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Arithmetic Sequences (the nth Term)

In this worksheet, students find the nth term in arithmetic sequences.

'Arithmetic Sequences (the nth Term)' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use Sequences to Find the nth Term

Difficulty level:  

Worksheet Overview

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.

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