Answer :

Let P(n): 32n + 7 is divisible by 8


Let’s check For n =1


P(1): 32 + 7 = 9 + 7


= 16


Since, it is divisible by 8


So, P(n) is true for n=1


Now, for n=k


P(k): 32k + 7 = 8λ - - - - - - - (1)


We have to show that,


32(k + 1) + 7 is divisible by 8


32k + 2 + 7 = 8μ


Now,


32(k + 1) + 7


= 32k.32 + 7


= 9.32k + 7


= 9.(8λ - 7) + 7


= 72λ - 63 + 7


= 72λ - 56


= 8(9λ - 7)


= 8μ


Therefore, P(n) is true for n = k + 1


Hence, P(n) is true for all nN by PMI


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