Visual Sequence Problem: Finding Square Count in 8th Element

Question

Below is a sequence represented by squares. How many squares will there be in the 8th element?

00:00 Find the 8th term

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

00:25 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

00:42 Let's substitute the corresponding term position and calculate

00:47 And this is the solution to the question

It is apparent, that for each successive number, a square is added in length and one in width.

Hence, the rule using the variable n is:

$a(n)=n^2$

Therefore, the eighth term will be:

$n^2=8\times8=16$

$64$