this is just an example of another question
Answer:
The total sales for one-night concert if all sales are taken is $2,024,000.00.
Further Explanation
The problem can be answered using the concepts in series and sequences. Sequence is a set of an ordered-numbers, that is, 1st term, 2nd term, 3rd term and so on. Series is the sum of the givens sequence.
Different Type of Sequences
1. Arithmetic Series
1. Arithmetic Series2. Geometric Series
1. Arithmetic Series2. Geometric Series3. Harmonic Series
1. Arithmetic Series2. Geometric Series3. Harmonic Series4. Fibonacci Series
Notice that the number of seats in each row follow a certain pattern, that is, 25, 27, 29, and so on. This means that we have an arithmetic sequence. Base on the first three terms, the sequence has a common difference of 2, d=2d=2 , its first term is a_1=25a
1
=25 , and the sequence has 20 total number of terms.
The last term of the sequence can be solved using the formula below.
a_n=a_1+(n-1)da
n
=a
1
+(n−1)d
To solve the last term, substitute the values a_1=25a
1
=25 , n=20n=20 , and d=2d=2 into the equation above, then simplify the right side.
\begin{gathered}\begin{aligned}a_n&=25+(20-1)(2)\\&=25+(19)(2)\\&=63\end{aligned}\end{gathered}
a
n
=25+(20−1)(2)
=25+(19)(2)
=63
This means that the sequence has 63 as its last term. To solve for the sum of the sequence or the series, use the formula below.
S_n=\frac{n}{2}(a_1+a_n)S
n
=
2
n
(a
1
+a
n
)
Substitute the values of \begin{gathered}n=20\\\end{gathered}
n=20
, a_1=25a
1
=25 , and a_n=63a
n
=63 into the formula above, then simplify the right side.
\begin{gathered}\begin{aligned}S_n&=\frac{20}{2}(25+63)\\&=10(88)\\&=880\end{aligned}\end{gathered}
S
n
=
2
20
(25+63)
=10(88)
=880
This means that the concert hall has a total of 880 seats. To solve the total sales, assuming that all seats filled, multiply the price for each ticket by the total number of seats.
\begin{gathered}\begin{aligned}\text{Total Sales}&=880\times{\$2300}\\&=\$2,024,000\end{aligned}\end{gathered}
Total Sales
=880×$2300
=$2,024,000
This means that the total sales amount is $2,024,000.00.
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