Prove that for any natural n the number 3^(n+4)−3n is divisible by 16.

Step-by-step explanation:

Prove that for any natural number 3^(n+4)-3n is divisible by 16.

(I'm going to assume that you mean 3^(n+4)-3^n.)

1. We can break up 3^(n+4)-3n into 3^n * 3^4-3^n (by the rule a^b*a^c = a^b+c).

2. Solve to get 3^n * 81 - 3^n

3. Factor out the 3^n, and you'll get 3^n(81-1), and simplify: 3^n(80)

        You may notice that 80 is divisible by 16.

4. Rewrite what we got from the last step as: 3^n*5(16).

Hope this helped you!

answer: you need to organize this better it does not make sense.

step-by-step explanation: ?

step-by-step explanation:

jbjuiuhuhuuy