n   a_n      diff     diff_2    diff_3

1   2             

2   12        10

3   36        24       14

4   80        44       20         6   

5   150       70       26         6 





Because the differences don't reach a constant for 3 levels, the form will be







Using the first four values, you get these 4 equations:

    

   

   

   

 

Which results in the following matrix equation:



   







Which can be solved using matrix inversion to find:











Therefore  



——

Check:

 n=1:     (ok)

 n=5:    (ok)









    





 

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
 .

Let me add to this solution 





that EVERY such puzzle IS NOT a Math problem.







You may ask me WHY ?





Because THE QUESTION DOES NOT MAKE SENSE.







 

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