Question

What is the explicit rule for this geometric sequence?

Answer 1

$a_1=\dfrac{2}{9},\ a_2=\dfrac{2}{3},\ a_3=2,\ a_4=6,\ ...\\\\r=a_2:a_1\\\\r=\dfrac{2}{3}:\dfrac{2}{9}=\dfrac{2}{3}\cdot\dfrac{9}{2}=3\\\\a_n=a_1r^{n-1}\\\\\boxed{a_n=\dfrac{2}{9}\cdot3^{n-1}}$