Question 1057206: Find the next number in the following series 3/4,1,9/8,6/5,5/4,9/7,?
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! Beginning with the second term, we find the ratios of the each term to the one preceding it.
   
  
  
  
  
The numerators of the ratios go 4,9,16,25,36, so the numerator
of the next ratio will be 49, since they are successive squares.
The denominators of the ratios go 3,8,15,24,35.
Beginning with the second denominator, we find the difference between
each denominator and the denominator preceding it.
8-3 = 5
15-8 = 7
24-15 = 9
35-24 = 11
Those difference are the odd numbers 5,7,9,11, so the next difference
will be 13. Therefore the next denominator of the next ratio will be
35+13 or 48.
Therefore
 
So we multiply both sides by 
 
Edwin
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