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AP EAMCET201823 Apr 2018Evening ShiftMathematicsMathematical InductionActual

If 2 (4^ 2 n+1 )+3^ 3 n+1 is divisible by k, k>1 for all n N , then the value of k is

Options

  1. A19
  2. B17
  3. C11
  4. D13

Correct answer

C. 11

Step-by-step solution

The given expression aligned & 2 (4^ 2 n+1 )+3^ 3 n+1 =P(n) & P(n)=8 (4^ 2 n )+3 (3^ 3 n ) & For n=1 , & n N & P(n=1)=128+81=209 & aligned is divisible by 19 and 11. Similarly, P(n=2)=2048+2187=4235 is divisible by 11 but not divisible by 19. So, the given expression 2 (4^ 2 n+1 )+3^ 3 n+1 is divisible by For all k=11 n N .

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