text: # geometric sequence. Determine the numbers a, b if 3 ,a ,b , 24 is a geometric sequence.
  
  The consecutive terms of a geometric sequence have a common ratio.
  
  We have the sequence given by 3 ,a ,b , 24
  
  24/b = b/a = a/3
  
  => 24a = b^2 or a = b^2/24
  
  substitute in b/a = a/3
  
  => 24b/b^2 = b^2/3*24
  
  => 24/b = b^2/24*3
  
  => b^3 = 24*24*3
  
  => b = 3^3*8*8
  
  => b = 3*4
  
  => b = 12
  
  a = 144/24 = 6
  
  The value of a = 6 and b = 12
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