Step-by-step Solution:

Pattern Analysis

This series is composed of two independent, alternating sequences. We can analyze them separately:

• 
  Odd-Positioned Terms (1st, 3rd, 5th, etc.):
  

  The sequence is 17, 9, 5, 3, ?

  
  

  The amount subtracted is halved at each step:

  
  
  
  
  • 17 - 8 = 9
  
  
  • 9 - 4 = 5
  
  
  • 5 - 2 = 3
  
  
  • Following the pattern, the next subtraction is 1: 3 - 1 = 2.
  
  
  
  

  So, the first missing number is 2.

  
  


• 
  Even-Positioned Terms (2nd, 4th, 6th, etc.):
  

  The sequence is 20, 12, 6, 2, ?

  
  

  The amount subtracted decreases by 2 at each step:

  
  
  
  
  • 20 - 8 = 12
  
  
  • 12 - 6 = 6
  
  
  • 6 - 4 = 2
  
  
  • Following the pattern, the next subtraction is 2: 2 - 2 = 0.
  
  
  
  

  So, the second missing number is 0.

  
  

The next two numbers in the series are 2 and 0.