### Describe the sequences of matchstick patterns with a formula.

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

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

This is level 1; Linear sequences of matchstick patterns.

 Pattern 1 Pattern 2 Pattern 3 Pattern 4
 Pattern Number: Number of Matchsticks: 1 2 3 4 ... n ... 99 ... ...
 Pattern Number: Number of Matchsticks: 1 2 3 4 ... n ... 78 ... ...
 Pattern Number: Number of Matchsticks: 1 2 3 4 ... n ... 149 ... ...
 Pattern Number: Number of Matchsticks: 1 2 3 4 ... n ... 100 ... ...
 Pattern Number: Number of Matchsticks: 1 2 3 4 ... n ... 109 ... ...
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This is Matchstick Patterns level 1. You can also try:
Level 2

## 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.

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## Teachers

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## Description of Levels

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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

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## 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.

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