Question

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

Answer 1

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