A) \[\frac{-2}{5}\]
B) \[\frac{-3}{5}\]
C) \[\frac{2}{5}\]
D) None of these
Correct Answer: A
Solution :
Let\[{{a}_{1}}=1,\,\,{{a}_{2}}=r,\,\,{{a}_{3}}={{r}^{2}},.....\] \[\therefore \] \[4{{a}_{2}}+5{{a}_{3}}=4r+5{{r}^{2}}\] To be its minimum,\[\frac{d}{dr}(4r+5{{r}^{2}})=0\] \[\Rightarrow \] \[4+10r=0\] \[\Rightarrow \] \[r=\frac{-2}{5}\] \[\because \frac{{{d}^{2}}}{d{{r}^{2}}}(4r+5{{r}^{2}})=\frac{d}{dr}(4+10r)=10>0\] \[\therefore \] \[4{{a}_{2}}+5{{a}_{3}}\]is least, when\[r=\frac{-2}{5}\].
You need to login to perform this action.
You will be redirected in
3 sec
