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.
