There are 13 seats in the first row around a semicircular stage. Each row behind the first has 2 more seats than the row in front of it. How many rows of seats are there if there is a total of 448 seats? The number of rows is (Simplify your answer.)

Step 1 ：We are given a semicircular stage with 13 seats in the first row. Each subsequent row has 2 more seats than the previous row. The total number of seats is 448. We need to find the number of rows.

Step 2 ：We can solve this problem using the formula for the sum of an arithmetic series. The first term of the series (a) is 13, the common difference (d) is 2, and the sum of the series (S) is 448. We need to find the number of terms in the series (n), which represents the number of rows.

Step 3 ：The formula for the sum of an arithmetic series is \(S = \frac{n}{2} * (a + l)\), where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

Step 4 ：We don't know the last term (l), but we can express it in terms of the first term (a) and the common difference (d): \(l = a + (n - 1)*d\).

Step 5 ：Substituting this into the sum formula gives: \(S = \frac{n}{2} * (2a + (n - 1)*d)\).

Step 6 ：We know S, a, and d, so we can solve this equation for n.

Step 7 ：Solving the equation gives two solutions: -28 and 16. However, the number of rows (n) cannot be negative, so we discard -28.

Step 8 ：Thus, the number of rows is 16.

Step 9 ：Final Answer: The number of rows is \(\boxed{16}\).