Fibonacci QuestA number of self marking quizzes based on the fascinating Fibonacci Sequence. 
This is level 2; Continue the Fibonacci sequence in reverse.
Imagine if the Fibonacci sequence was written backwards!
Can you fill in the gaps to show more terms of the Fibonacci sequence in reverse?
Count the number of spirals of the bracts on a pineapple. The answer will be a fibonacci number! There are three different sets of spirals and the number in each set is a different fibonacci number.
The following was seen in the Grange Academy Mathematics Department Newsletter (@aap03102).
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...
Every third term is divisible by 2:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...
Every fourth term is divisible by 3:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...
Every fifth term is divisible by 5:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...
Every sixth term is divisible by 8:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...
If you follow this pattern on, the divisibility numbers actually generate the Fibonacci Sequence!
This is Fibonacci Quest level 2. You can also try:
Level 1
Level 3
Level 4
Level 5
Level 6
InstructionsTry 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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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 Fibonaccitype sequences.
More Sequences including lesson Starters, visual aids, investigations and selfmarking 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.
See the National Curriculum page for links to related online activities and resources.
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 doubleclick the 'Check' button to make it float at the bottom of your screen.
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.
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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 rightangled 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."