Arithmetic Sequences (the nth Term)
• Introduction

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 x 5 - 2 = 30 - 2 = 28

• Question 1

Work out the nth term in this sequence:

1, 2, 3, 4, 5, 6 ...

• Question 2

Work out the nth term in this sequence:

2, 4, 6, 8, 10, 12 ...

• Question 3

Work out the nth term in this sequence:

5, 10, 15, 20, 25, 30 ...

• Question 4

Work out the nth term in this sequence:

2, 3, 4, 5, 6, 7 ...

• Question 5

Work out the nth term in this sequence:

1, 3, 5, 7, 9, 11  ...

• Question 6

Work out the nth term in this sequence:

1, 4, 7, 10, 13, 16 ...

• Question 7

Work out the nth term in this sequence:

4, 7, 10, 13, 16, 19 ...

• Question 8

Work out the nth term in this sequence:

1, 6, 11, 16, 21, 26 ...

• Question 9

Work out the nth term in this sequence:

10, 17, 24, 31, 38, 45 ...

• Question 10