Step-by-step Solution:

Pattern Analysis

The pattern for this series is revealed by examining the differences between the terms over multiple levels.

1. 
   First Level of Differences: Calculating the difference between each number gives a new sequence.
   
   17, 43, 81, 131, ...
   
   (e.g., 20 - 3 = 17)
   


2. 
   Second Level of Differences: Calculating the difference between the numbers in the new sequence reveals the core pattern.
   
   26, 38, 50, ...
   
   (e.g., 43 - 17 = 26)
   


3. 
   The Core Pattern: The second level of differences shows a constant increase of +12 at each step.
   

Calculating the Next Term

We work backwards from the core pattern to find the answer:

• The next number in the second-level difference sequence is 50 + 12 = 62.


• Add this to the last number in the first-level difference sequence: 131 + 62 = 193.


• Finally, add this result to the last term in the original series: 275 + 193 = 468.

The next number in the series is 468.