Chapter 12.4, Problem 9SB

In Problems 1-22, use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers $n$.

$1{\text{ + 4 + 4}}^{\text{2}}\text{ + }\mathrm{...}{\text{ + 4}}^{n-\text{ 1}}\text{ = }\frac{1}{3}\left(4^n-\text{ 1}\right)$