[tex]\displaystyle b_1=2,b_2=\frac{2}{3},q=?,b_{14}=?,S_5=?\\q= \frac{\frac{2}{3}}{2} \Rightarrow q= \frac{2}{3} :2 \Rightarrow q= \frac{2}{3} \cdot \frac{1}{2} \Rightarrow q=\frac{2}{6} \Rightarrow q= \frac{1}{3} \\ b_{14}=2 \cdot \left( \frac{1}{3} \right)^{14-1} =2 \cdot \left( \frac{1}{3} \right)^{13}= \frac{2^{14}}{3^{13}} \\ S_5=2 \cdot \frac{\left( \frac{1}{3} \right)^5-1}{ \frac{1}{3}-1}=2\cdot \frac{ \frac{1}{243}-1}{-\frac{2}{3} }=2\cdot\frac{- \frac{242}{243} }{- \frac{2}{3} }= \frac{121}{81} [/tex]
