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A-73.

Examine the tile pattern below.

 tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure 1

 tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure 2

 tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure 3

1. On graph paper, draw Figures 4 and 5.

Figure 1 is a 2-by-2 square;
Figure 2 is a 3-by-3 square;
Figure 3 is a 4-by-4 square.
That means Figure x should be a $\left(x + 1\right)$-by-$\left(x + 1\right)$ square.

2. What would Figure 10 look like? How many tiles would it have on each side? What about Figure 100?

Refer to part (a)'s hint.

Figure 10: An 11-by-11 square that would have 121 tiles.
Can you use the pattern to find what Figure 100 would look like?

3. Cami has a different tile pattern. She decided to represent the number of tiles in her pattern in a table, as shown below. Can you use the table to predict how many tiles would be in Figure 5 of her tile pattern? How many tiles would Figure 8 have? Explain how you know.

Find the pattern in the chart.

  Figure Number  Number of Tiles 1 2 3 4 5 9 13 17