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 = $-0.4$