# Fibonacci Quest

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

##### Level 1Level 2Level 3Level 4Level 5Level 6DescriptionHelpMore Sequences

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

 x,   y,   x+y, , , , , , , ,
Check

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!

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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## 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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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.

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

Transum,

Tuesday, May 26, 2020

"November 23 is celebrated as Fibonacci day because when the date is written in the mm/dd format (11/23), the digits in the date form a Fibonacci sequence: 1,1,2,3."

Leonardo, Pisa

Sunday, July 3, 2022

"I’ve written yet another book on the Fibonacci sequence. It’s as big as the previous two books put together!"

Transum,

Friday, November 10, 2023

"I am writing this on Friday, 10th November 2023. I have noticed that today must be some kind of special Fibonacci day because each of the digits in the date, starting with the third, is the sum of the previous two.

"

Kyle Evans, A Year In Numbers

Monday, June 17, 2024

"Terms in the Fibonacci sequence can be used to create a Pythagorean triple (that's three numbers that could represent the lengths of the sides of a right-angled triangle). Here’s how you do it. Take four consecutive Fibonacci terms. Multiply the smallest and largest numbers. Multiply the two middle numbers, but then double the product. Square the two middle numbers and then add."

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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.

More Sequences including lesson Starters, visual aids, investigations and self-marking exercises.

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.

## 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. You can double-click the 'Check' button to make it float at the bottom of your screen.

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