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:
Let $t_k=u_k+Ak^2+Bk+C,$
$u_k+Ak^2+Bk+C=u_{k-1}+A(k-1)^2+B(k-1)+C+3k+1 $
$\iff u_k+2Ak+B-A=u_{k-1}+3k+1 $
Set $B-A=1,2A=3$ so that $u_k=u_{k-1}\implies u_k=u_1=u_0$
As $\implies t_0=0, 0=u_0+C\iff u_0=-C\implies t_k=Ak^2+Bk$ for integer $k\ge0$
Now find $A,B$
