Question 1162852
<pre>


k       {{{a[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 {{{n^2}}}, noting that we must subtract 1,  to write:

{{{ a[k] = 3 + (k^2-1) }}}  k=1,2,3,...