The numbers of seats in the first 12 rows of a high school auditorium form an arithmetic sequence. The first row has nine seats. The second row has 11 seats. 
a). Write a recursive formula to represent the sequence.
b). Write an explicit formula to represent the sequence.
c). How many seats are in the 12th row?

Ans:
a) Recursive formula for the number of seats in n'th row is: S(n) = S(n-1) + 2
b) Explicit formula is that of an arithmetic progression. If a is the first term, 
and d is the common difference, the nth term is given by a + (n - 1)*d
Here a is 9 and d is 2. Hence the number of seats in the n'th row will be
9 + 2*(n - 1)
c) Applying the above formula, number of seats in 12th row (i.e. n = 12)
is 9 + 2*(12 - 1) = 9 + 2*11 = 31 seats.

Hope this helps :)