The numbers of seats in the first 12 rows of a high-school auditorium form an arithmetic sequence. The first row has 9 seats. The second row has 11 seats. a) Write a recursive formula to represent the sequence. b) Write an explicit formula to represent the sequence. c) How many seats are in the 12th row?

A₁ = 9

a₂ = 9+2 → a₂ = a₁ + 2. Since it's an AP, d, the common difference is 2

1) Then the recursive formula is:

a (n) = a (n-1) + 2

2) Explicit formula:

It's an AP, with first term a₁, d = common difference and n = number of term, which is the number of rows in this problem.

the value of the nth term is given by the formula is:

value of nth term = a₁ + (n-1). d

3) Number of seats in the 12th row:

9 + (12-1).2 = 31 seats