By Principle of Mathematical Induction, prove that: 12n + 2.5n-1 is divisible by 7. Share with your friends Share 5 Manbar Singh answered this Let Pn be the given statement given by Pn : 12n + 2 . 5n-1 is divisible by 7.Now, P1 : 121 + 2 . 51-1 is divisible by 7.Since, 121+2 . 51-1 = 12 + 2 = 14 which is divisible by 7So, P1 is true.Let Pm be true. Then,12m + 2 . 5m-1 is divisible by 7.⇒12m + 2 . 5m-1 = 7λ, for some λ∈N .....1We shall now show that Pm+1 is true.For this, we have to show that 12m+1 + 2 . 5m is divisible by 7.Now, 12m+1 + 2 . 5m = 12m . 12 + 2 . 5m⇒12m+1 + 2 . 5m = 127λ-2.5m-1 + 2.5m⇒12m+1 + 2 . 5m = 84λ - 24 . 5m-1 + 2. 5m⇒12m+1 + 2 . 5m = 84λ + 5m2 - 245⇒12m+1 + 2 . 5m =84λ + 5m×-145⇒12m+1 + 2 . 5m =84λ - 5m-1 . 14⇒12m+1 + 2 . 5m = 712λ - 2. 5m-1 = 7μ, where μ = 12λ - 2. 5m-1∈N⇒12m+1 + 2 . 5m is divisible by 7⇒Pm+1 is trueThus, Pm is true ⇒Pm+1 is true.Hence, by PMI, Pn is true for all n∈N. 3 View Full Answer Rashad Abdullah answered this No similar links Please 6