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

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

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:

$r = \frac{8}{4} = 2$

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.

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

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

$a_5= 4 \times 16 = 64$

Great!

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