Fibonacci Addition TrickDate: 10/10/2002 at 23:29:56 From: Kate Subject: Fibonacci addition trick When you write out 10 numbers in a Fibonacci sequence, multiplying the seventh number by 11 gives the total sum of all 10 numbers: 2,3,5,8,13,21,34,55,89,144 the sum is 374 and 34 x 11 = 374 I don't understand why this works for every Fibonacci sequence. Can you help me? Date: 10/11/2002 at 02:44:39 From: Doctor Ian Subject: Re: Fibonacci addition trick Hi Kate, That's a pretty interesting trick! Usually the way to explain something like this is to try it with variables, instead of with numbers. Suppose we start the sequence with the numbers a and b. Then the first 10 terms are 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 Now, what's the sum? It's 55a + 88b And what's the seventh term? It's 5a + 8b Kind of neat, isn't it? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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