prove that 72n+233n-3*3n-1is divisible by 25 for all natural numbers n... plz say hw to do it..

Let p(n) be the statement given by 

p(n) : 72n+233n-3×3n-1 is divisible by 25.

Step 1: We have p(1) = 72(1) + 233(1)-3 × 3(1)-1

=  72 + 233-3 × 31-1 = 49 + 230 × 30

= 49 + 1 = 50 which is divisible by 25.

 

Again, we have p(2) = 72(2) + 233(2)-3 × 3(2)-1

=  74 + 236-3 × 32-1 = 74 + 233 × 31

= 2401 + 12167 × 3 = 2401 + 36501 = 38902 which isn't divisible by 25.

 

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