\( s_k = \sum\limits_{n=1}^{k}{[ 84 +(n-1)*3}] \)
\( s_k = \sum\limits_{n=1}^{k}{[ 84 + 3n -3] } \)
\( s_k = \sum\limits_{n=1}^{k}{[ 81 + 3n] } = 3* \sum\limits_{n=1}^{k}{[ 27 + n] } \)
\( s_k = 3 * ( 27*k + \sum\limits_{n=1}^{k}{n } ) \)
\( s_k = 3*(27*k + \frac{k*(k+1)}{2}) \)
Somit folgt
\( s_{23} = 3*(27*23 + \frac{23*(23+1)}{2}) = 2691 \)
