Question

The first row of a theater has 15 seats. Each subsequent row has 3 additional seats. Which of the following is an explicit expression that represents the number of seats in a row?

A. (a(n) = 15 + (n - 1)3)
B. (a(n) = 3 + (n - 1)15)
C. (a(n) = 15 - (n - 1)3)
D. (a(n) = 3 - (n + 1)5)

Answer 1

The explicit expression that represents the number of seats in a row is (a(n) = 15 + (n - 1)3).

Step-by-step explanation:

The correct explicit expression that represents the number of seats in a row is option A: (a(n) = 15 + (n - 1)3).

This expression starts with 15 as the first row, and then adds 3 additional seats for each subsequent row. The term (n - 1)3 accounts for the extra seats added for each row after the first row.

For example, if we substitute n = 5 into the expression, we would get: a(5) = 15 + (5 - 1)3 = 15 + 4 * 3 = 15 + 12 = 27. So the fifth row would have 27 seats.