Solving the Street Light Problem: A Comprehensive Guide

Understanding the Problem

The problem at hand involves determining the distance between the first and seventh street lights placed along a straight road at equal intervals. Understanding the arithmetic sequence formed by these street lights is crucial to solving the problem.

The Positioning of Street Lights

Let's denote the distance between each pair of street lights as d. The positions of the street lights can be represented as follows:

1st Light: Position 0 2nd Light: Position d 3rd Light: Position 2d 4th Light: Position 3d 5th Light: Position 4d 6th Light: Position 5d 7th Light: Position 6d

The problem states that the distance between the third and fifth street lights is 16.8 meters. This will be our starting point for solving the problem.

Calculating the Distance Between Each Light

Let's start by identifying the distance between the 3rd and 5th street lights:

The position of the 5th light: 4d The position of the 3rd light: 2d The distance between them: 4d - 2d 2d

This distance is given as 16.8 meters:

2d 16.8

Solving for d (the common difference), we get:

d 16.8 divide; 2 8.4 meters

Total Distance Between the 1st and 7th Street Light

Now, let's calculate the distance between the first and seventh street lights:

The position of the 7th light: 6d The distance between them: 6d - 0 6d

Substituting d 8.4 meters into the equation, we get:

6d 6 × 8.4 50.4 meters

Therefore, the distance from the first street light to the seventh street light is 50.4 meters.

Conclusion

By following the steps outlined above, we can solve the problem of determining the distance between the first and seventh street lights. Understanding the common difference and the arithmetic sequence formed by the street lights is key to finding the solution.

If you're dealing with similar problems or need further clarification, feel free to explore more resources on arithmetic sequences and basic algebraic equations.