SOLUTION: What are the next three terms in each sequence? 9,109,209,309,409 1/2, 1/2,3/8, 1/4, 5/32

9, 109, 209, 309, 409

Consider the first term 9, to be written 009, then we have:

009, 109, 209, 309, 409

Then the last two digits of them all are 09 and the
first digits go 0,1,2,3,4.  So the next three are, 
of course 5,6,7.  Putting 09 after them we get:

009, 109, 209, 309, 409, 509, 607, 709.

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, , , , 

We notice that all the denominators are powers of 2.

We notice that the 1st term has a numerator of 1 and a denominator of .
We notice that the 3rd term has a numerator of 3 and a denominator of .
We notice that the 5th term has a numerator of 5 and a denominator of .

So the 1st, 3rd, and 5th terms are , , and  

That's a pattern with the 3 odd-numbered terms, so for the odd-numbered
terms, we have the pattern  where n is odd 1, 3, and 5.

So we wonder if the two even numbered terms might follow
the same pattern. 

They would if the 2nd term, , were , 
and the 4th term, , were .  Sure enough
they are, since  =  = , and
 =  = 

So we have the pattern.  The nth term is 

So the 6th term is  =  = ,
the 7th term is  = , and
the 8th term is  =  = 

, , , , , , , .

Edwin