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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

  • question_answer
    If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of the AP is

    A)  1700                                     

    B)  1650

    C)  3300                     

    D)         3400

    E)  3500

    Correct Answer: B

    Solution :

    Let the first term of an AP is a and common difference is d. \[\therefore \]  \[{{T}_{12}}=a+(12-1)d\]                        \[=a+11d\] and        \[{{T}_{22}}=a+(22-1)d\]                         \[=a+21d\]  Since,    \[S={{T}_{12}}+{{T}_{22}}\] \[\therefore \]  \[100=a+11d+a+21d\]                 \[100=2(a+16d)\] \[\Rightarrow \]               \[a+16d=50\]                                     ?.. (i) Now,     \[{{S}_{33}}=\frac{33}{2}[2a+(33-1)d]\]                 \[=\frac{33}{2}(2a+32d)\]                 \[=33(a+16d)\]                 \[=33\times 50\]                              [from Eq. (i)] \[=1650\]


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