Throughout this lab, we will be transforming a triangle into the beginning stages of a fractal, called Sierpinski's triangle. Start with a solid equilateral triangle with sides of length 1.We will create two sequences, one whose terms are the area of the fractal at each step and another whose terms are the perimeter at each step.We will denote the terms of the area sequence by an and the terms of the perimeter sequence by pn.In order to create Sierpinski's triangle, at each step, we will be implementing the rule that everywill be replaced withWe can see that Question 1Under the proposed rule above, using the image given, determine a2 and p2. Question 2Create the third iteration of Sierpinski's Triangle and determine a3 and p3. Question 3Determine an and pn for n = 4, 5, and 6, and fill out the table below:n = 1anpn1 32 3 4 5 6 Question 4Find a closed-form for the nth term of .Question 5Determine the convergence/divergence of and explain. Question 6Construct a few steps of a similar fractal, called Sierpinski's Carpet, using the rule that everywill be replaced withSo, the 3rd stage would be .Determine if the behavior of the area and perimeter are similar to that of the Sierpinski's Triangle as n approaches .Explain and support your answers. Please see attached to fully understand the questios being asked. QUESTION 4Find a diosed form for the nth term of (a,): -1 and (p,) -1.PathpQUESTION 5Determine the convergence/divergence of (a,)-1 and (P.-1 and explain.TTT AnPuthpQUESTION 6Construct a few steps of asimilar fractal, called Sierpinskts Carpet, using the rule that everywill be replaced withSo, the 3rd stage would beDetermine if the behavior of the area and perimeter are similar to that of the Sierpinskis Triangle as napproachesExplain and support your arwers.ALlech lileBrowse My Computer Test InformationDescriptionYou have 1 attempt to complete this labassignment. You don't have to compiete the lab inane sitting and can oxit out of it to retum back at a later time. Do NOT select "Submir" until you're ready to submit your lab for gradingInstructionsThroughout this lab, we will be trancforming a triangle into the beginning stages of a fractal, called Sierpinski's triangle. Start with a sold equilateral triangle with sides of length 1.We will create two sequences, one whose terms are the area of the fractal at each step and another whose terms are the perimeter at cach step.We wil denote the terms of the area sequence by an and the terms of the perimeter sequence by Pn-In order to create Sierpinsk's triangle, at cach step, we will be implementing the rule that everywil be replaced withWe can see that a,- and p- 3Multiple Allempts Not allowed. This test can only be takem onceTurce Completian This test can be saved and resumed later.Question Completian Status:QUESTION 1Under the proposed rule above, using the iImage given, determineaz and P2Upload your work and your answersALlech lileBrowne My ComputarQUESTION 2Create the third iteration of Sierpinskt's Triangle and determine az and P3-Upload your work and your answers.ALlech lileBrowse My CompularQUESTION 3Determine an and pn for n=4,5, and 6, and fill out the table below:anPn1323.4ALlech fileBrowne My Copular

Question

Throughout this lab, we will be transforming a triangle into the beginning stages of a fractal, called Sierpinski's triangle. Start with a solid equilateral triangle with sides of length 1.We will create two sequences, one whose terms are the area of the fractal at each step and another whose terms are the perimeter at each step.We will denote the terms of the area sequence by an and the terms of the perimeter sequence by pn.In order to create Sierpinski's triangle, at each step, we will be implementing the rule that everywill be replaced withWe can see that     Question 1Under the proposed rule above, using the image given, determine a2 and p2.  Question 2Create the third iteration of Sierpinski's Triangle and determine a3 and p3.  Question 3Determine an and pn for n = 4, 5, and 6, and fill out the table below:n = 1anpn1 32  3  4  5  6    Question 4Find a closed-form for the nth term of  .Question 5Determine the convergence/divergence of    and explain. Question 6Construct a few steps of a similar fractal, called Sierpinski's Carpet, using the rule that everywill be replaced withSo, the 3rd stage would be  .Determine if the behavior of the area and perimeter are similar to that of the Sierpinski's Triangle as n approaches   .Explain and support your answers.   Please see attached to fully understand the questios being asked. QUESTION 4Find a diosed form for the nth term of (a,): -1 and (p,) -1.PathpQUESTION 5Determine the convergence/divergence of (a,)-1 and (P.-1 and explain.TTT AnPuthpQUESTION 6Construct a few steps of asimilar fractal, called Sierpinskts Carpet, using the rule that everywill be replaced withSo, the 3rd stage would beDetermine if the behavior of the area and perimeter are similar to that of the Sierpinskis Triangle as napproachesExplain and support your arwers.ALlech lileBrowse My Computer Test InformationDescriptionYou have 1 attempt to complete this labassignment. You don't have to compiete the lab inane sitting and can oxit out of it to retum back at a later time. Do NOT select &#34;Submir&#34; until you're ready to submit your lab for gradingInstructionsThroughout this lab, we will be trancforming a triangle into the beginning stages of a fractal, called Sierpinski's triangle. Start with a sold equilateral triangle with sides of length 1.We will create two sequences, one whose terms are the area of the fractal at each step and another whose terms are the perimeter at cach step.We wil denote the terms of the area sequence by an and the terms of the perimeter sequence by Pn-In order to create Sierpinsk's triangle, at cach step, we will be implementing the rule that everywil be replaced withWe can see that a,- and p- 3Multiple Allempts Not allowed. This test can only be takem onceTurce Completian This test can be saved and resumed later.Question Completian Status:QUESTION 1Under the proposed rule above, using the iImage given, determineaz and P2Upload your work and your answersALlech lileBrowne My ComputarQUESTION 2Create the third iteration of Sierpinskt's Triangle and determine az and P3-Upload your work and your answers.ALlech lileBrowse My CompularQUESTION 3Determine an and pn for n=4,5, and 6, and fill out the table below:anPn1323.4ALlech fileBrowne My Copular

Accepted Answer

We are entitled to solve only one question at a time. Please post other questions separately.
Given…

n = 1	a_n	p_n
1		3
2
3
4
5
6