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Fibonacci Quest

A number of self marking quizzes based on the fascinating Fibonacci Sequence.

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Description Help More Sequences

This is level 3; Find algebraic expressions for each term of a Fibonacci sequence.

x,   y,   x+y,     , , , , , , ,
  Correct Wrong Correct Wrong Correct Wrong Correct Wrong Correct Wrong Correct Wrong Correct Wrong
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If the first term of a Fibonacci sequence is represented by x and the second term is y, the third term will be these first two terms added together giving x+y

Fill in the gaps above showing more terms of the Fibonacci sequence in terms of x and y.

There is a magic trick that can be performed if you understand the algebraic expressions for the Fibonacci sequence. The trick is called Fibbing about Adding!

Fibonacci Spiral GeoGebra

The Fibonacci spiral is created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling pattern where the squares have sides equal to the terms of the Fibonacci sequence.

This is Fibonacci Quest level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 Level 6

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.

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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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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:

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Description of Levels

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Level 1 - Continue the basic Fibonacci sequence

Level 2 - Continue the Fibonacci sequence in reverse

Level 3 - Find algebraic expressions for each term of a Fibonacci sequence

Level 4 - Finding the ratio of two successive numbers in Fibonacci's sequence

Level 5 - Investigate the highest common factor of every nth term of the Fibonacci sequence.

Level 6 - Finding missing terms from Fibonacci-type sequences.

The Magic of Fibonacci Numbers

Arthur Benjamin gives a TED talk on Fibonacci numbers.

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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