Given Data:
The total number of rows in a large multiplex movie house is: n=50
The total number of seats in the first raw is: a=11
The difference between the number of seats of the two successive row is: d=3
The arrangement of seats will be,
[tex]\begin{gathered} 11,11+1\times3,11+2\times3,11+3\times3,\ldots\ldots\ldots,11+49\times3 \\ 11,14,17,20,\ldots\ldots\ldots,158 \end{gathered}[/tex]The above series is a arithemetic series (AP) with common diference d=3 and the first term a=11.
The expression to calculate the sum of elemenst in an AP series is,
[tex]S=\frac{n}{2}(2a+(n-1)\times d)[/tex]Substitute values in the above expression.
[tex]\begin{gathered} S=\frac{50}{2}\times(2\times11+(50-1)\times3) \\ =25\times(22+49\times3) \\ =25\times(22+147) \\ =25\times169 \\ =4225 \end{gathered}[/tex]Thus, the total number of seats in the movie house is 4225.
