Answer: [tex]\bold{a_1=\dfrac{1}{2}\qquad a_n=\bigg(\dfrac{4}{3}\bigg)a_{n-1}}[/tex]
Step-by-step explanation:
The explicit rule for a geometric sequence is: [tex]a_n=a_1(r)^{n-1}\quad \text{where}\ a_1\ \text{is the first term and r is the common ratio}[/tex]
[tex]\text{From the explicit rule provided:}\ a_n=\dfrac{1}{2}\bigg(\dfrac{4}{3}\bigg)^{n-1}}\\ \text{we know that}\ a_1=\dfrac{1}{2}\ \text{and r =} \dfrac{4}{3}[/tex]
[tex]\text{The recursive rule for a geometric sequence is:}\ a_n = (r)a_{n-1} \\\\\text{So, the recursive rule is:}\ a_n=\bigg(\dfrac{4}{3}\bigg)a_{n-1}[/tex]
