Square Pattern Sequence: Predicting the 4th Element Count

Below is a sequence represented by squares. How many squares will there be in the 4th element?

Video Solution

Solution Steps

00:00 Find the next member

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

00:29 We can see that the number of squares equals the member's position in the sequence

00:43 Therefore we can conclude this is the sequence formula

00:48 Let's substitute the appropriate member position and calculate

00:55 And this is the solution to the question

Step-by-Step Solution

To solve this problem, let's carefully determine the number of squares in each sequence element:

Step 1: Identify the sequence pattern.
Element 1: $1^2 = 1$ square.
Element 2: $2^2 = 4$ squares.
Element 3: $3^2 = 9$ squares.
Step 2: Recognize the pattern as the sequence of perfect squares.
For each element $n$ , the number of squares is $n^2$ .
Step 3: Calculate the number of squares in the fourth element.
Element 4: $4^2 = 16$ squares.

Thus, the fourth element in the sequence will have $16$ squares.