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: \( a_1 = 9 \), \( a_n = a_{n-1} + 2 \)
Explicit formula: \( a_n = 9 + (n-1)2 = 7n + 2 \)
Plugging in \( n = 12 \) into the explicit formula:
\( a_{12} = 7(12) + 2 = 84 + 2 = 86 \)
Therefore, there are 86 seats in the 12th row.