To find the recursive formula for the sequence, we first need to identify the common difference. Since the number of seats increases by 2 from one row to the next, the common difference is 2.
Recursive formula:
a(1) = 9
a(n) = a(n-1) + 2
To find the explicit formula for the sequence, we know the formula for the nth term of an arithmetic sequence is given by:
a(n) = a(1) + (n-1)d
Substitute a(1) = 9 and d = 2 into the formula:
a(n) = 9 + 2(n-1)
a(n) = 9 + 2n - 2
a(n) = 2n + 7
To find how many seats are in the 12th row, substitute 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.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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?
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