Answer: In total, the theater seats 1650 people.
Step-by-step explanation:
Given : The number of rows in the theater = 25
The number of chairs in first row = 18
The number of rows in the second row = 22
The number of rows in the third row = 26
The common difference in the number of chairs for the consecutive rows =
[tex]=4[/tex]
Thus its a Arithmetic progression.
Let n be the number of rows and d be the common difference , then the total number of chairs in n rows is given by :-
[tex]S_n=\dfrac{n}{2}(2a+(n-1)d)[/tex], where a is the umber of chairs in first row .
Put a = 18, d=4 and n = 25, we get
[tex]S_{25}=\dfrac{25}{2}(2(18)+(25-1)4)=1650[/tex]
Hence, In total, the theater seats 1650 people.
