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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 24

  • question_answer
    The first term of an arithmetic progression is 1 and the sum of the first nine terms is 369. The first and the ninth terms of a geometric progression coincide with the first and the ninth terms, respectively, of the arithmetic progression. The seventh term of the geometric progression is

    A) \[9\]                      

    B)        \[18\]                    

    C) \[27\]        

    D)        \[36\]

    Correct Answer: C

    Solution :

       [c] We have \[369=\frac{9}{2}[2+(9-1)d]\] \[\Rightarrow \,\,\,\,\,82=2+8d\] \[\Rightarrow \,\,\,\,\,d=10\] Now,  \[a{{r}^{8}}=a+8d=1+8\times 10=81\] or \[{{r}^{8}}=81\]  or  \[r=\sqrt{3}\] \[\therefore \,\,\,{{7}^{th}}\]  term of G.P. \[=a{{r}^{(7-1)}}=1\times {{(\sqrt{3})}^{6}}=27\]        


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