Arithmetic Sequences (the Nth Term)

In an Arithmetic sequence like this:

 

4, 10, 16, 22, 28, 34 ...

 

the nth term is found as follows:

 

Step 1

Find the common difference between the terms

Here it is 6.

 

Step 2

The common difference is the coefficient (this just means the number in front.) of n

Here we get 6n

 

Step 3

Compare this to the actual sequence and adjust the formula by adding or subtracting a fixed number.

Here 6n would give us the terms 6, 12, 18, 24, 30 etc.... which is 2 more than our sequence of 4, 10, 16, 22, 28 etc.

So we must subtract 2.

So the nth term is 6n - 2

 

We can test this by putting in n = 5 to check that the 5th term is really 28.

It is, because 6 x 5 - 2 = 30 - 2 = 28

 

For this worksheet, It is important that you do not put spaces in your answer (For example, you would need to put in 5n-3 instead of 5n  -  3. If you put in spaces, the system will mark it as wrong.