# Please explain the answer. Example 6 prove that                  2.7 n + 3.5 n  – 5 is divisible by 24, for all n$\in$ N. solution Let the statement p (n) be defined as             P(n) : 2.7 n +3.5 n  – 5 is divisible by 24. We note that P(n) is true for n =1, since 2.7 + 3.5  5 = 24, which is divisible by 24.  Assume that p(k) is true  i.e 2.7k+3.5 k  – 5 = 24q, when q  $\in$  N Now we wish to prove that P(k + 1) is true whenever P(k) is true. We have              ​The expression on the R.H.S. of (1) is divisible by 24. Thus P(k + 1) is true whenever P(k) true  Hence, by principle of mathematical induction, P(n) is true for all n$\in$ N.​

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