To determine the number of matchsticks needed for each figure, let's analyze the pattern.
Assuming each figure is a square made from matchsticks, we can look for a formula for the number of matchsticks required.
- Figure 1: 16 matchsticks
- Figure 2: 36 matchsticks
Let's first calculate the number of matchsticks for subsequent figures. From the information provided, we might notice that the numbers relate to the number of squares formed in the figure.
General Formula: If we denote \( n \) as the number of squares in the figure (this includes both the outer squares and any inner squares), we might find that there's a relationship such as:
- Each added square requires additional matchsticks to form its sides.
Let's calculate the amounts for the subsequent figures. We can start by finding the total number of matchsticks using the formula derived from squares.
Figure Breakdown
- A single square figure (1x1) requires 4 matchsticks for each square.
- A figure with \( n \) squares that include inside squares would require additional matchsticks.
If we observe the matchstick counts:
- Figure 1: \( 4 \times 1^2 + 4 \times (1-1) = 4 \)
- Figure 2: \( 4 \times 2^2 + 4 \times (2-1) = 16 + 4 = 20 \)
We can extrapolate further a bit incorrectly. Instead, note that:
- For Figure 3 onward, therefore calculate based on a specific addition for matchsticks needed.
Calculating based on the given values:
- Figure 3: 64, (Building a logical assumption based on match usage such as increased by next layer).
- Figure 4: 100 (total of 4 matchsticks per edge squares counted)
- Figure 5: correct find \(16, 36, 64, 100\).
Completed Table:
| Figure Number | Matchsticks Needed | |---------------|--------------------| | 1 | 16 | | 2 | 36 | | 3 | 64 | | 4 | 100 | | 5 | 144 |
Thus the matchsticks counts are \( 16, 36, 64, 100 \), and for \( Figure 5\), it can be inferred based on a continuing formation which is 144 \( clustering squares forms. \)
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