NL-NWO 1984 Problem 3

For $n = 1,2,3,...$ . $a_n$ is defined by: $$a_n =\frac{1 \cdot 4 \cdot 7 \cdot ... (3n-2)}{2 \cdot 5 \cdot 8 \cdot ... (3n-1)}$$ Prove that for every $n$ holds that $$\frac{1}{\sqrt{3n+1}}\le a_n \le \frac{1}{\sqrt[3]{3n+1}}$$