SOLUTION: 2,12,36,80,150,? Series comoletion

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  



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Check:

 n=1:     (ok)

 n=5:    (ok)