Question

A large multiplex movie house has many theaters. The largest theater has 50 rows. There are 20 seats in the first row. Each row has four seats more than the previous row. How many total seats are there in this theater?

A) 1,150
B) 1,250
C) 1,350
D) 1,450

Answer 1

To find the total number of seats in the theater, we apply the formula for the sum of an arithmetic series. The theater has a total of 5,900 seats based on the given parameters of 50 rows, 20 seats in the first row, and each subsequent row having 4 more seats than the previous one.

Step-by-step explanation:

Total Seats in the Theater Calculation

The problem describes a scenario where there is an arithmetic sequence in the number of seats in each row of a theater. The first row has 20 seats and each subsequent row has 4 more seats than the previous one. With 50 rows in total, we can use the formula for the sum of an arithmetic series to calculate the total number of seats.

The sum of an arithmetic series is given by the formula:

S = (n/2) * (a1 + an)

Where:
S = sum of the series
n = number of terms
a1 = first term
an = last term

In this scenario:

• n = 50 (total number of rows)
• a1 = 20 (seats in the first row)
• an = a1 + (n - 1) * d, where d is the common difference, which is 4 seats per row in this case.

Therefore, an can be calculated as follows:

an = 20 + (50 - 1) * 4

an = 20 + 49 * 4

an = 20 + 196

an = 216 (seats in the 50th row)

Now we use these values in the sum formula:

S = (50/2) * (20 + 216)

S = 25 * 236

S = 5,900

Thus, the total number of seats in the theater is 5,900.