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```Date: 10/10/2002 at 23:29:56
From: Kate

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

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/
```
Associated Topics:
High School Fibonacci Sequence/Golden Ratio

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