Question

A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?

Answer 1

`a_n=5n`

Explanation:

They gave us the first two terms in the sequence which is 5,10.

They then tell us the sequence is arithmetic which means all you need to do to get the next term is add/subtract.

To get from 5 to 10, you would need to add 5.

So that is what we are doing every time here.

5,10,15,20,25,... so on...

Now we want to make an equation for this.

When you see arithmetic sequence, you should think linear equations.

x | y

-----------

1 5

2 10

3 15

4 20

Can you see the relationship between y and x?

Slope is 5 because that is what the sequence is going up by.

y=5x+b

Maybe you can already see b is 0. If not, you can use a point on the line to find b.

Let's use (1,5).

5=5(1)+b

5=5+b

0=b

So b=0.

The equation is y=5x.

Our since we are talking about sequences maybe you prefer to say
`a_n=5n`