By principle of mathematical induction 32n+2−8n−9 is divisible by

Let the given statement be P(n)P(n):32n+2−8n−9 is divisible by 8.Step l: For n=1, P(1):32×1+2−8×1−9=34−8−9=81−17=64=8x8which is divisible by 8.Step ll: Let it is true for n - k,i..e. 32k+2−8k−9=8λ ...(i)Step III: For n = k+1,32(k+1)+2−8(k+1)−9 =32k+2+2−8k−8−9=32k+232−8k−17 =(8λ+8k+9)32−8k−17 [ using Eq. (i) ] =(8λ+8k+9)9−8k−17 =72λ+72k+81−8k−17 =72λ+64k+64=8(9λ+8k+8)which is divisible by 8.Therefore, P(k + 1) is true when P(k) is true.Hence, from the principle of mathematical induction,the statement is true for all natural numbers 2l,.