# CBSE Class 11-science Answered

**If P(n) is the statement 7**

^{2n}+ 2^{3n - 3}.3^{n - 1}is divisible by 25 for all n N, then what is P(k + 1)?
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM

Expert Answer

We note that P(n) is true for n=1,since 7

^{2 }+1=50 ,which is divisible by 25.Assume that P(k) is true i.e +=25d,when d

We will prove P(k+1) is true whenever P(k)is true.

P(k+1)=+

=7

^{2}[+ -]+ =[25d-]+

=x25d + 50x

=25(+2x)

=25r

the expression is divisible by 25.

Thus,P(k+1) is true whenever P(k) is true.

Answered by | 04 Jun, 2014, 03:23: PM

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