Find the nth Term in Arithmetic Sequences

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.