• # question_answer If the first term of a G.P. ${{a}_{1}},\ {{a}_{2}},\ {{a}_{3}},..........$is unity such that $4{{a}_{2}}+5{{a}_{3}}$ is least, then the common ratio of G.P. is A) $-\frac{2}{5}$ B) $-\frac{3}{5}$ C) $\frac{2}{5}$ D) None of these

${{a}_{1}}=1,\ {{a}_{2}}=r,\ {{a}_{3}}={{r}^{2}},.......$ $\therefore$$4{{a}_{2}}+5{{a}_{3}}=4r+5{{r}^{2}}$ To be its minimum$\frac{d}{dr}(4r+5{{r}^{2}})=0$$\Rightarrow$$r=\frac{-2}{5}$.