finding explicit formula through substitution method The question ask us to guess an explicit formula for the sequence
$$t_k = t_{k-1} + 3k + 1 ,$$ for all integers $k$ greater than or equal to 1 and 
$t_0 = 0$
Can someone help me with this? Because I am not really familiar with substitution method.
Thanks in advance.

Hint
Another solution : define $y_k=t_k-t_{k-1}=3k+1$. Adding all terms together, since they telescope,
 $$y_k=t_k-t_0=\sum_{i=1}^{k}(3i+1)=3\sum_{i=1}^{k}i+\sum_{i=1}^{k}1=???$$
I am sure that you can take from here.
