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 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 × 5 - 2 = 30 - 2 = 28.

Let's try some questions now.