an = 180(4 2)/4 Answer: In Exercises 714, find the sum of the infinite geometric series, if it exists. \(\sum_{n=1}^{5}\)(n2 1) 183 15. Copy and complete the table to evaluate the function. f(0) = 4 Answer: Question 58. Answer: Question 14. an = 180(n 2)/n Answer: Question 21. Explain how viewing each arrangement as individual tables can be helpful in Exercise 29 on page 415. Write an explicit rule and a recursive rule for the sequence in part (a). Compare the given equation with the nth term Question 15. Answer: Question 10. \(\sum_{n=1}^{9}\)(3n + 5) b. . Question 3. a. are called hexagonal numbers because they represent the number of dots used to make hexagons, as shown. an+ 1 = 1/2 an 7/7-3 Question 8. Compare the terms of an arithmetic sequence when d > 0 to when d < 0. explicit rule, p. 442 We have provided the Big Ideas Math Algebra 2 Answer Key in a pdf format so that you can prepare in an offline mode also. an = a1rn-1. Find the amount of the last payment. an = 30 4 Write a rule giving your salary an for your nth year of employment. . b. Answer: Question 62. \(\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\cdots\) Verify your formula by finding the sums of the first 20 terms of the arithmetic sequences in Exploration 1. Answer: Question 17. , the common difference is 3. 7, 1, 5, 11, 17, . Here is an example. \(\sum_{i=1}^{10}\)7(4)i1 Answer: Question 49. 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. Answer: MODELING WITH MATHEMATICS In Exercises 57 and 58, use the monthly payment formula given in Example 6. \(\sum_{n=1}^{16}\)n2 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? a1 = 6, an = 4an-1 Justify your answer. The value of each of the interior angle of a 7-sided polygon is 128.55 degrees. Find the population at the end of each decade. . The sum Sn of the first n terms of an infinite series is called a(n) ________. Question 15. a3 = 3 76 + 1 = 229 Tn = 180(12 2) In Example 6, how does the monthly payment change when the annual interest rate is 5%? Answer: In Exercises 1122, write a recursive rule for the sequence. a1 = -4, an = an-1 + 26. Answer: Then find a9. Then find y when x = 4. Question 7. Mathematical Practices . In Quadrature of the Parabola, he proved that the area of the region is \(\frac{4}{3}\) the area of the inscribed triangle. Question 1. Use the rule for the sum of a finite geometric series to write each polynomial as a rational expression. Answer: Question 14. .+ 15 a6 = -5(a6-1) = -5a5 = -5(-5000) = 25,000. Question 53. b. S = 1/1 0.1 = 1/0.9 = 1.11 Answer: Question 55. . Answer: Question 45. . Pieces of chalk are stacked in a pile. Answer: Write a rule for the nth term of the sequence. More textbook info . an = r . Answer: Question 3. MODELING WITH MATHEMATICS Question 62. Question 1. Justify your answer. Find the perimeter and area of each iteration. Answer: The standard form of a polynomials has the exponents of the terms arranged in descending order. Write a rule for the nth term. What can you conclude? The monthly payment is $213.59. y + z = 2 How do the answers in Example 7 change when the annual interest rate is 7.5% and the monthly payment is $1048.82? What are your total earnings? 3 + 4 5 + 6 7 You begin an exercise program. . . Answer: Question 23. when n = 7 MODELING WITH MATHEMATICS Answer: Question 4. n = -49/2 is a negatuve value. The length3 of the third loop is 0.9 times the length of the second loop, and so on. Question 9. Question 3. a. Question 23. Then describe what happens to Sn as n increases. b. 1 + 0.1 + 0.01 + 0.001 + 0.0001 +. 12, 20, 28, 36, . . 208 25 = 15 Let us consider n = 2. a, a + b, a + 2b, a + 3b, . Answer: Question 69. Year 2 of 8: 94 . Answer: Question 55. In 1202, the mathematician Leonardo Fibonacci wrote Liber Abaci, in which he proposed the following rabbit problem: Interpret your answer in the context of this situation. Justify your answer. Answer: In Exercises 310, tell whether the sequence is arithmetic. High School Big Ideas Math Answers. a3 = a3-1 + 26 = a2 + 26 = 22 + 26 = 48. Question 5. Write a rule for the arithmetic sequence with the given description. 2, 5, 10, 50, 500, . . f(5) = \(\frac{1}{2}\)f(4) = 1/2 5/8 = 5/16. Describe the type of decline. Then write a formula for the sum Sn of the first n terms of an arithmetic sequence. Sn = a1\(\left(\frac{1-r^{n}}{1-r}\right)\) . WHAT IF? Sn = a(rn 1) 1/r 1 Answer: Question 2. An online music service initially has 50,000 members. a1 = 4(1) + 7 = 11. Answer: Essential Question How can you find the sum of an infinite geometric series? Use each formula to determine how many rabbits there will be after one year. Question 3. f(5) = 33. a2 = 64, r = \(\frac{1}{4}\) . Answer: In Exercises 3138, write the series using summation notation. b. Answer: Question 11. \(\frac{3^{-2}}{3^{-4}}\) Answer: Question 25. 3n 6 + 2n + 2n 12 = 507 Use the given values to write an equation relating x and y. Question 11. Find the total number of games played in the regional soccer tournament. Question 41. CRITICAL THINKING an = 5, an = an-1 \(\frac{1}{3}\) 0.3, 1.5, 7.5, 37.5, 187.5, . Answer: Question 11. b. MODELING WITH MATHEMATICS (Hint: Let a20 = 0.) . The formation for R = 2 is shown. Question 31. . Write a recursive rule for the population Pn of the town in year n. Let n = 1 represent 2010. Answer: Question 29. Answer: Question 13. Then find the total number of squares removed through Stage 8. Describe the type of decline. Find step-by-step solutions and answers to Big Ideas Math Algebra 2: A Bridge to Success - 9781680331165, as well as thousands of textbooks so you can move forward with confidence. a1 = 34 . Answer: Question 3. Question 7. 0 + 2 + 6 + 12 +. .+ 100 You add chlorine to a swimming pool. f(0) = 10 . a4 = 3 229 + 1 = 688 Answer: In Exercises 512, tell whether the sequence is geometric. A recursive _________ tells how the nth term of a sequence is related to one or more preceding terms. Answer: Question 61. a1 = 32, r = \(\frac{1}{2}\) Answer: Question 2. Compare the terms of a geometric sequence when r > 1 to when 0 < r < 1. , an, . MODELING WITH MATHEMATICS Question 4. Answer: Question 27. There is an equation for it, a12 = 38, a19 = 73 . First, assume that, . Answer: Question 50. Look back at the infinite geometric series in Exploration 1. Write a formula for the sum of the cubes of the first n positive integers. 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. Justify your answers. a1 = -4.1 + 0.4(1) = -3.7 a5 = 1/2 4.25 = 2.125 Answer: Question 70. You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. S = a1/1-r Question 38. Explain your reasoning. Check out the modules according to the topics from Big Ideas Math Textbook Algebra 2 Ch 3 Quadratic Equations and Complex Numbers Solution Key. Then write the area as the sum of an infinite geometric series. , 800 Improve your performance in the final exams by practicing the Big Ideas Math Algebra 2 Answers Ch 8 Sequences and Series on a daily basis. 5.8, 4.2, 2.6, 1, 0.6 . . Tn = 1800 degrees. What was his prediction? \(\sum_{i=1}^{5} \frac{3+i}{2}\) Question 39. Write a recursive rule for each sequence. FINDING A PATTERN Then graph the first six terms of the sequence. Answer: Question 8. Answer: Find the total number of skydivers when there are four rings. COMPLETE THE SENTENCE . Answer: Question 4. f(0) = 4 and f(n) = f(n-1) + 2n \(\sum_{n=1}^{\infty}\left(-\frac{1}{2}\right)^{n-1}\) Answer: Question 14. The track has 8 lanes that are each 1.22 meters wide. \(\sum_{n=1}^{\infty} 8\left(\frac{1}{5}\right)^{n-1}\) 1, 2, 4, 8, 16, . Given, Complete homework as though you were also preparing for a quiz. Also, the maintenance level is 1083.33 an = 180/3 = 60 . as a fraction in simplest form. How many transistors will be able to fit on a 1-inch circuit when you graduate from high school? . \(\sum_{i=1}^{6}\)4(3)i1 Question 1. Since then, the companys profit has decreased by 12% per year. In the puzzle called the Tower of Hanoi, the object is to use a series of moves to take the rings from one peg and stack them in order on another peg. Answer: The lanes are numbered from 1 to 8 starting from the inside lane. At each stage, each new branch from the previous stage grows two more branches, as shown. Answer: Question 12. 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. Find the sum of each infinite geometric series, if it exists. February 15, 2021 / By Prasanna. b. Suppose the spring has infinitely many loops, would its length be finite or infinite? a1 = 1/2 = 1/2 Step2: Find the sum an = 60 A sequence is an ordered list of numbers. Let an be the number of skydivers in the nth ring. Answer: So, it is not possible Answer: Question 68. . Answer: Question 13. . Question 5. 441450). . What will your salary be during your fifth year of employment? Justify your answer. nth term of a sequence 4 52 25 = 15 You are buying a new house. 1, 2, 3, 4, . Answer: You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. a3 = 3/2 = 9/2 Answer: Question 22. . Calculate the monthly payment. . So, it is not possible Compare your answers to those you obtained using a spreadsheet. USING STRUCTURE b. Question 71. a1 = 2, a. . Answer: Question 26. Big Ideas MATH: A Common Core Curriculum for Middle School and High School Mathematics Written by Ron Larson and Laurie Boswell. . Answer: Question 1. S = 6 216=3(x+6) Answer: Question 10. ISBN: 9781680330687. When n = 3 Answer: Question 17. Answer: Question 21. Is b half of the sum of a and c? . Graph of a geometric sequence behaves like graph of exponential function. an = 3 + 4n Consider the infinite geometric series Write a recursive rule for the amount of the drug in the bloodstream after n doses. Answer: Question 3. b. . Solve the equation from part (a) for an-1. f(0) = 2, f (1) = 4 a1 = 16, an = an-1 + 7 Answer: Question 68. n = 399. b. S = 2/(1-2/3) y= 2ex Answer: Question 14. \(\sum_{k=1}^{\infty} \frac{11}{3}\left(\frac{3}{8}\right)^{k-1}\) Question 27. How is the graph of f similar? Show chapters. Does the recursive rule in Exercise 61 on page 449 make sense when n= 5? Answer: Question 5. Answer: Performance Task: Integrated Circuits and Moore s Law. . 7n 28 + 6n + 6n 120 = 455 If you plan and prepare all the concepts of Algebra in an effective way then anything can be possible in education. 2: Teachers; 3: Students; . Answer: In Exercises 1320, write a rule for the nth term of the sequence. \(\sum_{i=1}^{n}\)(3i + 5) = 544 Question 49. Partial Sums of Infinite Geometric Series, p. 436 The constant difference between consecutive terms of an arithmetic sequence is called the _______________. Answer: Question 32. a1 = 1 1 = 0 In each successive round, the number of games decreases by a factor of \(\frac{1}{2}\). a. b. WRITING Big Ideas Math Book Algebra 2 Answer Key Chapter 3 Quadratic Equations and Complex Numbers. Write a recursive rule for the balance an of the loan at the beginning of the nth month. What is the total distance your cousin swings? The value of each of the interior angle of a 4-sided polygon is 90 degrees. C. an = 51 8n Describe the pattern shown in the figure. Question 32. a8 = 1/2 0.53125 = 0.265625 ABSTRACT REASONING f(n) = f(n 1) f(n 2) Then find the sum of the series. \(\sum_{i=3}^{n}\)(3 4i) = 507 Answer: Question 8. . The graph shows the partial sums of the geometric series a1 + a2 + a3 + a4+. Answer: Question 16. an = (an-1 0.98) + 1150 (9/49) = 3/7. REWRITING A FORMULA an = 0.4 an-1 + 325 Answer: Question 25. . a. 3 x + 6x 9 n = 15 or n = -35/2 Section 1.2: Transformations of Linear and Absolute Value Functions. Thus, tap the links provided below in order to practice the given questions covered in Big Ideas Math Book Algebra 2 Answer Key Chapter 4 Polynomial Functions. a1 = 8, an = -5an-1. 36, 18, 9, \(\frac{9}{2}\), \(\frac{9}{4}\), . Answer: Question 10. Question 41. Question 70. .. \(\left(\frac{9}{49}\right)^{1 / 2}\) Answer: Question 30. . an = 3/5 x an1 . e. x2 = 16 + (-3 4n) = -507 Answer: . 417424). Explain your reasoning. b. Answer: Big Ideas Math Book Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions Trignometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Question 31. For example, in the arithmetic sequence 1, 4, 7, 10, . WHAT IF? Answer: Find the sum Justify your answers. . -18 + 10/3 a5 = -5(a5-1) = -5a4 = -5(1000) = -5000. WRITING b. . The numbers 1, 6, 15, 28, . . We cover textbooks from publishers such as Pearson, McGraw Hill, Big Ideas Learning, CPM, and Houghton Mifflin Harcourt. One term of an arithmetic sequence is a12 = 19. f(0) = 10 Question 1. MODELING WITH MATHEMATICS r = rate of change. Answer: 1 + x + x2 + x3 + x4 What does n represent for each quilt? 7x + 3 = 31 MODELING WITH MATHEMATICS . b. Then describe what happens to Sn as n increases. \(\sum_{k=3}^{6}\)(5k 2) MAKING AN ARGUMENT Answer: Core Vocabulary 2.3, 1.5, 0.7, 0.1, . REWRITING A FORMULA an= \(\frac{1}{2}\left(\frac{1}{4}\right)^{n-1}\) n = 3 Answer: Question 2. Answer: Question 13. Answer: Question 61. You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. Sequences and Series Big Ideas Math Algebra 2 Chapter 8 Answer Key encourages students and teachers to learn math in a simple and fun learning way. Answer: Question 2. In Exercises 514, write the first six terms of the sequence. a5 = 2/5 (a5-1) = 2/5 (a4) = 2/5 x 1.664 = 0.6656 Answer: Essential Question How can you recognize a geometric sequence from its graph? f(6) = f(6-1) + 2(6) = f(5) + 12 . a. Answer: WRITING EQUATIONS In Exercises 4146, write a rule for the sequence with the given terms. There can be a limited number or an infinite number of terms of a sequence. Using the table, show that both series have finite sums. Based on the type of investment you are making, you can expect to earn an annual return of 8% on your savings after you retire. Answer: Question 49. an = an-1 + d 6 + 36 + 216 + 1296 + . Explain your reasoning. Answer: Question 46. Use the sequence mode and the dot mode of a graphing calculator to graph the sequence. Write a rule for the number of people that can be seated around n tables arranged in this manner. Answer: Question 18. Answer: Question 36. x=4, Question 5. Answer: . 5, 10, 15, 20, . Write a rule for your salary in the nth year. . You save an additional penny each day after that. Answer: Question 6. a. Given that, Answer: In Exercises 2326, write a recursive rule for the sequence shown in the graph. Answer: For what values of n does the rule make sense? (3n + 13n)/2 + 5n = 544 c. Use the rule an = \(\frac{n^{2}}{2}+\frac{1}{4}\)[1 (1)n] to find an for n = 1, 2, 3, 4, 5, 6, 7, and 8. Find the sum \(\sum_{i=1}^{9}\)5(2)i1 . Explain your reasoning. Question 3. q (x) = x 3 6x + 3x 4. 7 + 10 + 13 + 16 + 19 The following problem is from the Ahmes papyrus. 7x+3=31 The first term is 7 and each term is 5 more than the previous term. Answer: Question 45. 9 + 16 + 25 + . Question 2. One term of an arithmetic sequence is a8 = 13. WRITING f(x) = \(\frac{1}{x-3}\) 44, 11, \(\frac{11}{4}\), \(\frac{11}{16}\), \(\frac{11}{64}\), . Write a conjecture about how you can determine whether the infinite geometric series The nth term of a geometric sequence has the form an = ___________. Given that the sequence is 7, 3, 4, -1, 5. . Big Ideas Math Answers for Grade K, 1, 2, 3, 4, 5, 6, 7, 8, Algebra 1, 2 & Geometry February 24, 2022 by Prasanna Big Ideas Math Answers Common Core 2019 Curriculum Free PDF: To those students who are looking for common core 2019 BigIdeas Math Answers & Resources for all grades can check here. \(\sum_{i=1}^{10}\)9i a. Writing Rules for Sequences 1, 8, 15, 22, 29, . a6 = 96, r = 2 r = 0.01/0.1 = 1/10 9, 16.8, 24.6, 32.4, . . On the first day, the station gives $500 to the first listener who answers correctly. Answer: Answer: Question 26. Section 8.1Sequences, p. 410 a2 = 2 1 = 4 1 = 3 (The figure shows a partially completed spreadsheet for part (a).). Enter each geometric series in a spreadsheet. Big ideas math algebra 2 student journal answer key pdf. Answer: Question 18. . b. \(\sum_{i=1}^{10}\)4(\(\frac{3}{4}\))i1 WRITING . . Question 25. . Question 1. Given that, Question 5. 0, 1, 3, 7, 15, . . Answer: Question 9. . Question 34. The questions are prepared as per the Big Ideas Math Book Algebra 2 Latest Edition. We have included Questions . Answer: Question 48. = 60 a sequence is a12 = 19. f ( 6 ) = 507 answer: Exercises... Exercises 1320, write the area as the sum of an arithmetic sequence is 7, 1,,! It, a12 = 19. f ( 0 ) = 3/7 Section 1.2 Transformations! Is geometric 11, 17, an for your nth year of employment to evaluate the.. 325 answer: Question 49 23. when n = -49/2 is a negatuve value a geometric sequence when r 1... Than the previous term one or more preceding terms as the sum of the third loop is times! And c q ( x ) = f ( 6-1 ) + 12 day, the maintenance level is an! Circuits and Moore s Law sum Sn of the sequence formula given in Example.! Removed through stage 8 Question 15 /n answer: Question 70, 4 7... 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You just need to tap on them and avail the underlying concepts it... 16 + 19 the following problem is from the inside lane its length finite... Writing Big Ideas Math Book Algebra 2 Ch 3 Quadratic Equations and Complex numbers 514, write the week. Series in Exploration 1 = 2/ ( 1-2/3 ) y= 2ex answer: Question 58 new branch from inside... Has 8 lanes that are each 1.22 meters wide the standard form of a sequence = 0. Let! The underlying concepts in it and score better grades in your exams first six of!, 29, hexagonal numbers because they represent the number of skydivers when there four! 0.001 + 0.0001 + Transformations of Linear and Absolute value Functions such as Pearson, McGraw,! } \ ) 4 ( 3 ) i1 Question 1 the exponents of third! Mathematics Written by Ron Larson and Laurie Boswell 128.55 degrees Question 49. an = ( an-1 0.98 +! Ounces of chlorine the first term is 7, 10, 50, 500, also preparing for quiz! Be the number of people that can be seated around n tables arranged in descending order the loan the... Rewriting a formula for the sequence be a limited number or an infinite geometric series to write an rule! N tables arranged in this manner 9 } \ ) 5 ( 2 /n! 0.0001 +, 32.4,, write a recursive rule for the sequence, is! We cover textbooks from publishers such as Pearson, McGraw Hill, Big Ideas Math Book Algebra student. 23. when n = -35/2 Section 1.2: Transformations of Linear and value... Soccer tournament 3n 6 + 2n + 2n 12 = 507 answer Question! There will be after one year in Exercises 4146, write the series using summation notation n=1 } ^ 9!
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