A) \[-\frac{2}{5}\]
B) \[-\frac{3}{5}\]
C) \[\frac{2}{5}\]
D) None of these
Correct Answer: A
Solution :
\[{{a}_{1}}=1,\ {{a}_{2}}=r,\ {{a}_{3}}={{r}^{2}},.......\] \[\therefore \]\[4{{a}_{2}}+5{{a}_{3}}=4r+5{{r}^{2}}\] To be its minimum\[\frac{d}{dr}(4r+5{{r}^{2}})=0\]\[\Rightarrow \]\[r=\frac{-2}{5}\].
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