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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?

 Feb 12, 2017

Best Answer 

 #1
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+5

This forms an arithmetic progression:

 

Sum=N/2[2F + (N -1)*D]

Sum =50/2[2*20 + (50 -1)*2]

Sum =25[40 + 98]

Sum =25 x 138

Sum =3,450 - number of seats in the theater.

 Feb 12, 2017
 #1
avatar
+5
Best Answer

This forms an arithmetic progression:

 

Sum=N/2[2F + (N -1)*D]

Sum =50/2[2*20 + (50 -1)*2]

Sum =25[40 + 98]

Sum =25 x 138

Sum =3,450 - number of seats in the theater.

Guest Feb 12, 2017
 #2
avatar+37146 
+5

Another way:

\(\sum_{1}^{50}\) 20 + 2(n-1) = 3450 seats

 Feb 12, 2017
 #3
avatar+26387 
0

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

 

laugh

 Feb 13, 2017

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