The sales of homes in a new development have been increasing. In January, 8 homes were sold, in February, 12 homes were sold. In March, 16 homes were sold. This pattern continued for the remainder of the year.What is the explicit rule that can be used to find the number of homes sold in the nth month of the year?an=4n−4an=−4n−4an=4n+4an=−4n+4

Accepted Solution

For the first month we have:
 a1 = 8
 For the second month we have:
 a2 = 12
 For the third month we have:
 a3 = 16
 Let's assume that n is the number of months.
 The rule that meets the number of homes sold is:
 an = 4n + 4
 We observe for example that for the third month: (n = 3)
 a3 = 4 (3) +4
 a3 = 12 + 4
 a3 = 16 (result that we already knew according to the statement).

 an = 4n + 4