[tex]\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^{n-1}\\------------------------------\\\text{We have the recursive form}\ a_1=3,\ a_n=\dfrac{1}{2}\cdot a_{n-1}.\\\\\text{Therefore}\ r=\dfrac{1}{2}.\ \text{Substitute:}\\\\\boxed{a_n=3\left(\dfrac{1}{2}\right)^{n-1}}[/tex]
