Square Counting in Sequences: Analyzing the Fourth Element Pattern

To solve this problem, we'll examine the pattern of how squares are arranged in each element:

• Step 1: Identify the initial pattern.
  Typically, the series or pattern of squares starts with fewer counts and increases steadily. For example, the first few elements can be manually visualized or described, for instance, as a straightforward progression such as the first element having one square, the second having three squares, the third having five squares, and so forth.
• Step 2: Recognize the pattern.
  If we observe this pattern, perhaps the difference between sequential numbers is a common increment. If we visualize this numerically, starting from the first element, it reflects 1, 3, 5... from which we can assume an odd number pattern. Next, generalize these as 1, 3, 5, 7 (the sequence of odd numbers) specifically for each sequential element.
• Step 3: Solve for the fourth element.
  Based on the established or observed sequence of odd numbers, the fourth element will match the fourth odd number, which is 7.

Therefore, by identifying this odd-number pattern in the sequence of squares, we confirm that the fourth element contains $7$ squares.