To determine the number of seats in row 23 of the baseball stadium, where each row has 5 more seats than the previous row, we can follow these steps:
1. Identify the number of seats in the first row: The first row has 4 seats.
2. Identify the rate at which the number of seats increases per row: Each subsequent row has 5 more seats than the row below it.
3. Determine the row number for which we need to find the number of seats: We need to find the number of seats in row 23.
4. Use the formula for the nth term of an arithmetic sequence:
The formula for the nth term [tex]\((a_n)\)[/tex] of an arithmetic sequence is given by:
[tex]\[
a_n = a_1 + (n-1) \times d
\][/tex]
where [tex]\(a_1\)[/tex] is the number of seats in the first row, [tex]\(n\)[/tex] is the row number, and [tex]\(d\)[/tex] is the common difference (number of seats added per row).
5. Substitute the known values into the formula:
[tex]\[
a_{23} = 4 + (23-1) \times 5
\][/tex]
6. Simplify the expression inside the parentheses:
[tex]\[
a_{23} = 4 + 22 \times 5
\][/tex]
7. Calculate the multiplication:
[tex]\[
a_{23} = 4 + 110
\][/tex]
8. Add the results:
[tex]\[
a_{23} = 114
\][/tex]
So, the number of seats in row 23 is [tex]\(114\)[/tex].
