Question 61
A sequence $\langle a_n \rangle$ with $a_n = a + nd$ is called an arithmetic sequence. The sequence $\langle b_n \rangle$ with $b_n = \sum_{k=0}^{n} a_k$ is called an arithmetic sequence of second degree. Let $a$ and $d$ be positive integers.
We consider all such arithmetic sequences of second degree containing the number $2010$. What is the highest possible index $n$ if $b_n = 2010$? Determine all possible arithmetic sequences $\langle a_n \rangle$, for which $b_n = 2010$ holds for this index.
We consider all such arithmetic sequences of second degree containing the number $2010$. What is the highest possible index $n$ if $b_n = 2010$? Determine all possible arithmetic sequences $\langle a_n \rangle$, for which $b_n = 2010$ holds for this index.