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2. Fibonnacci Numbers

Fibonacci numbers are formed by starting with any two whole numbers and calculating each number in the sequence as the sum of the two previous numbers. So if we start with 0 and 1 we get:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on

You don't have to start with 0 and 1. Pick any two starting numbers and write down the first ten numbers of the sequence. Now add those ten numbers. Now multiply the seventh number in the sequence by 11. What do you notice? Can you demonstrate why this is true?
 

Scroll down the page for the answer.


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

The sum of the first ten numbers is equal to the seventh number multiplied by 11. The table shows the first 10 numbers, assuming we start with, say, a and b

1   a
2   b
3   a + b
4   a + 2b
5   2a + 3b
6   3a + 5b
7   5a + 8b
8   8a + 13b
9   13a + 21b
10   21a + 34b

Adding the 10 numbers we have...
 
55a + 88b

...which is equal to the 7th number, 5a + 8b, multiplied by 11
 

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