The numbers of seats in the first 12 rows of a high-school auditorium form an arithmetic sequence. The first row has 9 seats. Th
e 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
