Question

May i ask for some help? 1: There are 11 rows of seats in a concert hall: 15 seats are in the 1st row, 18 seats in the 2nd row, 21 seats in the 3rd row, and so on. What's the explicit equation and the recursive equation?

2: If the price per ticket is 27$, how much will be the total sales for a one-night concert if all the seats are taken?

Answer 1

1. equations for an arithmetic sequence:

`a_n=a_1+d(n-1)`

`\displaystyle\left \{\begin{array}{l}a_1=a_1\\ a_n=a_(n-1)+d\end{array} \right.`

2. total sales: $8910

Explanation:

1. The explicit equation for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...

`a_n=a_1+d(n-1)`

The recursive formula for the n-th term is ...

`\displaystyle\left \{\begin{array}{l}a_1=a_1\\ a_n=a_(n-1)+d\end{array} \right.`

Filling in a₁ = 15, d = 3, the explicit formula becomes ...

`a_n=15+3(n-1)`

And the recursive equation becomes ...

`\displaystyle\left \{\begin{array}{l}a_1=15\\ a_n=a_(n-1)+3\end{array} \right.`

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2. The revenue will be the product of ticket price and number of seats. The number of seats will be the average number in a row times the number of rows. For an odd number of rows (11), the middle row (6) has the average number of seats.

revenue = $27 × (11)a₆ = $297 × (15 +3(6-1)) = $8910

Total sales for a sold-out concert will be $8910.