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?

Video Solution

Solution Steps

00:00 Will there be a term with 64 squares? If so, at what position?

00:04 Let's count the squares in each term

00:26 We see that the number of squares equals the term's position in the sequence

00:32 Therefore we can conclude this is the sequence formula

00:42 We want to find if there's a term with 64 squares

00:47 We'll substitute in the formula and solve for N

00:50 We'll take the square root to isolate N

00:54 N must be positive, there's no negative position in the sequence

00:58 And this is the solution to the question

Step-by-Step Solution

To solve this problem, follow these steps:

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 $8$ .