Hello,
This figure shows the number of segments used to form longer and longer rows of squares.
It shows that 1 square has 4 segments
2 squars has 7 segments and 3 squares has 10 segments.
The question is how many segments will be in a row with 100 squares?
Thought maybe a proportion, but I'm not sure what to do.
If you make a table its simple
X|Y
1|4 (1*3+1=4)
2|7 (2*3+1=7)
3|10 (3*3+1=10)
100|? (100*3+1=301
SO the answer is there will be 301 segments.
Oh, so you had to find a pattern...
Thanks
To find the number of segments in a row with 100 squares, we can analyze the pattern in the given figures and look for any relationships that may help us find a solution.
Let's break it down step by step:
1. Analyzing the given figures:
- 1 square has 4 segments.
- 2 squares have 7 segments.
- 3 squares have 10 segments.
2. Determining the pattern:
- As the number of squares increases by 1 (i.e., from 1 to 2 or from 2 to 3), the number of segments increases by 3 (i.e., from 4 to 7 or from 7 to 10).
3. Identifying the relationship:
- There is a linear relationship between the number of squares and the number of segments.
- The increase in the number of segments is constant (3 additional segments for each additional square).
4. Calculating the number of segments in a row with 100 squares:
- We can use the relationship we identified to calculate the number of segments in a row with 100 squares by extending the pattern.
- To find the number of segments in a row with 100 squares, we can start with the number of segments in the last given figure (10 segments) and add 3 segments for every additional square until we reach 100 squares:
- 10 segments + (3 segments/square) × (100 squares - 3 squares) = 10 + (3 × 97) = 10 + 291 = 301 segments.
Therefore, a row with 100 squares will have 301 segments.