Question

Use the formula to determine the number of black squares in the first five figures of the Sierpinski Carpet given by the partial sum:

For this sum:
a1 = 1
r = 8
n = 5

The number of squares in the first five figures is = 4681

Answer 1

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:

$a_n = a_1r^{n-1}$

In which $a_1$ is the first term.

The sum of the first n terms of a sequence is given by:

$S_n = \frac{a_1(1 - r^n)}{1 - r}$

In this problem, the parameters are: $a_1 = 1, r = 8, n = 5$, hence:

$S_n = \frac{1(1 - 8^5)}{1 - 8} = 4681$

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

Answer 2

Answer:

1, 8, 5

Step-by-step explanation:

4681, 2,396,745