[tex]\displaystyle a_1= \frac{2}{7},~a_2= \frac{1}{5} ,~r=? \\ a_2= \frac{1}{5} \Rightarrow a_{2-1}+r= \frac{1}{5} \Rightarrow a_1+r= \frac{1}{5} \Rightarrow \frac{2}{7} +r= \frac{1}{5} \Rightarrow \\ \Rightarrow 2 \cdot 5+35r=1 \cdot 7 \Rightarrow 10+35r=7 \Rightarrow 35r=7-10 \Rightarrow \\ \Rightarrow 35r=-3 \Rightarrow \boxed{r=- \frac{3}{35} } [/tex]