Square Counting in Geometric Patterns: Finding the 6th Element

To solve this problem, we will determine the number of small squares in the 6th element of the given sequence:

• Step 1: Identify the pattern in the sequence of squares. Typically, a pattern like this follows square numbers, $n^2$, where $n$ is the order of the element.
• Step 2: Examine the progression from a previously known element. For a geometric sequence involving squares, the $n$-th element often has $n^2$ squares.
• Step 3: Compute the number of squares for the 6th element: Find $(6)^2 = 36$ squares. This confirms the pattern assumption and calculation.

Therefore, the solution to the problem is $36$.