Chapter Closure
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Look at the figure carefully. Notice what changes from figure to figure to identify the pattern.
a.
| Figure | Number of tiles |
|---|---|
| 1 | 5 |
| 2 | 8 |
| 3 | 11 |
| 4 | 14 |
| 5 | 17 |
b.
Each figure has one more column on the left, and one more two-tiled column on the right side than the previous figure.
c.
Figure 6: 20, Figure 10: 32
Looking at the given figures, we can see two main things:
Leftmost row:& 0+1 → 1+1 → 2+1 → 3 +1 →4 Rightmost column:& 0+2 → 2+2 → 4+2 → 6 +2 →8 Now we can sketch Figures 1 and 5.
Having drawn all the figures, we can calculate how many tiles are in each figure.
| Figure | Number of tiles |
|---|---|
| 1 | 5 |
| 2 | 8 |
| 3 | 11 |
| 4 | 14 |
| 5 | 17 |
As we noticed above, each next figure has one more column on the left side which adds 1 tile, and one more column on the right side which adds 2 tiles.
We saw above that each figure has 3 more tiles than the previous one, one on the left and two on the right. Using this information, we can find the number of tiles that the 6^(th) and the 10^(th) figures would have. Figure number:& 1+1 → 2+1 → 3 +1 → 4+1 → 5 +1 → 6... +4 ⟶ 10 Number of tiles:& 5+3 → 8+3 → 11+3 → 14 +3 →17+3 → 20...+3* 4 ⟶ 32