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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    If\[{{a}_{1}},{{a}_{2}},{{a}_{3}},{{a}_{4}},{{a}_{5}}\]and\[{{a}_{6}}\]are six arithmetic means between 3 and 31, then\[{{a}_{6}}-{{a}_{5}}\]and\[{{a}_{1}}+{{a}_{6}}\]are respectively equals to:

    A)  5 and 34                             

    B)  4 and 35

    C)  4 and 34             

    D)         4 and 36

    E)  6 and 36

    Correct Answer: C

    Solution :

    The given AP is \[3,{{a}_{1}},{{a}_{2}},{{a}_{3}},{{a}_{4}},{{a}_{5}},{{a}_{6}},31\] \[\therefore \]  \[31=3+7d\] \[\Rightarrow \]               \[d=4\] \[\therefore \]  \[{{a}_{1}}=3+4=7\]                 \[{{a}_{5}}=a+5d=3+20=23\] and        \[{{a}_{6}}=a+6d=3+24=27\] \[\therefore \]  \[{{a}_{6}}-{{a}_{5}}=27-23=4\] and        \[{{a}_{1}}+{{a}_{6}}=7+27=34\]


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