Question

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.

a) Write a recursive formula to represent the sequence.
b) Write an explicit formula to represent the sequence.

Answer 1

The following is not my work although I checked it.

a) Recursive formulas describe the relationship between a term and the previous one in the same sequence. In this case, a1=9 and a2=11 (1 and 2 are the rows).
So an= a(n-1)+2 (difference between 9 and 11 is 2)

Answer 2

b) Explicit formulas allow you to calculate an irrespective of whether you have the previous or latter term or not.

In this case: an= 2n+7 (if you plug 1, you get 2(1)+7 = 9; all you need is the row number and you can get the number of seats using the explicit formula.


c) a(12)= 2(12) + 7
= 31 seats

Solution courtesy of unknown solver at this location:
http://tinyurl.com/bhcg2gt