Using a geometric sequence, it is found that the number of black squares in the first five figures of the Sierpinski Carpet is of 4681.
What is a geometric sequence?
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio r.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of the first n terms of a sequence is given by:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
In this problem, the parameters are: [tex]a_1 = 1, r = 8, n = 5[/tex], hence:
[tex]S_n = \frac{1(1 - 8^5)}{1 - 8} = 4681[/tex]
The number of black squares in the first five figures of the Sierpinski Carpet is of 4681.
More can be learned about geometric sequences at https://brainly.com/question/11847927
