k                 Diff

--    ----------     ----

1          3           -

2          6           3

3          11          5 

4          18          7



The next difference will be 9, we see the differences are the odd integers starting with 3, so we can use the property that the sum of the first n odd numbers is , noting that we must subtract 1,  to write:



  k=1,2,3,...



 

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