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  • If 10^n + 3.4^{n+2} + k is divisible by 9 for all n ϵ N, then the least positive integral value of k is

If 10^n + 3.4^{n+2} + k is divisible by 9 for all n ϵ N, then the least positive integral value of k is

A. 5
B. 3
C. 7
D. 1

Answers (1)

The answer is the option (A) 5

Given:

P(n) = 10^n + 3.4^{n+2} + k is divisible by 9

Now, we’ll substitute different values for n,

At n = 1,

P(1) = 10^1 + 3.4^3+ k

            = 202 + k

 

Now, we know that sum of the digits of this no. should be 9 or multiples of 9, for it to be divisible by 9.

Thus 2 + 2 + k = 9

Thus,k = 5.

 

Posted by

infoexpert21

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