Square Sequence Analysis: Finding the 6th Element Pattern

To solve this problem, we'll follow these steps:

• Identify the sequence pattern: it follows perfect squares.
• Associate each step with its corresponding perfect square number.
• Calculate the 6th element's number of squares using the formula $n^2$.

Now, let's work through each step:
Step 1: The sequence is defined by the perfect square numbers: $1^2, 2^2, 3^2, \ldots$.
Step 2: Each element in this sequence corresponds to an integer squared, revealing the sequence as $1, 4, 9, 16, 25, \ldots$.
Step 3: For the 6th element, calculate $6^2$:
$6^2 = 36$

Therefore, the solution to the problem is 36.