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Arithmetic Sequences

An exercise on linear sequences including finding an expression for the nth term and the sum of n terms.

Matchsticks Level 1 Level 2 Level 3 Level 4 Exam-Style Description Help More

This is level 1: find the next term of these linear sequences. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

4, 8, 12, 16, 20, 24, ...

Correct Wrong

2, 5, 8, 11, 14, 17, ...

Correct Wrong

6, 9, 12, 15, 18, 21, ...

Correct Wrong

4, 9, 14, 19, 24, 29, ...

Correct Wrong

7, 14, 21, 28, 35, 42, ...

Correct Wrong

8, 17.5, 27, 36.5, 46, 55.5, ...

Correct Wrong

7, 14.2, 21.4, 28.6, 35.8, 43, ...

Correct Wrong

11, 3, -5, -13, -21, -29, ...

Correct Wrong

-9, 1, 11, 21, 31, 41, ...

Correct Wrong

-10, -20, -30, -40, -50, -60, ...

Correct Wrong

This is Arithmetic Sequences level 1. You can also try:
Matchsticks Level 2 Level 3 Level 4 Geometric Sequences


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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Sarah Murphy, Teacher

Monday, February 26, 2024

"For level 2 of this activity, it's not clear how the answer needs to be entered. In the help notes they make reference of things with subscripts. Guidance of the format to enter for the answer is needed.

[Transum: Thanks for your feedback Sarah. For level 2 the answer should be typed in as an expression (no equals sign) in its simplest form. For example, an answer might be '7n' or '5n-2'. No subscripts are required.]"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


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Description of Levels



Matchsticks - A beginner's exercise that lets you see how a sequence is structured.

Level 1 - Find the next term of these linear sequences

Level 2 - Find the nth term of these linear sequences

Level 3 - Find a given term of these linear sequences

Level 4 - Mixed questions about linear sequences and their sums

Missing Terms - Find the missing terms of arithmetic, geometric and Fibonacci-type sequences in this self marking quiz.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Geometric Sequences - A similar exercise on geometric sequences.

Sigma - Practise using the sigma notation to find the sum of various number series.

More on this topic including lesson Starters, visual aids and investigations.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Arithmetic Sequences

Here is a reminder of some facts that may help you answering the questions in this exercise.

An arithmetic sequence, sometimes called an arithmetic progression, is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 8, 11, 14, 17, 20, 23, . . . is an arithmetic sequence with common difference of 3.

The first term of the sequence can be written as u1

The nth term of the sequence can be written as un

The common difference is usually written as d

The formula for finding the nth term is un=u1+(n-1)d

The formula for finding the sum of n terms is Sn=½n(2u1+(n-1)d)

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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