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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • question_answer
    If a function F is such that \[f(0)=2,\,\,F(1)=3,\] \[F(n+2)=2F(n)-F(n+1)\]for \[n\ne 0,\] then \[F(5)\] is equal to

    A)  \[-7\]            

    B)  \[-3\]

    C)  \[7\]             

    D)  \[13\]

    Correct Answer: D

    Solution :

    Given that, \[F(0)=2,\,\,F(1)=3,\] \[F(n+2)=2F(n)-F(n+1)\] At \[n=0,\,\,F(0+2)=2F(0)-F(1)\] \[\Rightarrow \] \[F(3)=2(2)-3=1\] At \[n=1,\,F(1+2)=2F(1)-F(2)\] \[\Rightarrow \] \[F(3)=2(3)-1=5\] At \[n=2,\,\,F(2+2)=2F(2)-F(3)\] \[\Rightarrow \] \[F(4)=2(1)-5=-3\] At  \[n=3,\,F(3+2)=2F(3)-F(4)\] \[=2(5)-(-3)\] \[\Rightarrow \] \[F(5)=13\]


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