SOLUTION: 3/20, 3/10, 3/8, 3/4, 3/2, 3,...,....,....,......

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Question 976883: 3/20, 3/10, 3/8, 3/4, 3/2, 3,...,....,....,......
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
3/20, 3/10, 3/8, 3/4, 3/2, 3/1,...,....,....,......

The sequence of numerators is simply "all 3's":

3, 3, 3, 3, 3, 3,...

We look at the sequence of denominators:

20, 10, 8, 4, 2, 1, ?, ?, ?, ?

Start with 20

Divide by 2, get 10
Subtract 2, get 8
Divide by 2, get 4
Subtract 2, get 2

To continue the pattern of dividing by 2, then subtracting 2, over and over, 

Divide by 2, get 1
Subtract 2, get -1
Divide by 2, get -1/2
Subtract 2, get -1/2 - 2 = -1/2 - 4/2 = -5/2
Divide by 2, get -5/4
So the sequence of denominators is

20, 10, 8, 4, 2, 1, -1, -1/2, -5/2, -5/4

The sequence of numerators is "all 3's", so the sequence is

3/20, 3/10, 3/8, 3/4, 3/2, 3/1, 3/(-1), 3/(-1/2), 3/(-5/2), 3/(-5/4), ...

Simplifying:

3/20, 3/10, 3/8, 3/4, 3/2, 3, -3, -6, -6/5, -12/5, ...

Edwin
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