3. 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. b. Recursive: a = c. Explicit: a_ = f(m) = d. What would the perimeter of the 15 of the fractal? |Show your work here:
3. 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. b. Recursive: a = c. Explicit: a_ = f(m) = d. What would the perimeter of the 15 of the fractal? |Show your work here:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![### Fractal Pattern Analysis
**Instructions:**
Use the fractal pattern to write the recursive and explicit formula.
**Fractal Diagram:**
- The image shows four squares, increasing in number of smaller red squares within each larger square as they progress.
- Each square's side length seems to multiply by an increasing factor with each term.
**Tasks:**
**a. Calculate Perimeters:**
Determine the perimeter for the first four terms. Assume each side of the first term is 1 unit.
**b. Recursive Formula:**
Develop a recursive formula for the sequence:
- \( a_1 = \)
- \( a_n = \)
**c. Explicit Formula:**
Develop an explicit formula for the sequence:
- \( a_1 = \)
- \( r = \)
- \( f(n) = \)
**d. Perimeter Calculation:**
Calculate the perimeter of the 15th fractal term.
To solve, input your calculations in the space provided:
**Show your work here:**
[Space for calculation]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17474514-9340-40f1-94d8-ebb350c2aeb9%2Fa6ab6741-8d76-4269-8184-9a8b3dece923%2Fdrwzvrf_processed.png&w=3840&q=75)
Transcribed Image Text:### Fractal Pattern Analysis
**Instructions:**
Use the fractal pattern to write the recursive and explicit formula.
**Fractal Diagram:**
- The image shows four squares, increasing in number of smaller red squares within each larger square as they progress.
- Each square's side length seems to multiply by an increasing factor with each term.
**Tasks:**
**a. Calculate Perimeters:**
Determine the perimeter for the first four terms. Assume each side of the first term is 1 unit.
**b. Recursive Formula:**
Develop a recursive formula for the sequence:
- \( a_1 = \)
- \( a_n = \)
**c. Explicit Formula:**
Develop an explicit formula for the sequence:
- \( a_1 = \)
- \( r = \)
- \( f(n) = \)
**d. Perimeter Calculation:**
Calculate the perimeter of the 15th fractal term.
To solve, input your calculations in the space provided:
**Show your work here:**
[Space for calculation]
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