# Arithmetic Sequences

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

##### MatchsticksLevel 1Level 2Level 3Level 4Exam-StyleDescriptionHelpMore

This is level 2: find the nth 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, 10, 16, 22, 28, 34, ... 3, 6, 9, 12, 15, 18, ... 4, 11, 18, 25, 32, 39, ... 5, 12, 19, 26, 33, 40, ... 7, 14, 21, 28, 35, 42, ... 6, -2, -10, -18, -26, -34, ... 7, -1, -9, -17, -25, -33, ... 10, 23, 36, 49, 62, 75, ... -10, 3, 16, 29, 42, 55, ... -13, 0, 13, 26, 39, 52, ...
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This is Arithmetic Sequences level 2. You can also try:
Matchsticks Level 1 Level 3 Level 4 Geometric Sequences

## Instructions

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.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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Can you get your car out of the very crowded car park by moving other cars forwards or backwards? There are five levels of increasing difficulty and the interactive interface makes this a fun problem solving exercise.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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© Transum Mathematics :: This activity can be found online at:
www.transum.org/Maths/Exercise/Sequences/Arithmetic.asp?Level=2

## Description of Levels

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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.

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

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.

## 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)

The excellent video above is from Corbettmaths.

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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