proof writing - Question on Induction (Very Simple)

I've just started a course in mathematics at university, and our current topic is mathematical induction.

I've been given the following question:

$$1+4+4^2+....+4^{n-1}=\frac{4^{n}-1}{3}.$$

I get the first step - $P(1) = 1$.

I get the second step - Assume $n = k$.

It's this third step that gets me. I've seen it done a few ways.. but this is what I've got so far:

$$\begin{align} 1+4+4^2+...+4^{k-1}+4^{k} & = [1+4+4^2+...+4^{k-1}] +4^{k} \\ & = \frac{4^{k}-1}{3} + 4^{k} \end{align}$$

I've no idea where to go after this. I'm assuming I want it to look something like:

$$\frac{4^{k+1}-1}{3}.$$

However, no idea how to get there, or if that's even the direction I want to be heading in.

I would appreciated any help. Especially if there's an easier way of doing this.

Cheers. =)