ANSWER
The explicit rule is:
[tex]a_n=2{( \frac{1}{3} )}^{n - 1} [/tex]
EXPLANATION
The recursive rule is
[tex]a_1=2[/tex]
and
[tex]a_n= \frac{1}{3} a_ {n - 1}[/tex]
We can rewrite to get,
[tex] \frac{a_n}{a_ {n - 1}} = \frac{1}{3} [/tex]
This implies that, the constant ratio is:
[tex]r = \frac{1}{3} [/tex]
The explicit rule is given by:
[tex]a_n=a_1 {r}^{n - 1} [/tex]
We substitute the values to obtain, the explicit rule as:
[tex]a_n=2{( \frac{1}{3} )}^{n - 1} [/tex]
