Problem 80 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The sequence for the number of seats per row in our movie theater as the rows move toward the back is arithmetic with \(d=1\) so people don't block the view of those in the row behind them.

Step-by-Step Solution

Answer

The statement does not make sense because the reasoning given is incorrect. Having an arithmetic sequence for the number of seats doesn't ensure an unobstructed view. It's the step-up from one row to the next that could help the viewers in the back see past those in front.

Step 1: Understanding the problem

The problem discusses a movie theater where the number of seats per row increases as we move toward the back. It is stated that this is an arithmetic sequence with a common difference (d) of 1. An arithmetic sequence is characterized by a common difference, i.e., each term is obtained by adding a constant difference to the previous term.

Step 2: Analyzing the statement's logic

The provided explanation assumes that increasing the number of seats by one in each successive row (forming an arithmetic sequence with d=1) will prevent viewers in the back rows from having their view blocked by viewers in front of them. Note that increasing the number of seats wouldn't raise the height of the seats in the back rows, so it doesn't directly prevent obstruction of view. It's the slope or step-up from one row to the next that could help viewers see past those in front. Therefore, the given reasoning for sequence doesn't effectively assure the unobstructed view.

Step 3: Conclusion based on the analysis

Based on the analysis, the statement does not make sense, as the explanation provided is incorrect. While the seating arrangement may indeed follow an arithmetic sequence, this does not necessarily ensure that viewers in the back rows will have an unobstructed view.