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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?

Respuesta :

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:

[tex]\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}[/tex]

so, 83 is the last term:

[tex]S_n=\frac{n}{2}(a_1+a_n)=\frac{30}{2}(25+83)=15(108)=1620[/tex]

that mean 1620 total seats, therefore:

[tex]\text{total sales = }1620\times2500=4050000[/tex]

answer: $4,050,000

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