Question

1. figures 1–3 represent the square growing in size.

here are the number of tiles in figures 1–3 of the pattern.

figure #	number of tiles
2	16
3	25

a draw three figures to match the patterns in the table.

b how many tiles will there be in figure 4?

Explanation:

Part a

To draw the figures:

• Figure 1: Since it has 9 tiles, it should be a \( 3\times3 \) square (because \( 3^2 = 9 \)). Shade or mark a \( 3\times3 \) grid of tiles.
• Figure 2: With 16 tiles, it is a \( 4\times4 \) square (as \( 4^2=16 \)). Shade or mark a \( 4\times4 \) grid of tiles.
• Figure 3: Having 25 tiles, it is a \( 5\times5 \) square (since \( 5^2 = 25 \)). Shade or mark a \( 5\times5 \) grid of tiles.

Part b

Step 1: Identify the pattern

Notice that for Figure 1 (\( n = 1 \)), number of tiles \( = 9=(1 + 2)^2 \); for Figure 2 (\( n = 2 \)), number of tiles \( = 16=(2 + 2)^2 \); for Figure 3 (\( n = 3 \)), number of tiles \( = 25=(3 + 2)^2 \). So the general formula for the number of tiles in Figure \( n \) is \( (n + 2)^2 \).

Step 2: Calculate for Figure 4

For Figure 4, \( n = 4 \). Substitute \( n = 4 \) into the formula \( (n + 2)^2 \).
\[
(4 + 2)^2=6^2 = 36
\]

Answer:

• Part a: Draw a \( 3\times3 \) square for Figure 1, a \( 4\times4 \) square for Figure 2, and a \( 5\times5 \) square for Figure 3.
• Part b: \(\boldsymbol{36}\)