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J & K CET Engineering J and K - CET Engineering Solved Paper-2006

  • question_answer
    If \[\left\{ {{a}_{n}} \right\}_{n}^{x}\] is a sequence with \[{{a}_{0}}=p\] and \[{{a}_{n}}-{{a}_{n-1}}=r{{a}_{n-1}}\] for \[n\ge 1,\] then the terms of the sequence are in

    A)  an arithmetic progression

    B)  a geometric progression

    C)  a harmonic progression

    D)  an arithmetico-geometric progression

    Correct Answer: B

    Solution :

    Given,   \[{{a}_{0}}=p\] and \[{{a}_{n}}-{{a}_{n-1}}=r{{a}_{n-1}}\] \[\Rightarrow \] \[{{a}_{n}}={{a}_{n-1}}(r+1)\] For  \[n=1,\,\,{{a}_{1}}={{a}_{0}}(r+1)=p(r+1)\] \[n=2,{{a}_{2}}={{a}_{1}}(r+1)=p{{(r+1)}^{2}}\] \[n=3,{{a}_{3}}={{a}_{2}}(r+1)=p{{(r+1)}^{3}}\] This shows that the sequence are in a geometric progression.


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