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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

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


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.

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.

Please contact me if you have any suggestions or questions.

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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?

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK:

"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

Featured Activity



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.


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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.


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:

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



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.