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JCECE Engineering JCECE Engineering Solved Paper-2015

  • question_answer
    In a \[GP\] with alternatively positive and negative terms and any term is the \[AM\] of the next two terms: Then, the common ratio of the \[GP\] is

    A) \[-1\]                                    

    B) \[-3\]

    C) \[-2\]                                    

    D) \[-1/2\]

    Correct Answer: C

    Solution :

    Let the first term and the common ratio of \[GP\] be \[a\] and \[r\] respectively. Since, any term is the AM of the next two terms. \[\therefore \]  \[{{a}_{n}}=\frac{{{a}_{n+1}}{{a}_{n+2}}}{2}\] \[\Rightarrow \]               \[a{{r}^{n-1}}=\frac{a{{r}^{n}}+a{{r}^{n+1}}}{2}\] \[\Rightarrow \]               \[2=r+{{r}^{2}}\] \[\Rightarrow \]               \[{{r}^{2}}+r-2=0\] \[\Rightarrow \]               \[(r+2)(r-1)=0\] \[\Rightarrow \]               \[r=-2\]                                \[[\because r\ne 1]\]


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