Apply problem-solving strategies. A classic problem in the study of patterns is the “border problem.” A landscaper wants to construct a patio with light and dark bricks. The figure shows the 2-by-3, 3-by-4, and 4-by-5 patio.
a. Find a formula for the number of dark bricks needed for an n-by-(n + 1) patio.
b. Can you make a patio with this pattern that has 456 dark bricks?
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