Question

5. There are 30 rows of seats on a concert hall: 25 seats are in the1st row, 27 seats on the 2nd row, 29 seats on the 3rd row, and soon. If the price per ticket is $2,500, how much will be the totalsales for a one-night concert if all seats are taken?

Answer 1

First row = 25

Second row = 27

Third row = 29

This is 25, 27, 29...

there are 30 rows, this is n = 30

common difference = d = 27 - 25 = 2

then, we use the formula:

`\begin{gathered} a_n=a_1+(n-1)d \\ a_n=25+(30-1)2 \\ a_n=25+(29)(2) \\ a_n=25+58 \\ a_n=83 \end{gathered}`

so, 83 is the last term:

`S_n=(n)/(2)(a_1+a_n)=(30)/(2)(25+83)=15(108)=1620`

that mean 1620 total seats, therefore:

`\text{total sales = }1620*2500=4050000`

answer: $4,050,000