### Describe the number of chairs needed with a formula.

This exercise will help you interpret mathematical relationships both algebraically and geometrically.

##### Level 1Level 2Exam-StyleDescriptionHelpMore Sequences

This is level 2; Linear sequences of chairs and tables.

 Number of Tables: Number of Chairs: 1 2 3 4 ... n ... 95 ... ...
 Number of Tables: Number of Chairs: 1 2 3 4 ... n ... 93 ... ...
 Number of Tables: Number of Chairs: 1 2 3 4 ... n ... 96 ... ...
 Number of Tables: Number of Chairs: 1 2 3 4 ... n ... 128 ... ...
 Number of Tables: Number of Chairs: 1 2 3 4 ... n ... 115 ... ...
Check

This is Seating Arrangements level 2. You can also try:
Level 1

## 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.

## More Activities:

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?

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:

"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

#### Pentransum

Answer multiple choice questions about basic mathematical ideas. If you get a number of questions correct you will be invited to post a question of your own. The bank of questions grows larger every day.

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

Subscribe

## 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.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## 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:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

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.

For Students:

For All:

## Description of Levels

Close

Level 1 - Linear sequences of matchstick patterns

Level 2 - Linear sequences of chairs and tables

When you have done those why not progress to:

Sequences Level 2 - Find the nth term of linear sequences

Sequences Level 3 - Find a given term of linear sequences

Sequences Level 4 - Mixed questions about geometric sequences

Sequences Level 5 - Mixed questions about sequences and series

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.

## Example

Filling in the first three cells of the table is simply a case of counting the number of matches needed to make the first three patterns.

You may have noticed by now how many additional matches it takes to make the next pattern in the sequence. It's the same each time you change one pattern to the next. In this case it is 5.

The numbers in the table go up by 5 each time just like the five times table. The general term of the five times table is 5n where n are the counting numbers (1, 2, 3, 4...).

The first four terms of the five times table are 5, 10, 15 and 20.

The numbers in our table are each one more than that so the nth term is 5n+1. This formula can be used to work out the 92nd term of the sequence i.e. 5x92+1 = 461

###### 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.

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.

Close