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?

Answer 1

To find the recursive formula, we first need to find the common difference between each row's number of seats. The common difference is 11 - 9 = 2.

Therefore, the recursive formula to represent this sequence is:
a(n) = a(n-1) + 2, where a(1) = 9

To find the explicit formula, we can use the formula for arithmetic sequences:
a(n) = a(1) + (n-1)d, where a(1) = 9 and d = 2

So, the explicit formula to represent the sequence is:
a(n) = 9 + 2(n-1)
a(n) = 9 + 2n - 2
a(n) = 2n + 7

To find the number of seats in the 12th row, we can plug in n = 12 into the explicit formula:
a(12) = 2(12) + 7
a(12) = 24 + 7
a(12) = 31

Therefore, there are 31 seats in the 12th row of the auditorium.