Question

Alejandra made the number pattern shown below 4,8,16,32,64 Part AWrite a rule for the pattern.Explain how u know the rule is correct

Answer 1

ANSWER

The rule for the pattern is


`a_n = 4 {(2)}^(n - 1)`

Step-by-step explanation

The terms in the pattern are:

4,8,16,32,64

The first term is


`a_1 = 4`

There is a constant ratio of:


`r = (8)/(4) = 2`

The rule for the pattern is given by:


`a_n = a_1 {r}^(n - 1)`

We substitute the values into the general rule to get,


`a_n = 4 {(2)}^(n - 1)`

Therefore the rule for the pattern is


`a_n = 4 {(2)}^(n - 1)`

Now let us check to see if our rule works by using it to find the 5th term in the pattern.


`a_5= 4 {(2)}^(5 - 1)`


`a_5= 4 {(2)}^(4)`


`a_5= 4 * 16 = 64`

Great!

The 5th term is actually 64, hence our rule works.