Question

In a music stadium, there are 18 seats in the first row and 21 seats in the second row. The number of seats in a row continues to increase by 3 with each additional row.

(a) Write an explicit rule to model the sequence formed by the number of seats in each row. Show your work.

(b) Use the rule to determine which row has 120 seats. Show your work.

Answer 1

(a) an = 18 +3(n -1)

(b) row 35

Explanation:

(a) The general term (an) of an arithmetic sequence can be expressed in terms of the first term (a1) and the common difference (d) as ...

an = a1 +d(n -1)

The given sequence has a1 = 18 and d = 3, so the explicit formula is ...

an = 18 + 3(n -1)

__

(b) We want to find n such that an = 120.

120 = 18 + 3(n -1)

40 = 6 + n - 1 . . . . . . . divide by 3

35 = n . . . . . . . . . . . . . subtract 5

Row 35 has 120 seats.