Let's solve this problem step-by-step.
1. Identify the pattern: The problem states that each row has 5 more seats than the row below it, and we know there are 4 seats in the 1st row. This means that the sequence of the number of seats in each row forms an arithmetic progression (AP), where the difference between consecutive terms (denoted as the common difference, [tex]\( d \)[/tex]) is 5.
2. First term: The number of seats in the 1st row is given as 4. Let this be the first term of the AP, denoted as [tex]\( a_1 \)[/tex].
3. Common difference: The common difference [tex]\( d \)[/tex] between each row is 5. This means that each subsequent row has 5 more seats than the previous one.
4. General formula for the [tex]\(n\)[/tex]-th term of an AP:
[tex]\[
a_n = a_1 + (n-1) \cdot d
\][/tex]
Here, [tex]\( a_n \)[/tex] represents the number of seats in the [tex]\( n \)[/tex]-th row.
5. Determine the row: We need to find the number of seats in the 23rd row (i.e., [tex]\( n = 23 \)[/tex]).
6. Apply the formula:
[tex]\[
a_{23} = 4 + (23-1) \cdot 5
\][/tex]
7. Simplify the calculations:
[tex]\[
a_{23} = 4 + 22 \cdot 5
\][/tex]
[tex]\[
a_{23} = 4 + 110
\][/tex]
[tex]\[
a_{23} = 114
\][/tex]
So, the number of seats in row 23 is 114.
Therefore, the answer is 114.
