Question

Use the fractal pattern to write the recursive and explicit formula. a. What is the perimeter of each term? List the perimeter of the first 4 terms. Assume each side of the first term is 1 unit.

Answer 1

The recursive formula for the perimeter of the fractal pattern is P(n) = 4 * P(n-1), and the explicit formula is P(n) = 4^n. The perimeter of the first 4 terms is 4, 16, 64, and 256.

Step-by-step explanation:

The perimeter of each term in the fractal pattern can be determined by multiplying the side length by 4. So, the recursive formula for the perimeter (P) is P(n) = 4 * P(n-1), where P(n-1) is the perimeter of the previous term. The explicit formula for the perimeter of the nth term is P(n) = 4^n.

The perimeter of the first 4 terms can be calculated using the recursive formula or the explicit formula. Using the recursive formula, the perimeter of the first term is 4, the perimeter of the second term is 16, the perimeter of the third term is 64, and the perimeter of the fourth term is 256. Using the explicit formula, the perimeter of the first term is 4^1 = 4, the perimeter of the second term is 4^2 = 16, the perimeter of the third term is 4^3 = 64, and the perimeter of the fourth term is 4^4 = 256.