Figure 13.4 shows the first four members in a sequence of square-shaped grids. In each
Chapter 13, Problem 10(choose chapter or problem)
Figure 13.4 shows the first four members in a sequence of square-shaped grids. In each successive grid, new dots are shown in black (). For instance, the second grid has 3 more dots than the first grid, the third has 5 more dots than the second, and the fourth has 7 more dots than the third. (a) Write down the sequence of the total number of dots in each grid (black and white). Using the fact that each grid is a square, find a formula in terms of n for the number of dots in the nth grid. (b) Write down the sequence of the number of black dots in each grid. Find a formula in terms of n for the number of black dots in the nth grid. (c) State the relationship between the two sequences in parts (a) and (b). Use the formulas you found in parts (a) and (b) to confirm this relationship.
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