The numbers of seats in the first 12 rows of a high school auditorium form and arithmetic sequence the first row nine seats second row has 11

a) The recursive formula for the number of seats in the n th row will be;

S1 = 9

S (n) = S (n-1) + 2

b) Explicit formula; is that of an arithmetic progression; such that if a is the first term, and d is the common difference, then the n th term will be given by the formula: a + (n-1) d; where a is 9, and d is 2

Hence; for n th row = 9 + 2 (n-1)

c) Number of seats in 12 th row using the formula in b.

n = 12, a = 9, d = 2

therefore; 9 + 2 (12-1)

= 9 + 2 (11)

= 31 seats