Examine the tile pattern below.  

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

   Hint (a):

   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 $(x+1)$-by-$(x+1)$ square.

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

   Hint (b):

   Refer to the Hint in part (a).

   Answer (b):

   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 of 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.

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

   Hint (c):

   Find the pattern in the chart.