Certainly! Let's analyze the pattern and complete the table for the given sequence of patterns.
From the problem, we have information about the number of white and pink tiles for pattern 1 and pattern 2. Let's study these and establish a general formula that we can use to calculate the number of tiles for any pattern number, [tex]\( n \)[/tex].
### Given:
- Pattern 1: 2 white tiles, 1 pink tile.
- Pattern 2: 4 white tiles, 3 pink tiles.
To find a pattern or relationship:
#### White Tiles:
Observe the number of white tiles in patterns 1 and 2:
- Pattern 1: 2 white tiles.
- Pattern 2: 4 white tiles.
We notice that the number of white tiles increases by 2 for each subsequent pattern:
So, a formula for the white tiles in pattern [tex]\( n \)[/tex] can be:
[tex]\[ \text{Number of white tiles} = 2n \][/tex]
#### Pink Tiles:
Observe the number of pink tiles in patterns 1 and 2:
- Pattern 1: 1 pink tile.
- Pattern 2: 3 pink tiles.
The number of pink tiles increases by 2 for each subsequent pattern:
So, a formula for the pink tiles in pattern [tex]\( n \)[/tex] can be:
[tex]\[ \text{Number of pink tiles} = 2n - 1 \][/tex]
### Let's apply these formulas:
#### For Pattern 7:
[tex]\[ \text{Number of white tiles} = 2 \times 7 = 14 \][/tex]
[tex]\[ \text{Number of pink tiles} = 2 \times 7 - 1 = 14 - 1 = 13 \][/tex]
#### For Pattern 11:
[tex]\[ \text{Number of white tiles} = 2 \times 11 = 22 \][/tex]
[tex]\[ \text{Number of pink tiles} = 2 \times 11 - 1 = 22 - 1 = 21 \][/tex]
### For General Pattern [tex]\( n \)[/tex]:
[tex]\[ \text{Number of white tiles} = 2n \][/tex]
[tex]\[ \text{Number of pink tiles} = 2n - 1 \][/tex]
### Summary
Here is the completed table:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
\text{pattern number} & \text{number of white tiles} & \text{number of pink tiles} \\
\hline
7 & 14 & 13 \\
\hline
11 & 22 & 21 \\
\hline
n & 2n & 2n - 1 \\
\hline
\end{tabular}
\][/tex]
