Question

Can u help me Answer this question.A large multiplex movie house has many theaters. The largest theater has 50 rows. There are 11 seats in the first row. Each row has 3 seats more than the previous row. How many total seats are there in this theater?

Answer 1

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,

`\begin{gathered} 11,11+1*3,11+2*3,11+3*3,\ldots\ldots\ldots,11+49*3 \\ 11,14,17,20,\ldots\ldots\ldots,158 \end{gathered}`

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,

`S=(n)/(2)(2a+(n-1)* d)`

Substitute values in the above expression.

`\begin{gathered} S=(50)/(2)*(2*11+(50-1)*3) \\ =25*(22+49*3) \\ =25*(22+147) \\ =25*169 \\ =4225 \end{gathered}`

Thus, the total number of seats in the movie house is 4225.