How do you calculate the summation when the top is n-1?

For example, if I want to find the general term of the sequence $\displaystyle \{ a_n \}1,3,7,13,21,31,...$

The first order difference is $\displaystyle \{ b_n \} 2,4,6,8,10,...$

$\displaystyle \{ b_n \}=2n$

$\displaystyle \{a_n \}=a_1+ \sum_{k=1}^{n-1} b_k=\sum_{k=1}^{n-1} 2k$

How do I calculate the sum of k?