AT-OEMO-REG 2010 Problem 4

Let $(b_n)_{n \ge 0}=\sum_{k=0}^{n} (a_0+kd)$ for positive integers $a_0$ and $d$ . We consider all such sequences containing an element $b_i$ which equals $2010$ . Determine the greatest possible value of $i$ and for this value the integers $a_0$ and $d$ .

(41th Austrian Mathematical Olympiad, regional competition, problem 4)