Question

The seats at a local baseball stadium are arranged so that each row has 5 more seats than the row below it, and there are 4 seats in the 1st row, how many total seats are there in the first 24 rows?

a) 1,428
b) 1,476

Answer 1

To find the total number of seats in the first 24 rows of the stadium, we can use arithmetic progression. Using the formula for the sum of an arithmetic progression, the total number of seats is 1476.

Step-by-step explanation:

To find the total number of seats in the first 24 rows of the stadium, we can use arithmetic progression. Since the first row has 4 seats and each subsequent row has 5 more seats than the row below it, we can write the sequence as: 4, 9, 14, 19, ...

Now we need to find the sum of this arithmetic progression up to the 24th term. We can use the formula for the sum of an arithmetic progression: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. In this case, n = 24, a = 4, and d = 5. Plugging these values into the formula, we get:

Sn = (24/2)(2(4) + (24-1)(5)) = (12)(8 + 23(5)) = (12)(8 + 115) = (12)(123) = 1476

Therefore, there are a total of 1476 seats in the first 24 rows of the stadium.