Square Pattern Sequence: Finding the Structure with 64 Units

The following is a series of structures formed by squares with side lengths of 1 cm.

In which structure (element) of the series are there 64 squares?

To solve this problem, follow these steps:

• Step 1: Identify the formula for the sequence.
• Step 2: Set up the equation to reflect the total number of squares as n².
• Step 3: Solve for n such that n² = 64.

Now, let's work through each step:

Step 1: The sequence in question forms larger squares with each subsequent position based on the SVG graphic provided.

Step 2: We know that the nth position has n² squares: $n^2 = 64$.

Step 3: Solving for n in the equation $n^2 = 64$, we take the square root of both sides:

$n = \sqrt{64} = 8$.

Therefore, the structure with 64 squares occurs at the 8th position in the series.

Thus, the correct answer is $8$.