To complete the table for the number of matchsticks needed for constructing figures using squares of matchsticks, we can identify the pattern based on the provided numbers.
From the example you gave, we know:
- Figure 1 uses 16 matchsticks.
- Figure 2 uses 34 matchsticks.
- We need to find out how many matchsticks are needed for Figures 3, 4, and 5.
Understanding the Pattern
The increase in the number of matchsticks appears to follow a specific pattern as additional squares are added.
To determine how many matchsticks are needed for the next figures in the sequence, let’s calculate the differences between the number of matchsticks used for Figures 1 and 2:
- From Figure 1 to Figure 2:
- 34 - 16 = 18 (increase of 18 matchsticks)
Now, let’s see if the pattern continues in a similar manner.
Let's Calculate Figures 3, 4, and 5:
Now let’s write down the additional matchsticks needed for further figures:
-
For Figure 3, we have to find how many matchsticks are needed after Figure 2:
- Figure 3: We add 18 matchsticks (as we assume the increase remains the same here):
- \(34 + 18 = 52\)
-
For Figure 4:
- Continuing with the assumption of increasing by 18 matchsticks:
- \(52 + 18 = 70\)
-
For Figure 5:
- Again increasing by 18 matchsticks from Figure 4:
- \(70 + 18 = 88\)
Table Completion
Now, we can fill in the missing values in the table:
| Figure Number | Matchsticks Needed | |---------------|--------------------| | 1 | 16 | | 2 | 34 | | 3 | 52 | | 4 | 70 | | 5 | 88 |
Final Answer:
So the completed table will be:
| Figure Number | Matchsticks Needed | |---------------|--------------------| | 1 | 16 | | 2 | 34 | | 3 | 52 | | 4 | 70 | | 5 | 88 |