Question

13) A theater has 38 rows of seats. The first row has 25 seats, the second

row has 29 seats, the third row has 33 seats, and so on.
What is the total number of seats in the theater?
O3,762
O3,838
O 7,524
O 7,676

Answer 1

Explanation:

To find the total number of seats in the theater, we can use the formula for the sum of an arithmetic series, which is given by:

S = n/2 * (a_1 + a_n)

where n is the number of terms in the series, a_1 is the first term, and a_n is the last term.

In this case, the first term is 25 seats and the last term is 25 + (38-1) * 4 seats (since the number of seats in each row increases by 4 each time). So, we have:

n = 38 (the number of rows)

a_1 = 25

a_n = 25 + (38-1) * 4 = 25 + 37 * 4 = 25 + 148 = 173

Now, we can substitute these values into the formula:

S = n/2 * (a_1 + a_n) = 38/2 * (25 + 173) = 19 * 198 = 3,762

So, the total number of seats in the theater is 3,762, which corresponds to option O3,762.