Question

: In an auditorium, there are 22 seats in the first row and 28 seats in the second row. The number of seats in a row continues to increase by 6 with each additional row.

(a) Write an iterative rule to model the sequence formed by the number of seats in each row.
A. Seats(n) = 22 + 6(n - 1)
B. Seats(n) = 22 + 6n
C. Seats(n) = 28 + 6(n - 1)
D. Seats(n) = 28 + 6n

(b) Use the rule to determine which row has 100 seats.
A. Row 13
B. Row 14
C. Row 15
D. Row 16

Answer 1

The iterative rule to model the sequence of seats is Seats(n) = 22 + 6(n - 1). Row 14 has 100 seats.

Step-by-step explanation:

The iterative rule to model the sequence formed by the number of seats in each row is given by option A. Seats(n) = 22 + 6(n - 1). This is because the number of seats in the first row is 22 and with each additional row, the number of seats increases by 6. The expression Seats(n) represents the number of seats in the nth row.

To determine which row has 100 seats, we can substitute the number of seats (100) into the iterative rule expression and solve for n. Rearranging the equation, we have the following:

100 = 22 + 6(n - 1)

78 = 6(n - 1)

13 = n - 1

n = 14

Therefore, row 14 has 100 seats.