ANSWER
[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]
EXPLANATION
The recursive formula is given as:
[tex]a_n= \frac{1}{3} a_{n-1}[/tex]
where
[tex]a_1=2[/tex]
The explicit rule is given by:
[tex]a_n=a_1 {r}^{n-1}[/tex]
From the recursive rule , we have
[tex]r = \frac{1}{3} [/tex]
We substitute the known values into the formula to get;
[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]
Therefore, the explicit rule is:
[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]
