Answer: [tex]\bold{a_n=2\bigg(\dfrac{1}{3}\bigg)^{n-1}}[/tex]
Step-by-step explanation:
[tex]\text{The general form of the recursive rule is:}\ a_n=r\cdot a_{n-1}\\ \text{where r is the common ratio.}\ \text{The recursive rule provided is:}\\ a_n=\dfrac{1}{3}a_{n-1}\ \text{so, r} = \dfrac{1}{3}}\\\\\text{The general form of the explicit rule is:}\ a_n=a_1(r)^{n-1}\\\text{where}\ a_1\ \text{is the first term and r is the common ratio}.\\\\\text{So, the explicit rule with the information provided is:}\\a_n=2\bigg(\dfrac{1}{3}\bigg)^{n-1}[/tex]
