Find the number of theater seats in an auditorium with 50 rows where
the first row has 20 seats and
each successive row has 2 more seats than the previous?
Formula:
\(\begin{array}{|rcll|} \hline t_n &=& t_1 + (n-1)\cdot d \\ s_n &=& \left(\frac{t_1+t_n}{2} \right) \cdot n \\ \hline \end{array} \)
\(\begin{array}{|rcll|} \hline n &=& 50 \\ t_1 &=& 20 \\ d &=& 2 \\\\ t_{50} &=& 20 + (50-1)\cdot 2 \\ t_{50} &=& 20 + 49\cdot 2 \\ t_{50} &=& 118 \\\\ s_{50} &=& \left(\frac{20+118}{2} \right) \cdot 50 \\ s_{50} &=& \left(\frac{138}{2} \right) \cdot 50 \\ s_{50} &=&69 \cdot 50 \\ s_{50} &=&3450 \\ \hline \end{array}\)
The number of theater seats in an auditorium is 3450
