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COMEDK2023MathematicsMathematical Induction

If 49^n+16^n+k is divisible by 64 for n N , then the least negative integral value of k is

Options

  1. A-1
  2. B-2
  3. C-3
  4. D-4

Correct answer

A. -1

Step-by-step solution

Let P(n)=49^n+16^n+k For n=1 , we get P(1)=49^ (1) +16^ (1) +k=65+k As P(1) is divisible by 64 , we take k=-1P(1)=65-1=64 , which is divisible by 64 . Thus, the least negative integral value of k be -1 .

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