Amortized time of insertion into an Array list
The question might be a little misleading.


  So, after n elements inserted, we've resized at sizes 1, 2, 4, ... , n. 


This is only true if $n = 2^k$ for some $k \in \mathbb{N}$, because for a growth factor of 2, we only need to resize when $n$ is a power of 2. 

So in your case we would only resize at 1, 2, 4. Not 7. 



You should keep in mind this only applies to a growth factor of 2. We could change the growth factor however we wish. For example we set the growth factor to 3. Then we resize at powers of 3; $\{1, 3, 9, \dots 3^k\}$. You can still use the same analysis procedure to get a constant amortized time though.