Solution: Let the number of shelves be \( n \). The number of panels forms an arithmetic sequence: 7, 11, 15, ..., with first term \( a = 7 \) and common difference \( d = 4 \). The sum of the first \( n \) terms is:

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

Solution: Let the Number of Shelves Be \\( n \\)—Understanding the Panel Arrangement in an Arithmetic Sequence In modular design and retail shelving, optimizing space while maintaining aesthetic harmony is crucial. One practical solution involves arranging panels in a structured arithmetic sequence—a method ideal for uniform display and scalable construction. This article explores a key mathematical solution for shelves arranged using a specific arithmetic progression, helping designers and engineers calculate total panel count efficiently. Let the number of shelves be \\( n \\). The width or placement of panels follows an arithmetic sequence starting with first term \\( a = 7 \\) and common difference \\( d = 4 \\). This means the number of panels at each shelf increases consistently: 7, 11, 15, ..., forming a clear pattern. ### The Arithmetic Sequence in Shelf Design