# Thread: Expression and value of Sn

1. ## Expression and value of Sn

a) Write an expression for Sn, for the series 1 + 7 + 13 + ...

b) Hence, find the value of n for which Sn=833

$\begin{gathered} \sum\limits_{k = 0}^n {(1 + 6k)} = 6\sum\limits_{k = 0}^n k + \sum\limits_{k = 0}^n 1 \\ = 6\frac{{n(n + 1)}}{2} + (n + 1) \\ = 3n(n + 1) + (n + 1) \\ = 3{n^2} + 4n + 1 \\ \end{gathered}$