SOLUTION: n : 1st term, 2nd term, 3rd term, 4th term, 5th term, 6th term, ………. 15th term series: -3, 0,4,9,15,22 Find the 15th term. HINT: I think we need to multiply the series by 2 and

     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.