To find the distance between the first and the last sapling when there are 4 saplings planted in a row with a distance of [tex]\(\frac{3}{4}\)[/tex] meters between each adjacent sapling, let's go through the problem step-by-step.
1. Visualize the Saplings: Imagine the saplings are placed in a straight line:
```
S1 - S2 - S3 - S4
```
Here, [tex]\(S1\)[/tex] is the first sapling, [tex]\(S2\)[/tex] is the second sapling, [tex]\(S3\)[/tex] is the third sapling, and [tex]\(S4\)[/tex] is the fourth sapling.
2. Counting the Intervals: Notice that between 4 saplings, there are 3 intervals.
- The interval between [tex]\(S1\)[/tex] and [tex]\(S2\)[/tex]
- The interval between [tex]\(S2\)[/tex] and [tex]\(S3\)[/tex]
- The interval between [tex]\(S3\)[/tex] and [tex]\(S4\)[/tex]
3. Calculating Each Interval's Distance: Given that the distance between each pair of adjacent saplings is [tex]\(\frac{3}{4}\)[/tex] meters, each of these intervals measures [tex]\(\frac{3}{4}\)[/tex] meters.
4. Total Distance Calculation: Add the distances of all intervals to find the distance between the first sapling [tex]\(S1\)[/tex] and the last sapling [tex]\(S4\)[/tex]:
[tex]\[
\text{Total Distance} = (\text{Number of Intervals}) \times (\text{Distance per Interval})
\][/tex]
There are 3 intervals (as we have 4 saplings, so [tex]\(4 - 1 = 3\)[/tex]), and each interval is [tex]\(\frac{3}{4}\)[/tex] meters. Thus, the total distance is:
[tex]\[
\text{Total Distance} = 3 \times \frac{3}{4}
\][/tex]
5. Simplify the Multiplication:
[tex]\[
3 \times \frac{3}{4} = \frac{9}{4} = 2.25
\][/tex]
Therefore, the distance between the first and the last sapling is 2.25 meters.
