Prove the following by using the principle of mathematical induction for all

is a multiple of 27 for all

Let P(n): is a multiple of 27.
I.       For n = 1,
        P(1): is a multiple of 27
   41 - 14 is a multiple of 27 27 is a multiple of 27
         which is true.

∴       P(n) is true for n = 1
II.    Suppose P(n) is true for n = m,
   P(m) : is a multiple of 27   ...(i)
III.   For n = m + 1,
        P (m + 1) : is a multiple of 27
        But,
           
           =        [By (i)]
             where
is a multiple of 27

∴           P(m + 1) is true.

∴           P(m) is true P(m + 1) is true.
Hence, by induction, P(n) is true for all