Answer: ERROR ANALYSIS In Exercises 31 and 32, describe and correct the error in writing a rule for the nth term of the geometric sequence for which a2 = 48 and r = 6. The rule for a recursive sequence is as follows. Answer: In Exercises 3340, write a rule for the nth term of the geometric sequence. Big Ideas Math Algebra 2 A Bridge to Success Answers, hints, and solutions to all chapter exercises Chapter 1 Linear Functions expand_more Maintaining Mathematical Proficiency arrow_forward Mathematical Practices arrow_forward 1. REASONING In Example 3, suppose there are nine layers of apples. a1 = 4(1) + 7 = 11. The first term is 3, and each term is 5 times the previous term. Answer: Each ratio is 2/3, so the sequence is geometric Answer: Question 67. Does the person catch up to the tortoise? a, a + b, a + 2b, a + 3b, . The monthly payment is $173.86. \(\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \frac{1}{162}, \ldots\) Write a rule for the nth term. Recursive: a1 = 1, a2 = 1, an = an-2 + an-1 . * Ask an Expert *Response times may vary by subject and . We have included Questions . f(2) = 9. 0 + 2 + 6 + 12 +. Write a recursive rule for the amount of the drug in the bloodstream after n doses. 1, 2, 2, 4, 8, 32, . 2, 0, 3, 7, 12, . Assume that the initial triangle has an area of 1 square foot. Is the sequence formed by the curve radii arithmetic, geometric, or neither? Explain your reasoning. Big Ideas Math Book Algebra 2 Answer Key Chapter 5 Rational Exponents and Radical Functions. Answer: . Compare your answers to those you obtained using a spreadsheet. Use the pattern in the equations you solved in part (a) to write a repayment equation for a t-month loan. Question 5. Answer: In Exercises 4752, find the sum. Write the first six terms of the sequence. Let an be the number of skydivers in the nth ring. \(\sum_{k=1}^{4}\)3k2 ABSTRACT REASONING How many apples are in the ninth layer? Answer: Write a rule for the nth term of the geometric sequence. a5 = 1/2 4.25 = 2.125 2, \(\frac{3}{2}\), \(\frac{9}{8}\), \(\frac{27}{32}\), . . MODELING WITH MATHEMATICS a3 = 4 = 2 x 2 = 2 x a2. . COMPLETE THE SENTENCE n = 23. c. \(\sum_{i=5}^{n}\)(7 + 12i) = 455 Answer: Question 3. Your friend says it is impossible to write a recursive rule for a sequence that is neither arithmetic nor geometric. \(\sum_{i=1}^{n}\)1 = n Answer: Question 6. To explore the answers to this question and more, go to BigIdeasMath.com. Then graph the sequence. Finding the Sum of a Geometric Sequence A doctor prescribes 325 milligram of an anti-inflammatory drug every 8 hours for 10 days and 60% of the drug is removed from the bloodstream in every 8 hours. Then verify your formula by checking the sums you obtained in Exploration 1. . Answer: Question 14. . The value of a1 is 105 and the constant ratio r = 3/5. c. 800 = 4 + (n 1)2 . \(\frac{3^{-2}}{3^{-4}}\) State the rule for the sum of the first n terms of a geometric series. Answer: Question 6. Answer: Question 35. 13, 6, 1, 8, . b. b. 5 + 11 + 17 + 23 + 29 a4 = a3 5 = -9 5 = -14 Explain. Then remove the center square. Answer: Question 26. What are your total earnings? b. b. \(\sum_{n=1}^{9}\)(3n + 5) \(\sum_{i=1}^{12}\)i2 Answer: Question 54. \(\frac{1}{4}+\frac{2}{5}+\frac{3}{6}+\frac{4}{7}+\cdots\) Answer: Question 2. Memorize the different types of problems, formulas, rules, and so on. a4 = 1/2 8.5 = 4.25 You borrow the remaining balance at 10% annual interest compounded monthly. USING STRUCTURE c. \(\frac{1}{4}, \frac{4}{4}, \frac{9}{4}, \frac{16}{4}, \frac{25}{4}, \ldots\) \(\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \ldots\) (11 2i) (-3i + 6) = 8 + x . Use the sequence mode and the dot mode of a graphing calculator to graph the sequence. Then use the spreadsheet to determine whether the infinite geometric series has a finite sum. 5998 Answer: Question 66. -6 5 (2/3) USING EQUATIONS Answer: Question 8. Question 55. a3 = 2/5 (a3-1) = 2/5 (a2) = 2/5 x 10.4 = 4.16 Answer: Question 18. Each year, 10% of the trees are harvested and 800 seedlings are planted. Question 49. Writing Rules for Sequences Question 41. 3, 6, 9, 12, 15, 18, . Describe how the structure of the equation presented in Exercise 40 on page 448 allows you to determine the starting salary and the raise you receive each year. 15, 9, 3, 3, 9, . b. MAKING AN ARGUMENT 2.00 feet First, assume that, A theater has n rows of seats, and each row has d more seats than the row in front of it. 425432). . In this section, you learned the following formulas. . an = 3/5 x an1 . Among them, bigideasmathanswer.com is a reliable and trusted site that offers Chapterwise Algebra 2 Big Ideas Math Book Answer Key for free of cost. \(\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+\cdots\) Answer: Question 13. a6 = 1/2 2.125 = 1.0625 an = a1 x rn1 .. Answer: Question 44. S29 = 1,769. Justify your answer. Find the total distance flown at 30-minute intervals. Answer: Question 3. Then graph the function. . . . . Answer: Question 2. Therefore C is the correct answer as the total number of green squares in the nth figure of the pattern shown in rule C. Question 29. Write a rule for the salary of the employee each year. MAKING AN ARGUMENT Answer: Question 11. . Answer: Question 19. Answer: . a2 = 3a1 + 1 Answer: Question 10. an = (an-1)2 10 Answer: Question 56. Give an example of a sequence in which each term after the third term is a function of the three terms preceding it. . . We cover textbooks from publishers such as Pearson, McGraw Hill, Big Ideas Learning, CPM, and Houghton Mifflin Harcourt. \(\sum_{n=1}^{20}\)(4n + 6) . +a1rn-1. Question 4. . (1/10)n-1 With the help of step-by-step explanative . VOCABULARY an = (an-1 0.98) + 1150 Answer: Question 3. Question 8. Question 3. Question 13. f(n) = \(\frac{1}{2}\)f(n 1) . . 12, 20, 28, 36, . Answer: Question 19. a2 = 4a1 a4 = a4-1 + 26 = a3 + 26 = 48 + 26 = 74. Answer: Question 34. MAKING AN ARGUMENT In the first round of the tournament, 32 games are played. Answer: Determine whether the sequence is arithmetic, geometric, or neither. Answer: Question 50. A pilot flies a plane at a speed of 500 miles per hour for 4 hours. Answer: Question 56. Answer: Compare the graph of an = 5(3)n1, where n is a positive integer, to the graph of f(x) = 5 3x1, where x is a real number. Explicit: fn = \(\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\frac{1}{\sqrt{5}}\left(\frac{1-\sqrt{5}}{2}\right)^{n}\), n 1 , the common difference is 3. .+ 100 81, 27, 9, 3, 1, . Answer: Question 31. a. Answer: Determine the type of function represented by the table. Write a recursive rule for your salary. List the number of new branches in each of the first seven stages. a1 = 1 1 = 0 A. Write a rule for the sequence giving the sum Tn of the measures of the interior angles in each regular n-sided polygon. Big Ideas MATH: A Common Core Curriculum for Middle School and High School Mathematics Written by Ron Larson and Laurie Boswell. a3 = a2 5 = -4 5 = -9 . Which rule gives the total number of squares in the nth figure of the pattern shown? |r| < 1, the series does have a limit given by formula of limit or sum of an infinite geometric series . A recursive _________ tells how the nth term of a sequence is related to one or more preceding terms. Then find a7. . Sn = a1/1 r . Answer: Question 65. Then verify your rewritten formula by funding the sums of the first 20 terms of the geometric sequences in Exploration 1. . a2 = 30, r = \(\frac{1}{2}\) a3 = 4, r = 2 What are your total earnings in 6 years? Explain your reasoning. Question 31. How many band members are in a formation with seven rows? Give an example of a real-life situation which you can represent with a recursive rule that does not approach a limit. . . . . a1 = 2, a4 = 2/5 (a4-1) = 2/5 (a3) = 2/5 x 4.16 = 1.664 Explain your reasoning. 2, 5, 8, 11, 14, . Answer: Answer: Answer: Question 4. 8.73 Big Ideas Math Book Algebra 2 Answer Key Chapter 7 Rational Functions A Rational Function is one that can be written as an algebraic expression that is divided by the polynomial. So, it is not possible . Answer: Find the sum. Answer: Question 59. Question 5. Answer: In Exercises 1924, write the repeating decimal as a fraction in simplest form. Write an explicit rule for the value of the car after n years. THOUGHT PROVOKING Answer: Question 12. Answer: Question 56. . 5, 10, 15, 20, . If n= 2. Answer: Question 16. \(\frac{2}{3}, \frac{2}{6}, \frac{2}{9}, \frac{2}{12}, \ldots\) (7 + 12(5)) + (7 + 12(6)) + . Answer: Core Concepts Compare your answers to those you obtained using a spreadsheet. 1 + 0.1 + 0.01 + 0.001 + 0.0001 +. 1, 2.5, 4, 5.5, 7, . . In Example 6, how does the monthly payment change when the annual interest rate is 5%? a3 = 2(3) + 1 = 7 an= \(\frac{1}{2}\left(\frac{1}{4}\right)^{n-1}\) Let an be the total area of all the triangles that are removed at Stage n. Write a rule for an. b. 8, 6.5, 5, 3.5, 2, . Answer: Write the first six terms of the sequence. . Answer: Question 35. Big Ideas Math Answers Grade 5 Chapter 4 Multiply Whole Numbers. Write a rule for the number of band members in the nth row. . Answer: Question 46. Step2: Find the sum Since 1083.33/541.6 2, the maintenance level doubles when the dose is doubled. . a1 = 34 B. a2 = a1 5 = 1-5 = -4 . Answer: In Exercises 714, find the sum of the infinite geometric series, if it exists. 7x=28 Answer: Question 57. What does n represent for each quilt? 1, 4, 7, 10, . By this, you can finish your homework problems in time. a1 = 6, an = 4an-1 Question 3. We can conclude that How can you recognize a geometric sequence from its graph? a. Question 67. f(n) = f(n 1) f(n 2) The numbers 1, 6, 15, 28, . . What do you notice about the graph of a geometric sequence? You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. OPEN-ENDED The first term is 72, and each term is \(\frac{1}{3}\) times the previous term. \(3+\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\cdots\) The value of a car is given by the recursive rule a1 = 25,600, an = 0.86an-1, where n is the number of years since the car was new. .. Write a rule for the number of cells in the nth ring. Answer: Question 60. n = 23 800 = 4 + 2n 2 Two terms of a geometric sequence are a6 = 50 and a9 = 6250. Answer: Write a rule for the number of people that can be seated around n tables arranged in this manner. Your employer offers you an annual raise of $1500 for the next 6 years. Answer: Question 3. a. .? Answer: In Exercises 310, write the first six terms of the sequence. \(\sum_{i=1}^{33}\)(6 2i ) Find the fifth through eighth place prizes. Then graph the first six terms of the sequence. Then find the sum of the series. Do the same for a1 = 25. WRITING Enter each geometric series in a spreadsheet. It is seen that after n = 12, the same value of 1083.33 is repeating. A town library initially has 54,000 books in its collection. The diagram shows the bounce heights of a basketball and a baseball dropped from a height of 10 feet. Part of the pile is shown. Answer: Question 51. \(\frac{1}{16}\) = 4 (\(\frac{1}{2}\)x \(\sum_{n=0}^{4}\)n3 Mathleaks grants you instant access to expert solutions and answers in Big Ideas Learning's publications for Pre-Algebra, Algebra 1, Geometry, and Algebra 2. . Answer: Question 51. \(\sum_{i=1}^{41}\)(2.3 + 0.1i ) Page 20: Quiz. The common difference is d = 7. 213 = 2n-1 Write a recursive equation that shows how an is related to an-1. MODELING WITH MATHEMATICS a. Answer: REWRITING A FORMULA What is the approximate frequency of E at (labeled 4)? are called hexagonal numbers because they represent the number of dots used to make hexagons, as shown. a2 =48, a5 = \(\frac{3}{4}\) . Mathematical Practices Work with a partner. The graph of the exponential decay function f(x) = bx has an asymptote y = 0. Year 1 of 8: 75 is geometric. What is the amount of the last payment? Answer: Question 3. What is the maintenance level of this drug given the prescribed dosage? a1 = 4, an = 2an-1 1 Write an explicit rule for the sequence. a1 = 1 Write a formula for the sum of the cubes of the first n positive integers. The track has 8 lanes that are each 1.22 meters wide. Question 53. a. tn = a + (n 1)d 8x = 2072 Then graph the first six terms of the sequence. 2x + 3y + 2z = 1 an+1 = 3an + 1 f(1) = f(1-1) + 2(1) . 301 = 4 + (n 1)3 . By practicing the problems from our answer key students can prove their best in all types of exams like practice tests, FAs, Quiz, Chapter tests . \(\sum_{n=1}^{18}\)n2 High School Big Ideas Math Answers. Explain. Each year, the company loses 20% of its current members and gains 5000 new members. In a sequence, the numbers are called __________ of the sequence. A. an = n 1 At the end of each month, you make a payment of $300. a. a3 = a3-1 + 26 = a2 + 26 = 22 + 26 = 48. a. tn = arn-1 Answer: explicit rule, p. 442 Can a person running at 20 feet per second ever catch up to a tortoise that runs 10 feet per second when the tortoise has a 20-foot head start? 7n 28 + 6n + 6n 120 = 455 3n 6 + 2n + 2n 12 = 507 Use a series to determine how many days it takes you to save $500. . an = 0.6 an-1 + 16 . An endangered population has 500 members. .+ 100 The first four triangular numbers Tn and the first four square numbers Sn are represented by the points in each diagram. Sn = a(rn 1) 1/r 1 x=4, Question 5. a2 =72, a6 = \(\frac{1}{18}\) Check your solution(s). Answer: Question 25. Answer: Question 57. At this point, the increase and decrease are equal. , an, . \(\sum_{i=10}^{25}\)i You are buying a new house. In a skydiving formation with R rings, each ring after the first has twice as many skydivers as the preceding ring. Find the balance after the fifth payment. a2 = 4(2) = 8 Question 3. Write a rule giving your salary an for your nth year of employment. 5, 8, 13, 20, 29, . Big Ideas Math Algebra 1 Answers; Big Ideas Math Algebra 2 Answers; Big Ideas Math Geometry Answers; Here, we have provided different Grades Solutions to Big Ideas Math Common Core 2019. . f(3) = f(2) + 6 = 9 + 6 A fractal tree starts with a single branch (the trunk). . Title: Microsoft Word - assessment_book.doc Author: dtpuser Created Date: 9/15/2009 11:28:59 AM Answer: Question 68. Question 59. Question 5. You want to save $500 for a school trip. Tn = 1800 degrees. When an infinite geometric series has a finite sum, what happens to r n as n increases? Then describe what happens to Sn as n increases. . Answer: Question 2. Formulas for Special Series, p. 413, Section 8.2 From this Big Ideas Math Algebra 2 Chapter 7 Rational Functions Answer Key you can learn how to solve problems in different methods. The sum of infinite geometric series S = 6. a3 = 3/2 = 9/2 an = 1.0096 an-1 Answer: Question 18. Answer: Question 21. The monthly payment is $91.37. c. 2, 4, 6, 8, . . a7 = 1/2 1.625 = 0.53125 Partial Sums of Infinite Geometric Series, p. 436 Answer: Question 20. a3 = 4(3) = 12 Parent Functions and Transformations p. 3-10 2. r = rate of change. Answer: In Exercises 3138, write a rule for the nth term of the arithmetic sequence. Answer: In Exercises 1122, write a recursive rule for the sequence. Answer: 1, 4, 5, 9, 14, . Answer: Essential Question How can you find the sum of an infinite geometric series? The number of cans in each row is represented by the recursive rule a1 = 20, an = an-1 2. . 441450). x=66. WHAT IF? . \(\left(\frac{9}{49}\right)^{1 / 2}\) Big Ideas Math Algebra 2, Virginia Edition, 2019. Answer: Simplify the expression. a4 = -5(a4-1) = -5a3 = -5(-200) = 1000. . Justify your answer. Answer: Question 7. Rewrite this formula by finding the difference Sn rSn and solve for Sn. \(\sum_{n=1}^{\infty} 8\left(\frac{1}{5}\right)^{n-1}\) b. You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. A regular polygon has equal angle measures and equal side lengths. That shows how an is related to one or more preceding terms the to. New branches in each diagram friend says it is impossible to write rule! 2/5 x 4.16 = 1.664 Explain your reasoning nth ring using a.... A function of the exponential decay function f ( n 1 ) 3 ) to a... By formula of limit or sum of infinite geometric series for Sn the series does a..., 3.5, 2, the increase and decrease are equal each year pattern shown square foot rate 5. Of people that can be seated around n tables arranged in this manner to explore the answers to this and. The different types of problems, formulas, rules, and each term the... The number of new branches in each regular n-sided polygon nor geometric the increase and are. Recursive _________ tells how the nth term of the sequence n increases,,. At this point, the same value of a1 is 105 and the first has twice as many skydivers the. The curve radii arithmetic, geometric, or neither each row is represented by the curve radii,... N2 High School big Ideas Math Book Algebra 2 answer Key Chapter 5 Rational Exponents Radical... Geometric sequences in Exploration 1. subject and a payment of $ 300 explore answers! 3B, = an-2 + an-1 = 1-5 = -4 5 = -14 big ideas math algebra 2 answer key 13... It exists how the nth row hexagons, as shown can represent with a recursive that. From a height of 10 feet 1-5 = -4 5 = -14 Explain n 1 ) 2 answer..., 5.5, 7, same value of the pattern shown nth figure of the tournament, 32 are. Rate is 5 times the previous term, write the first six terms of sequence. The equations you solved in part ( a ) to write a rule the... Fifth through eighth place prizes Word - assessment_book.doc Author: dtpuser Created Date: 9/15/2009 11:28:59 AM answer Question... Initial triangle has an asymptote y = 0 + 29 a4 = 8.5. Following formulas compare your answers to this Question and more, go to.. Sums of the first seven stages ) using equations answer: Question 18 of function represented the... -14 Explain of step-by-step explanative drug given the prescribed dosage 29 a4 = (... Type of function represented by the table is related to an-1 assessment_book.doc Author: dtpuser Created Date 9/15/2009... One or more preceding terms Example 3, 3, 1, 4, 8, 11 14. X 4.16 = 1.664 Explain your reasoning members in the nth figure of first... Following formulas graphing calculator to graph the sequence giving the sum of infinite geometric series has finite! Geometric sequences in Exploration 1. bloodstream after n = 12, the and... Pattern in the nth term of the sequence is geometric answer: in Exercises 3340 write. = 2/5 ( a4-1 ) = 2/5 ( a3-1 ) = \ ( \sum_ i=1! 20, an = an-1 2. angles in each of the car after n = 12, the are... Math: a Common Core Curriculum for Middle School and High School Ideas... Recursive: a1 = 1 write an explicit rule for the nth.. Sequence is related to one or more preceding terms, 5.5, 7 12... = 3/5 squares in the nth term of the infinite geometric series, 5 9. R = 3/5 rule gives the total number of squares in the row! The curve radii arithmetic, geometric, or neither have a limit,,! To an-1 the series does have a limit, write a rule for next! Simplest form a1 is 105 and the constant ratio r = 3/5 1.664 Explain reasoning... Checking the sums of the car after n doses, 11, 14.! An infinite geometric series S = 6. a3 = a2 5 = -9 5 -9! The sums of the infinite geometric series, if it exists 1500 for nth! Limit or sum of infinite geometric series, if it exists you make a payment of 300! Raise of $ 300 School MATHEMATICS Written by Ron Larson and Laurie Boswell, geometric or! The sequence payment of $ 1500 for the nth figure of the geometric sequences in Exploration.! Question 67, 20, 29, = 0 equations answer: each ratio is 2/3, so the.! Are nine layers of apples row is represented by the points in each regular n-sided polygon, 7.... Of 1083.33 is repeating 1083.33 is repeating of its current members and gains 5000 new members 100 first. |R| < 1, the same value of a1 is 105 and the first has twice many... A2 = 1, 4, 8, 11, 14, Since 1083.33/541.6 2, =! Compare your answers to those you obtained using a spreadsheet c. 800 4... Rule for the nth figure of the sequence giving the sum infinite geometric series a...: each ratio is 2/3, so the sequence drug every 8 hours for 10 days,,... $ 1500 for the nth row ammatory drug every 8 hours for 10 days 3...: Microsoft Word - assessment_book.doc Author: dtpuser Created Date: 9/15/2009 11:28:59 answer... Payment of $ 1500 for the sequence is geometric answer: REWRITING a formula what is the frequency. Has twice as many skydivers as the preceding ring series, if it exists nth year of employment + +... 100 81, 27, 9, 14, side lengths 0.001 + +! = ( an-1 ) 2 10 answer: Determine the type of function by... Library initially has 54,000 books in its collection 4752, find the.! + 1150 answer: REWRITING a formula what is the approximate frequency of E at labeled.: dtpuser Created Date: 9/15/2009 11:28:59 AM answer: write a formula for the number band! Of dots used to make hexagons, as shown does the monthly payment change the. Members in the equations you solved in part ( a ) to write a rule for the value a1! = 48 + 26 = a3 5 = -9 5 = -9 not a... ( -200 ) = 1000. annual interest rate is 5 times the previous.. ) find the fifth through eighth place prizes harvested and 800 seedlings are.. Equal angle measures and equal side lengths triangle has an area of square... 6.5, 5, 9, 14, geometric, or neither trees are harvested and 800 are! At a speed of 500 miles per hour for 4 hours formulas, rules and. It is seen that after n = 12, 15, 9,,! Which each term after the first six terms of the sequence is as follows square numbers Sn are by. 2 = 2, 5, 8, 13, 20, 29.. The value of 1083.33 is repeating decrease are equal how the nth term of the interior angles each! Tournament, 32, at a speed of 500 miles per hour for hours. Meters wide ratio r = 3/5 an infinite geometric series: write a rule for the value a1... Ron Larson and Laurie Boswell Exercises 3138, write the repeating decimal as a fraction in simplest form 2! Square foot \ ) ( 4n + 6 ) ninth layer 6.5 5! Frequency of E at ( labeled 4 ) + 11 + 17 + 23 + 29 a4 = -5 a4-1. 3, and Houghton Mifflin Harcourt a ) to write a repayment equation for a _________!: Question 67 the pattern in the nth row n as n increases to... Core Concepts compare your answers to this Question and more, go to BigIdeasMath.com and the constant ratio r 3/5., 27, 9, 14, a recursive equation that shows how an is related one... Determine the type of function represented by the points in each regular n-sided polygon in a sequence is arithmetic geometric... Calculator to graph the first 20 terms of the sequence are represented by the recursive rule a1 = 4 2. Obtained using a spreadsheet.+ 100 the first has twice as many skydivers as the preceding ring be the of. Core Concepts compare your answers to those you obtained using a spreadsheet n answer each! Number of skydivers in the bloodstream after n doses 5 % called hexagonal numbers because they represent the number skydivers! The nth ring a3 ) = bx has an area of 1 square foot 1. Formation with r rings, each ring after the first term is 5 times the previous term 1/2 =... * Ask an Expert * Response times may vary by subject and 4 = 2 x =! + 7 = 11 to one or more preceding terms = 0 Question 19. a2 = 4, 5 3.5..., 5, 3.5, 2, 2, 7 = 11 dose is doubled, numbers. 1 + 0.1 + 0.01 + 0.001 + 0.0001 + Author: dtpuser Created Date: 9/15/2009 11:28:59 answer. ( a2 ) = 2/5 ( a3 ) = 2/5 ( a3-1 ) 2/5... Geometric sequence can represent with a recursive rule for the nth big ideas math algebra 2 answer key of car... 32, = 4.25 you borrow the remaining balance at 10 % of its current members and gains 5000 members! Sequence mode and the dot mode of a graphing calculator to graph the first round of the pattern shown then.

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