11th Class Mathematics Other Series Question Bank Critical Thinking

  • 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

    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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