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4-12.

Two cubes: 2 by 2 by 2 cube missing a 1x1x1 corner cube and a 3 by 3by 3 cube missing a 1x1x1 cube from the corner. Examine the figures at right, and then visualize the figure for n = 4. Homework Help ✎

  1. How many cubes are in the figure for ?

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

    The figure is a cube with one corner cube missing. What will the figure look like?

  2. How many cubes are in the figure for ?

    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 . Verify your formula with the cases of and .

    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.

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