.

## Multiplicative and Division Sequences

Patterns can also be formed by multiplying or dividing by a constant amount each time:

$2$2, $4$4,$8$8, $16$16 - doubling (or multiplying by $2$2) each time.

$3$3, $30$30, $300$300, $3000$3000 - multiplying by $10$10 each step.

$81$81, $9$9, $1$1, $\frac{1}{9}$19 - dividing by $9$9 each step, (could also be thought of as multiplying by $\frac{1}{9}$19).

$1$1, $\frac{1}{2}$12, $\frac{1}{4}$14, $\frac{1}{8}$18 - dividing by $2$2 each step, (could also be thought of as multiplying by $\frac{1}{2}$12)

#### Example 1

Using the instructions given, write the first 4 terms in the sequence.

Start with 11, and multiply by 3 each time.

#### Example 2

Find the next number in the sequence.

#### Example 3

Using the instructions given, write the first 4 terms in the sequence.

Start with 7, and each time, add 10 and multiply by 4.