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JEE Main & Advanced JEE Main Online Paper (Held On 23 April 2013)

  • question_answer
                    If\[{{a}_{1}},{{a}_{2}},{{a}_{.3.......}}{{a}_{n}}......\] are in A.P. such that \[{{a}_{4}}-{{a}_{7}}+{{a}_{10}}=\operatorname{m},\] then sum of first 13 terms of this A.P., is :     JEE Main Online Paper ( Held On 23  April 2013 )

    A)                    10 m                  

    B)                                           12 m

    C)                                           13 m                  

    D)                                           15 m

    Correct Answer: C

    Solution :

                      If d be the common difference, then \[m={{a}_{4}}-{{a}_{7}}+{{a}_{10}}={{a}_{4}}-{{a}_{7}}+{{a}_{7}}+3d={{a}_{7}}\] \[{{S}_{13}}=\frac{13}{2}[{{a}_{1}}+{{a}_{13}}]=\frac{13}{2}[{{a}_{1}}+{{a}_{7}}+6d]\] \[=\frac{13}{2}[2{{a}_{7}}]=13{{a}_{7}}=13m\]


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