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

Step-by-step 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 :

Second term :

Third term :

We can see that, Common difference = 7

Explicit rule for Arithmetic sequence :

Put and d=7

The required  explicit rule that can be used to find the number of homes sold in the nth month of the year :

an=7n−2

Step-by-step explanation:

Just took it and it's right!

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.