Question

1. Is the system geometric? If so find common ratio

Answer 1

Answer:

$\large\boxed{\text{yes,}\ \dfrac{2}{3}}$

Step-by-step explanation:

If it's a geometric sequence, then

$\dfrac{a_{n+1}}{a_n}=a_{n+1}:a_n=constant$

Check:

$\dfrac{2}{9}:\dfrac{1}{3}=\dfrac{2}{9}\cdot\dfrac{3}{1}=\dfrac{2}{3}\\\\\dfrac{4}{27}:\dfrac{2}{9}=\dfrac{4}{27}\cdot\dfrac{9}{2}=\dfrac{2}{3}\\\\\dfrac{8}{81}:\dfrac{4}{27}=\dfrac{8}{81}\cdot\dfrac{27}{4}=\dfrac{2}{3}\\\\\dfrac{16}{243}:\dfrac{8}{81}=\dfrac{16}{243}\cdot\dfrac{81}{8}=\dfrac{2}{3}$