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  • For all n ϵ N, 3.52n + 1 + 23n + 1 is divisible by

For all n ϵ N, 3.5^{2n + 1} + 2^{3n + 1} is divisible by

A. 19
B. 17
C. 23
D. 25

Answers (1)

The answer is the option (B) 17

Given:

P(n) = 3.5^{2n + 1} + 2^{3n + 1}

Now, we’ll substitute different values for n,

At n = 1,

P(1) = 3.5^{2+1} + 2^{3+1}           

       \\ = 375 + 16\\ = 391 \\=17\times 23

At n = 2,

P(2) = 3.5^{4+1} + 2^{6+1}
            \\= 9375 + 256 \\ = 9503 \\ = 17 \times 559

Therefore, it is divisible by 17.

 

     

Posted by

infoexpert21

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