Square Pattern Analysis: Locating the 16-Square Structure in a Geometric Sequence

To solve this problem, we need to recognize the sequence formed by the given structures of squares.

First, observe the pattern:
- Structure 1: 1 square
- Structure 2: 4 squares (a 2x2 grid)
- Structure 3: 9 squares (a 3x3 grid)
- Structure 4: 16 squares (a 4x4 grid)

The number of squares in each structure corresponds to square numbers: 1, 4, 9, 16, etc. These numbers are significant as they follow the pattern $n^2$ where $n$ represents the position of the structure in the sequence.

Next, let's apply the pattern:

• Step 1: Recognize that the number of squares in each structure is given by $n^2$.
• Step 2: We need to find an $n$ such that $n^2 = 16$.
• Step 3: Solving $n^2 = 16$, we find $n = 4$.

Thus, the structure with 16 squares is the 4th element in the sequence.

Therefore, the correct answer is $4$.