$a{{q}^{2}}\times a{{q}^{3}}=2aq\times a{{q}^{6}}\Rightarrow {{q}^{2}}=\frac{1}{2}\Rightarrow q=-\frac{\sqrt{2}}{2}$ $a{{q}^{9}}=a{{q}^{4}}({{q}^{5}})=1{{(-\frac{\sqrt{2}}{2})}^{5}}=-\frac{\sqrt{2}}{8}$