Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Arithmetic Sequences (the Nth Term)

In this worksheet, students find the Nth term in simple linear sequences.

'Arithmetic Sequences (the Nth Term)' worksheet

Key stage:  KS 2

Year:  Year 5 11+ worksheets

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Equations and Algebra

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 (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.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Try an activity or get started for free