Examine the figures at right, and then visualize the figure for $n=4$.

1. How many cubes are in the figure for $n = 4$?

   Hint (a):

   Assume that cubes which are blocked from view but would complete the figure are present.

   More Help (a):

   The $n = 2$ figure is a $2 \times 2 \times 2$ cube with one corner cube missing. What will the $n = 4$ figure look like?

2. How many cubes are in the figure for $n = 1$?

   Hint (b):

   Pay close attention to the position of the missing cube. Where would the missing cube be in the $n = 1$ figure?

3. Find the general equation for the number of cubes for any $n$. Verify your formula with the cases of $n = 1$ and $n = 5$.

   Hint (c):

   Imagine that the smaller cubes have side length $1$. What is the volume of each large cube?

4. Is the sequence arithmetic, geometric, or neither? Explain your reasoning.

   Hint (d):

   Do you need to add or multiply to determine the number of cubes in the 'next' figure?