\boxed{2520}Question: An industrial designer creates a series of modular shelves where each shelf has 4 more panels than the previous one. If the first shelf has 7 panels, how many shelves can be built with a total of 150 panels?

Sat, 02 May 2026 15:05:13 +0000

Title: How Industrial Designers Use Math: Building Modular Shelves with 2520 Panels Using Sequences When industrial designers craft modular shelving systems, they often rely on precise mathematical patterns to ensure efficiency, scalability, and aesthetic harmony. One fascinating example involves a modular shelf design where each shelf increases by a fixed number of panels—specifically 4 more panels than the previous one. Let’s explore how designers calculate the number of shelves possible when working within a limited material budget, using a real-world problem:
Given:
- The first shelf has 7 panels.
- Each subsequent shelf has 4 more panels than the prior.
- Total available panels: 150.
Question: How many modular shelves can be built? This scenario follows the arithmetic sequence pattern, where:
- First term \\( a = 7 \\)
- Common difference \\( d = 4 \\)
- Total panels for \\( n \\) shelves is \\( S_n = 150 \\)