Question

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.
1. Write a recursive formula to represent the sequence.
2. Write an explicit formula to represent the sequence.
3.How many seats are in the 12th row?

Answer 1

1. Recursive formula: a(n) = a(n-1) + 2
2. Explicit formula: a(n) = 7 + 2(n-1) = 2n + 5
3. Plug in n = 12 into the explicit formula: a(12) = 2(12) + 5 = 24 + 5 = 29 seats in the 12th row.