JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Critical Thinking

  • question_answer
    For every natural number n, \[{{3}^{2n+2}}-8n-9\] is divisible by [IIT 1977]

    A) 16

    B) 128

    C) 256

    D) None of these

    Correct Answer: A

    Solution :

    \[{{3}^{2n+2}}-8n-9,\,\forall n\in N\] Putting \[n=2\] \[{{3}^{2\times 2+2}}-8\times 2-9=729-16-9=704\] It is divisible by 16.


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