Question

The sales of homes in a new development have been increasing. In January, 5 homes were sold, in February,

12 homes were sold. In March, 19 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=7n+2
an=7n−5
an=7n−2
an=7n+5

Answer 1

an=7n−2

Explanation:

Just took it and it's right!

Answer 2

Answer:
`a_n=7n-2`

Explanation:

Let we consider sales of home in January as first term for sequence, then sales in February will be 2nd term and so on.

According to the given information, we have

First term :
`a_1=5`

Second term :
`a_2= 12=5+7`

Third term :
`a_3= 19=12+7`

We can see that, Common difference = 7

Explicit rule for Arithmetic sequence :

`a_n=a_1+(n-1)d`

Put
`a_1=5` and d=7

`a_n=5+(n-1)7\\\\ a_n=5+7n-7\\\\ a_n=7n+5-7\\\\ a_n=7n-2`

The required explicit rule that can be used to find the number of homes sold in the nth month of the year :
`a_n=7n-2`