Square Pattern Sequence: Finding the Number of Squares in the 5th Element

Below is a sequence represented by squares. How many squares will there be in the 5 element?

Video Solution

Solution Steps

00:00 Find the 5th term in the sequence

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

00:36 Therefore, we can conclude this is the sequence formula

00:43 Let's substitute the corresponding term position and calculate

00:51 And this is the solution to the question

Step-by-Step Solution

To solve the problem, we will analyze the sequence of element growth:

Step 1: Identify the pattern in the sequence from the image.
- Normally, a sequence of squares that increases in size might do so according to $n^2$ (a perfect square sequence).
- Observing the sequence, we see that the first element has $1^2 = 1$ square, the second element has $2^2 = 4$ squares, the third has $3^2 = 9$ squares, and the fourth follows similarly.
Step 2: Apply the identified pattern to compute the 5th element of the sequence.
- When following the pattern $n^2$ , the 5th element would naturally contain $5^2 = 25$ squares.

Thus, the number of squares in the 5th element of the sequence is $25$ .