1. ## Induction

Use the method of mathematical induction to prove that $4^n+14$ is a multiple of $6$ for $n \geq 1$.

Thanks

2. Let's see if this holds water.

$4^{1}+14=18$, true.

Assume 6 is a factor of $4^{k}+14$. The (k+1)st term is

$4^{k+1}+14=4\cdot{4^{k}}+14$

= $4\cdot{4^{k}}+56-42=4(4^{k}+14)-42$

By the induction hypothesis, 6 is a factor of $4^{k}+14$ and

6 is a factor of 42, so 6 is a factor of the (k+1)st term and $P_{k+1}

$
is true. And QED.