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_1 + (n-1)d
where:
a_n = number of seats in the nth row
a_1 = number of seats in the first row (9)
d = common difference (11-9 = 2)
Explicit formula:
a_n = 9 + 2(n-1)
a_n = 9 + 2n - 2
a_n = 7 + 2n
Number of seats in the 12th row:
a_12 = 7 + 2(12)
a_12 = 7 + 24
a_12 = 31
There are 31 seats in the 12th row.