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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 13

  • question_answer
    If a, b and c are the first three non-zero terms of a geometric progression such that \[a-2,\]2b and 12c form another geometric progression with common ratio 5, then the sum of the series \[a+b+c+......\infty \] is

    A) \[8\]                      

    B)        \[12\]                     

    C) \[18\]         

    D)        \[24\]

    Correct Answer: C

    Solution :

         [c] Given a, b, c are in G.P. i.e., \[a,\text{ }ar,\text{ }a{{r}^{2}}\]are in G.P. Now, \[a-2,\text{ }2b\]and \[12c\] are in G.P. or  \[a-2,\text{ }2ar,\text{ }12a{{r}^{2}}\]are in G.P. with common ratio 5 (given).                                          Hence, \[5=\frac{2ar}{a-2}=\frac{12a{{r}^{2}}}{2ar}\] \[\Rightarrow \,\,\,\,r=\frac{5}{6}\] and  \[a=3\] Hence, sum \[=a+b+c+...\infty =\frac{a}{1-r}=\frac{3}{1-\frac{5}{6}}=18\]     


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