Question

1. here is a visual pattern. figure 1 figure 2 figure 3 a describe what figure 4 will look like. b how many tiles will there be in figure 4?

Explanation:

Part (a)

To determine the appearance of Figure 4, we first analyze the pattern of the previous figures:

• Figure 1: It is a rectangle with 3 rows and 2 columns of tiles.
• Figure 2: It is a rectangle with 3 rows and 4 columns of tiles.
• Figure 3: It is a rectangle with 3 rows and 6 columns of tiles.

We observe that the number of columns is increasing by 2 each time (2, 4, 6...). For Figure \( n \), the number of columns seems to follow the pattern \( 2n \), and the number of rows remains constant at 3.

For Figure 4 (\( n = 4 \)):

• Number of rows: 3 (remains the same as previous figures).
• Number of columns: \( 2\times4=8 \).

So, Figure 4 will be a rectangle with 3 rows and 8 columns of tiles, similar in structure to the previous figures but with 8 columns.

Step 1: Identify the pattern for the number of tiles

We first find the number of tiles in each figure:

• Figure 1: Number of tiles \(=3\times2 = 6\) (3 rows, 2 columns).
• Figure 2: Number of tiles \(=3\times4=12\) (3 rows, 4 columns).
• Figure 3: Number of tiles \(=3\times6 = 18\) (3 rows, 6 columns).

We can see that for Figure \( n \), the number of columns is \( 2n \) and the number of rows is 3. So the formula for the number of tiles \( T(n) \) is \( T(n)=3\times(2n)=6n \).

Step 2: Calculate the number of tiles in Figure 4

For Figure 4, \( n = 4 \). Substitute \( n = 4 \) into the formula \( T(n)=6n \).
\( T(4)=6\times4 = 24 \)

Answer:

Figure 4 will be a rectangle with 3 rows and 8 columns of tiles (maintaining the 3 - row structure while having 8 columns, as the number of columns follows the pattern \( 2n \) where \( n = 4 \) here).

Part (b)