Answer:
1. equations for an arithmetic sequence:
[tex]a_n=a_1+d(n-1)[/tex]
[tex]\displaystyle\left \{\begin{array}{l}a_1=a_1\\ a_n=a_{n-1}+d\end{array} \right.[/tex]
2. total sales: $8910
Step-by-step explanation:
1. The explicit equation for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...
[tex]a_n=a_1+d(n-1)[/tex]
The recursive formula for the n-th term is ...
[tex]\displaystyle\left \{\begin{array}{l}a_1=a_1\\ a_n=a_{n-1}+d\end{array} \right.[/tex]
Filling in a₁ = 15, d = 3, the explicit formula becomes ...
[tex]a_n=15+3(n-1)[/tex]
And the recursive equation becomes ...
[tex]\displaystyle\left \{\begin{array}{l}a_1=15\\ a_n=a_{n-1}+3\end{array} \right.[/tex]
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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.
