Square Pattern Sequence: Finding the Number of Squares in the 7th Element

Question

Below is a sequence represented with squares. How many squares will there be in the 7th element?

Video Solution

Solution Steps

00:00 Find the 7th term
00:04 Let's count the squares in each term
00:26 We can see that the number of squares equals the term's position squared
00:33 Therefore we can conclude this is the sequence formula
00:41 Let's substitute the appropriate term position and calculate
00:45 And this is the solution to the question

Step-by-Step Solution

To solve the problem, follow these steps:

  • Step 1: Identify the pattern of the sequence in terms of squares.
  • Step 2: Verify that the sequence matches a particular formula or pattern, such as perfect squares.
  • Step 3: Calculate the 7th term using the pattern identified.

Now, let's work through the solution:

Step 1: Observe and decipher the pattern governing the sequence of squares. From the SVG hint of squares, it suggests a pattern linked to square numbers.

Step 2: Assume that the pattern is the sequence of perfect squares:
1st element has 12=11^2 = 1 square
2nd element has 22=42^2 = 4 squares
3rd element has 32=93^2 = 9 squares
This indicates a clear pattern of the nth element having n2n^2 squares.

Step 3: To find the 7th element, apply n2n^2 for n=7n=7:
72=49 7^2 = 49

Therefore, the number of squares in the 7th element of the sequence is 49\boxed{49}.

Answer

49 49