Term         Diff       



              3

              4    

              5         

             6  








 




The pattern is:

 + . . .  +  




If we write it a little differently:

 +  (1+2+3 + . . . +  (n+1)) - 3 




[ Then noting the sum of the first m integers: (1+2+ . . . + m )  =   (m)(m+1)/2  ] 




we can simplify:

 +   - 3 




Combining  with the -3 we introduced :

    n=1,2,3, . . . 






Check with given values:

a[1] = -6 + (2)(3)/2 = -6 + 3 = -3

a[2] = -6 + (3)(4)/2 = -6 + 6 = 0

a[3] = -6 + (4)(5)/2 = -6 + 10 = 4


  

You can plug in n=15 to find a[15] = 130.







 

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