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ANSWER

The rule for the pattern is

[tex]a_n = 4 {(2)}^{n - 1} [/tex]

EXPLANATION

The terms in the pattern are:

4,8,16,32,64

The first term is

[tex]a_1 = 4[/tex]

There is a constant ratio of:

[tex]r = \frac{8}{4} = 2[/tex]

The rule for the pattern is given by:

[tex]a_n = a_1 {r}^{n - 1} [/tex]

We substitute the values into the general rule to get,

[tex]a_n = 4 {(2)}^{n - 1} [/tex]

Therefore the rule for the pattern is

[tex]a_n = 4 {(2)}^{n - 1} [/tex]

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

[tex]a_5= 4 {(2)}^{5 - 1} [/tex]

[tex]a_5= 4 {(2)}^{4} [/tex]

[tex]a_5= 4 \times 16 = 64[/tex]

Great!

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

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