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.
Write a recursive formula to represent the sequence.
Write an explicit formula to represent the sequence.
How many seats are in the 12th row?
Recursive formula:
a_n = a_{n-1} + 2
Explicit formula:
a_n = 9 + 2(n-1)
Plugging in n = 12 into the explicit formula:
a_12 = 9 + 2(12-1)
a_12 = 9 + 2(11)
a_12 = 9 + 22
a_12 = 31
Therefore, there are 31 seats in the 12th row.