Final answer:
To find the number of seats in the auditorium, we can use the given information to calculate the sum of an arithmetic series. Each row has two more seats than the row before it, and the 11th row has 60 seats. By using the formula for the sum of an arithmetic series, we can find that there are 440 seats in the auditorium.
Step-by-step explanation:
The 11th row has 60 seats. Each successive row has two more seats than the row before it. To find the number of seats in the auditorium, we can find the number of seats in each row and sum them up. Let's start with the 11th row which has 60 seats. The 10th row would have 60 - 2 = 58 seats. Similarly, the 9th row would have 58 - 2 = 56 seats. Using this pattern, we can calculate the number of seats in each row until the 1st row. Finally, we can add all the seats together to get the total number of seats in the auditorium.
11th row: 60 seats
10th row: 58 seats
9th row: 56 seats
...
1st row: x seats (unknown)
To find the total number of seats, we need to sum up the number of seats in each row. We can use the formula for the sum of an arithmetic series to calculate the sum.
The sum of an arithmetic series can be calculated using the formula: S = (n/2)(first term + last term), where S is the sum, n is the number of terms, and the first and last terms are the starting and ending values of the series.
In this case, the first term is 60 and the number of terms is 11. The last term can be calculated using the formula: last term = first term + (number of terms - 1) * common difference. In this case, the common difference is 2. Plugging these values into the formula, we can calculate the sum of the seats in the auditorium.
S = (11/2)(60 + [(11-1) * 2])
= (11/2)(60 + [10 * 2])
= (11/2)(60 + 20)
= (11/2)(80)
= 11 * 40
= 440 seats