Liczymy

$a_2=\frac{3\cdot 2}{2+2}=\frac{6}{4}=\frac{3}{2}$  

$a_3=\frac{3\cdot \frac{3}{2}}{\frac{3}{2}+2}=\frac{\frac{9}{2}}{\frac{7}{2}}=\frac{9}{2}\cdot \frac{2}{7}=\frac{9}{7}$  

$a_4=\frac{3\cdot \frac{9}{7}}{\frac{9}{7}+2}=\frac{\frac{27}{7}}{\frac{23}{7}}=\frac{27}{7}\cdot \frac{7}{23}=\frac{27}{23}$