# Sequence pattern 2 - Consistent difference between differences

The next easiest pattern in a sequence to find is to look for a consistent difference between differences.

They also call this a quadratic sequence. (For a definition of quadratics see our mammoth memory quadratics section)

There is a consistent difference between the differences of the original sequence and this is 2.

Quadratic `=x^2` Involved here (something to the power of 2)

**Example 1**

Find the pattern in the following sequence:

`7`, `9`, `13`, `19`, `27`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `2`

** Example 2**

Find the pattern in the following sequence:

`5`, `12`, `25`, `44`, `69`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `6`

**Example 3**

Find the pattern in the following sequence:

`-3`, `3`, `13`, `27`, `45`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `4`

**Example 4**

Find the pattern in the following sequence:

`0`, `0`, `2`, `6`, `12`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `4`

**Example 5**

Find the pattern in the following sequence:

`1`, `11`, `20`, `28`, `35`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `-1`

# Sequence pattern 2 - Consistent difference between differences

The next easiest pattern in a sequence to find is to look for a consistent difference between differences.

They also call this a quadratic sequence. (For a definition of quadratics see our mammoth memory quadratics section)

There is a consistent difference between the differences of the original sequence and this is 2.

Quadratic `=x^2` Involved here (something to the power of 2)

**Example 1**

Find the pattern in the following sequence:

`7`, `9`, `13`, `19`, `27`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `2`

** Example 2**

Find the pattern in the following sequence:

`5`, `12`, `25`, `44`, `69`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `6`

**Example 3**

Find the pattern in the following sequence:

`-3`, `3`, `13`, `27`, `45`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `4`

**Example 4**

Find the pattern in the following sequence:

`0`, `0`, `2`, `6`, `12`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `4`

**Example 5**

Find the pattern in the following sequence:

`1`, `11`, `20`, `28`, `35`

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

There is not but now see if there is a constant difference between differences.

We can see that there is.

Answer = `-1`