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A new concert hall was built with 14 seats in the first row. Each subsequent row of the hall has two more seats than
A new concert hall was built with 14 seats in the first row. Each subsequent row of the hall has two more seats than the previous row. The hall has a total of 20 rows. (a) Find: (i) the number of seats in the last row. (ii) the total number of seats in the concert hall. [5] The concert hall opened in 2019. The average number of visitors per concert during that year was 584. In 2020, the average number of visitors per concert increased by 1.2%. (b) Find the average number of visitors per concert in 2020. [2] The concert organizers use this data to model future numbers of visitors. It is assumed that the average number of visitors per concert will continue to increase each year by 1.2%. (c) Determine the first year in which this model predicts the average number of visitors per concert will exceed the total seating capacity of the concert hall. [5] It is assumed that the concert hall will host 50 concerts each year. (d) Use the average number of visitors per concert per year to predict the total number of people expected to attend the concert hall from when it opens until the end of 2025. [4]
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a i The number of seats in the last row can be found by using the arithmetic sequence formula an a1 n1d where an is the nth term a1 is the first term ...Get Instant Access to Expert-Tailored Solutions
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