Sequence pattern 1 - Consistent difference

The easiest pattern in a sequence to find is when there is a consistent difference between the terms, either addition or subtraction.

They also call this a linear sequence.

In this example 2 is being added to each number so the consistent difference is 2

This is one of the most famous linear sequences

Linear as in draw one line between each

and in this case, we get a difference of 2.

Example 1

Find the differences between each number below:

`7`, `11`, `15` and `19`

First, see if there is a consistent difference between each number.

The consistent difference in this example is plus 4

Answer = 4

Example 2

Find the difference between each number below:

`0`, `-3`, `-6`, `-9`, `-12`

First, see if there is a consistent difference between each term.

Consistent difference here is minus 3

Answer = `-3`

Example 3

Find the difference between

`2`, `9`, `16`, `23`, `30`

First, see if there is a consistent difference between each term.

Consistent difference here is 7

Answer = `7`

Example 4

Find the differences between each number below:

`0`, `-4`, `-8`, `-12`, `-16`

First, see if there is a consistent difference

Consistent difference here is minis 4

Answer is `-4`

Example 5

Find the difference between each number below:

`-1/2`, `-1/4`, `0`, `1/4`, `1/2`

First, see if there is a consistent difference.

Consistent difference here is a quarter

Answer is `1/4`

Example 6

Find the difference between each number below:

`-1.1`, `-1.5`, `-1.9`, `-2.3`, `-2.7`

First, see if there is a consistent difference

Consistent difference here is minus 0.4

Answer = `-0.4`