Featured Strategy: Finding a Pattern. The chart below illustrates a repeating pattern. If...

Featured Strategy: Finding a Pattern. The chart below illustrates a repeating pattern. If this pattern continues, what symbol will be in the 538th square?

a. Understanding the Problem. To become more familiar with the problem, extend the pattern a few more squares. What symbol will be in the 19th square?

b. Devising a Plan. Because the pattern repeats itself after six squares, it is suggestive of a clock with six symbols. What symbol occurs in squares 6, 12, 18, etc.? Alternatively, you could think of the pattern as pieces of tile 6 squares long. To make the length 32 squares, how many tiles and squares would you need?

c. Carrying Out the Plan. Choose a method for finding the symbol on the 538th square. Explain your method.

d. Looking Back. The lengths and symbols of repeating patterns vary. What will be the 345th digit in the following number if the pattern continues? 142,857,142,857 . . .