Mammoth Memory

Next few terms in a sequence - consistent difference between differences

In order to work out the next few terms in a sequence when there is a consistent difference between difference follow the examples below:

To find the full nth term we need to extend the sequence 

 

Example 1

In the following sequence what are the next two sets of numbers?

`2`,   `4`,   `8`,   `14`,   `22`

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

Find the differences between numbers of a sequence 

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

Then find the differences of differences the differences need to be consistent for it to work

There is! Great!

To find the next two sets of numbers extend the sequence in the same pattern in stages as follows:

First the bottom line.

Now extend the bottom line of numbers so you can add some numbers on the middle line

Then the middle line.

Now add those middle line numbers

Finally the sequence (the top line)

Now you can work out the next numbers to be added in the main sequence

Answer: The next two in the sequence are `32`  and `44`

 

Example 2

In the following sequence what are the next two sets of numbers?

`6`,   `13`,   `26`,   `45`,   `70`

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

Find the differences between numbers of a sequence 

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

Then find the differences of differences the differences need to be consistent for it to work 

There is! Great!

To find the next two sets of numbers extend the sequence in the same pattern in stages as follows:

First the bottom line.

Now extend the bottom line of numbers so you can add some numbers on the middle line

Then the middle line.

Now add those middle line numbers

Finally the sequence (the top line)

Now you can work out the next numbers to be added in the main sequence

Answer: The next two in the sequence are `101`  and `138`

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