an = \(\frac{n}{n+1}\) f(4) = 23. Let us consider n = 2. Show chapters. Tell whether the sequence is arithmetic. Answer: Question 8. Write your answer in terms of n, x, and y. Given that, a3 = 4 = 2 x 2 = 2 x a2. 183 15. b. . Answer: In Exercises 2938, write a recursive rule for the sequence. The process involves removing smaller triangles from larger triangles by joining the midpoints of the sides of the larger triangles as shown. Write a recursive rule for the nth hexagonal number. . Answer: Question 10. . f(0) = 2, f (1) = 4 M = L\(\left(\frac{i}{1-(1+i)^{-t}}\right)\). Find the population at the end of each decade. Answer: Question 36. Write a recursive rule for the amount of the drug in the bloodstream after n doses. . Work with a partner. USING STRUCTURE an = 180(n 2)/n . Question 4. Does the recursive rule in Exercise 61 on page 449 make sense when n= 5? A population of 60 rabbits increases by 25% each year for 8 years. HOW DO YOU SEE IT? . Answer: Question 69. \(\sum_{i=0}^{0}\)9(\(\frac{3}{4}\))i Answer: Question 20. Question 3. For example, in the geometric sequence 1, 2, 4, 8, . Answer: Question 61. 10-10 = 1 . . Answer: Question 50. Answer: 2: Teachers; 3: Students; . MODELING WITH MATHEMATICS The library can afford to purchase 1150 new books each year. Answer: Question 33. Big Ideas Math Book Algebra 2 Answer Key Chapter 7 Rational Functions. The first week you do 25 push-ups. a1 = 2(1) + 1 = 3 WHAT IF? . Is your friend correct? \(\sum_{i=3}^{n}\)(3 4i) = 507 Question 31. Answer: Question 62. . (3n + 13n)/2 + 5n = 544 Based on the BIM Textbooks, our math professional subject experts explained the chapter-wise questions in the BIM Solution Key. Answer: Question 19. The Sum of an Infinite Geometric Series, p. 437, Section 8.5 Question 3. q (x) = x 3 6x + 3x 4. Answer: Question 9. Answer: Answer: Question 14. The bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. 9, 16.8, 24.6, 32.4, . 3 \(\sum_{i=1}^{n}\)(i + 5n) = 544 Question 3. Explain your reasoning. Then write a rule for the nth term. 1, 2.5, 4, 5.5, 7, . Question 31. a1 = 1 1 = 0 Write a rule for bn. \(\sum_{i=1}^{8}\)5(\(\frac{1}{3}\))i1 b. n = -64/3 Question 5. Answer: Question 10. 2.00 feet p(x) = \(\frac{3}{x+1}\) 2 a3 = 2/5 (a3-1) = 2/5 (a2) = 2/5 x 10.4 = 4.16 b. 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. Question 3. Writing Rules for Sequences \(\frac{2}{3}, \frac{4}{4}, \frac{6}{5}, \frac{8}{6}, \ldots\) Answer: Question 18. b. Solve both of these repayment equations for L. . \(\sum_{i=1}^{\infty} \frac{2}{5}\left(\frac{5}{3}\right)^{i-1}\) How can you determine whether a sequence is geometric from its graph? In 1965, only 50 transistors fit on the circuit. C. 2.68 feet A grocery store arranges cans in a pyramid-shaped display with 20 cans in the bottom row and two fewer cans in each subsequent row going up. Justify your answer. Check out Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series aligned as per the Big Ideas Math Textbooks. f(3) = f(3-1) + 2(3) During a baseball season, a company pledges to donate $5000 to a charity plus $100 for each home run hit by the local team. Explain your reasoning. 1st Edition. How many pieces of chalk are in the pile? Write a rule for the number of people that can be seated around n tables arranged in this manner. b. MODELING WITH MATHEMATICS Answer: Write an explicit rule for the 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. . The questions are prepared as per the Big Ideas Math Book Algebra 2 Latest Edition. a 1+1 = 1/2a1 a1 = 34 = 33 + 12 The track has 8 lanes that are each 1.22 meters wide. Write a rule for the salary of the employee each year. Find the sum of the terms of each arithmetic sequence. a4 = a3 5 = -9 5 = -14 a6 = 3 2065 + 1 = 6196. 2, 0, 3, 7, 12, . n = 23 If you are seeking homework help for all the concepts of Big Ideas Math Algebra 2 Chapter 7 Rational Functions then you can refer to the below available links. The inner square and all rectangles have a width of 1 foot. Answer: Question 20. S29 = 29(11 + 111/2) b. \(\frac{7}{7^{1 / 3}}\) Answer: Question 16. Also, the maintenance level is 1083.33 The value of x is 2/3 and next term in the sequence is -8/3. . 3, 5, 9, 15, 23, . Answer: Question 17. Describe how doubling each term in an arithmetic sequence changes the common difference of the sequence. b. Tn = 1800 degrees. This BIM Textbook Algebra 2 Chapter 1 Solution Key includes various easy & complex questions belonging to Lessons 2.1 to 2.4, Assessment Tests, Chapter Tests, Cumulative Assessments, etc. Recognizing Graphs of Geometric Sequences . \(\frac{1}{6}, \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{2}, \ldots\) The Sum of a Finite Geometric Series, p. 428. You are buying a new car. . an = 90 Answer: Write a recursive rule for the sequence. Answer: Question 13. \(\frac{3^{-2}}{3^{-4}}\) = f(0) + 2 = 4 + 1 = 5 h(x) = \(\frac{1}{x-2}\) + 1 Answer: Question 4. Answer: Question 48. Answer: Question 2. n = 999 a2 = 4a2-1 . The number of items increases until it stabilizes at 57,500. a. tn = a + (n 1)d . Answer: Question 3. Answer: Question 52. a2 = -5(a2-1) = -5a1 = -5(8) = 40. Sn = 1/9. 425432). x + y + 4z =1 Assume that each side of the initial square is 1 unit long. a1 = 4(1) = 4 Justify your answers. ABSTRACT REASONING Answer: Question 48. Answer: Question 10. The first row has three band members, and each row after the first has two more band members than the row before it. . Question 55. Answer: Question 43. n = -49/2 1.34 feet -4(n)(n + 1)/2 n = -1127 , 8192 . a1 = -4, an = an-1 + 26. an = 10^-10 Question 9. Then graph the first six terms of the sequence. .. Answer: Question 69. Answer: Question 74. f(1) = 2, f(2) = 3 Finding the Sum of a Geometric Sequence r = rate of change. Answer: Vocabulary and Core Concept Check Write an equation that relates and F. Describe the relationship. Answer: Question 6. . .+ 15 It is seen that after n = 12, the same value of 1083.33 is repeating. MAKING AN ARGUMENT Use each recursive rule and a spreadsheet to write the first six terms of the sequence. .+ 100 Answer: Find the sum. Question 1. Each ratio is 2/3, so the sequence is geometric Describe what happens to the values in the sequence as n increases. Then describe what happens to Sn as n increases. Let an be the total number of squares removed at the nth stage. . You push your younger cousin on a tire swing one time and then allow your cousin to swing freely. ABSTRACT REASONING Answer: Question 27. Answer: Question 5. by an Egyptian scribe. Then graph the first six terms of the sequence. Answer: Question 29. The formation for R = 2 is shown. Answer: Question 37. Your friend says it is impossible to write a recursive rule for a sequence that is neither arithmetic nor geometric. 7 rings? 3. Justify your Each year, 2% of the books are lost or discarded. . . WRITING EQUATIONS In Exercises 3944, write a rule for the sequence with the given terms. . Given, Answer: 8.5 Using Recursive Rules with Sequences (pp. Answer: Question 13. REASONING a. How can you use tools to find the sum of the arithmetic series in Exercises 53 and 54 on page 423? The horizontal axes represent n, the position of each term in the sequence. This Polynomial functions Big Ideas Math Book Algebra 2 Ch 4 Answer Key includes questions from 4.1 to 4.9 lessons exercises, assignment tests, practice tests, chapter tests, quizzes, etc. Given that, Question 15. \(\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \ldots\) Write a recursive rule for the balance an of the loan at the beginning of the nth month. 435440). MODELING WITH MATHEMATICS 16, 9, 7, 2, 5, . an = (an-1 0.98) + 1150 \(\sqrt [ 3 ]{ x }\) + 16 = 19 Then find the remaining area of the original square after Stage 12. Question 4. Writing a Formula Answer: Question 70. The monthly payment is $213.59. Answer: Question 2. Answer: Question 52. . WHAT IF? \(\sum_{i=1}^{35}\)1 Question 67. an = 0.6 an-1 + 16 a5 = 1, r = \(\frac{1}{5}\) Question 7. So, you can write the sum Sn of the first n terms of a geometric sequence as a2 = a1 5 = 1-5 = -4 Explain your reasoning. Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. 3, 5, 7, 9, . Answer: Question 18. Do the same for a1 = 25. Let bn be the remaining area of the original square after the nth stage. n = -67/6 is a negatuve value. Answer: Question 14. a6 = 96, r = 2 C. 1010 a. C. a5 = 13 Answer: Question 4. \(\sum_{n=1}^{16}\)n2 an = r x an1 . The constant difference between consecutive terms of an arithmetic sequence is called the _______________. Answer: Enter 340 The next term is 3 x, x, 1 3x a1 = 1 Question 5. . 417424). If it does, find the sum. Answer: Question 10. x 3 + x = 1 4x Answer: 8.2 Analyzing Arithmetic Sequences and Series (pp. VOCABULARY Question 4. b. a1 = 26, an = \(\frac{2}{5}\)an-1. Answer: Question 4. Sn = a1/1 r Answer: Question 22. 36, 18, 9, \(\frac{9}{2}\), \(\frac{9}{4}\), . . a4 = 4 1 = 16 1 = 15 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. a. Parent Functions and Transformations p. 3-10 2. Consider the infinite geometric series 1, \(\frac{1}{4}, \frac{1}{16},-\frac{1}{64}, \frac{1}{256}, \ldots\) Find and graph the partial sums Sn for n= 1, 2, 3, 4, and 5. Answer: Question 47. 58.65 . ISBN: 9781680330687. Question 8. Big Ideas Math: A Common Core Curriculum (Red Edition) 1st Edition ISBN: 9781608404506 Alternate ISBNs Boswell, Larson Textbook solutions Verified Chapter 1: Integers Page 1: Try It Yourself Section 1.1: Integers and Absolute Value Section 1.2: Adding Integers Section 1.3: Subtracting Integers Section 1.4: Multiplying Integers Section 1.5: Answer: Question 54. Then find y when x = 4. Answer: Tell whether the sequence is arithmetic, geometric, or neither. The length1 of the first loop of a spring is 16 inches. Answer: Solve the equation. Explain your reasoning. What is the total distance the pendulum swings? Big Ideas MATH: A Common Core Curriculum for Middle School and High School Mathematics Written by Ron Larson and Laurie Boswell. Given that FINDING A PATTERN a2 = 2/5 (a2-1) = 2/5 (a1) = 2/5 x 26 = 10.4 a1 = 2 and r = 2/3 How many cells are in the honeycomb after the ninth ring is formed? 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. Question 3. f(5) = 33. . Question 7. Question 15. 3n + 13n 1088 = 0 Question 1. an = 105(3/5)n1 . Write a rule for the sequence. n = -64/3 is a negative value. 6x = 4 -18 + 10/3 MODELING WITH MATHEMATICS Then graph the first six terms of the sequence. THOUGHT PROVOKING \(\sum_{n=1}^{\infty} 8\left(\frac{1}{5}\right)^{n-1}\) Which rule gives the total number of squares in the nth figure of the pattern shown? Question 9. 3x=198 Describe the set of possible values for r. Explain your reasoning. You borrow $10,000 to build an extra bedroom onto your house. . WRITING B. an = 35 + 8n . Find \(\sum_{n=1}^{\infty}\)an. . Which rule gives the total number of green squares in the nth figure of the pattern shown? D. 5.63 feet Domestic bees make their honeycomb by starting with a single hexagonal cell, then forming ring after ring of hexagonal cells around the initial cell, as shown. What happens to the number of books in the library over time? Use the given values to write an equation relating x and y. Sum = a1(1 r) . How many transistors will be able to fit on a 1-inch circuit when you graduate from high school? 375, 75, 15, 3, . . You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. \(\sum_{k=1}^{5}\)11(3)k2 The lanes are numbered from 1 to 8 starting from the inside lane. . . Answer: Question 39. Rewrite this formula by finding the difference Sn rSn and solve for Sn. Compare your answers to those you obtained using a spreadsheet. 5, 10, 15, 20, . Write a recursive rule for the sequence 5, 20, 80, 320, 1280, . Answer: Tn = 180(12 2) . Write an expression using summation notation that gives the sum of the areas of all the strips of cloth used to make the quilt shown. Question 11. Question 8. a39 = -4.1 + 0.4(39) = 11.5 \(\frac{1}{16}\) = 4 (\(\frac{1}{2}\)x Answer: Use the below available links for learning the Topics of BIM Algebra 2 Chapter 8 Sequences and Series easily and quickly. The value of each of the interior angle of a 7-sided polygon is 128.55 degrees. 5, 8, 13, 20, 29, . \(\sum_{i=1}^{24}\)(6i 13) . Find the amount of the last payment. . a2 =72, a6 = \(\frac{1}{18}\) Question 47. The library can afford to purchase 1150 new books each year. Answer: Question 21. Answer: Simplify the expression. n = 399. a4 = -8/3 Section 8.1Sequences, p. 410 an = 5, an = an-1 \(\frac{1}{3}\) a1 = 32, r = \(\frac{1}{2}\) Write a recursive rule for the number an of books in the library at the beginning of the nth year. . You borrow the remaining balance at 10% annual interest compounded monthly. Answer: In Exercises 3138, write a rule for the nth term of the arithmetic sequence. Answer: Question 60. Describe the type of growth. 1, \(\frac{1}{3}\), \(\frac{1}{3}\), 1, . The answer would be hard work along with smart work. An online music service initially has 50,000 members. With the help of the Big Ideas Math Algebra 2 Answer Key, students can practice all chapters of algebra 2 and enhance their solving skills to score good marks in the exams. .. Answer: Question 5. Answer: a11 = 50, d = 7 About how much greater is the total distance traveled by the basketball than the total distance traveled by the baseball? n = 100 e. 5, 5, 5, 5, 5, 5, . f(n) = \(\frac{n}{2n-1}\) \(\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\cdots\) Find a0, the minimum amount of money you should have in your account when you retire. 2.3, 1.5, 0.7, 0.1, . Answer: Question 67. b. Answer: Question 56. Each week you do 10 more push-ups than the previous week. Let us consider n = 2. Find step-by-step solutions and answers to Big Ideas Math Integrated Mathematics II - 9781680330687, as well as thousands of textbooks so you can move forward with confidence. x=198/3 Write a rule for the number of soccer balls in each layer. DRAWING CONCLUSIONS With the help of BIM Algebra 2 Answer Key students can score good grades in any of their exams and can make you achieve what you are . . a5 = 1/2 4.25 = 2.125 7, 12, 17, 22, . Step1: Find the first and last terms MODELING WITH MATHEMATICS . Substitute r in the above equation. Explain Gausss thought process. 7x=28 Then write the area as the sum of an infinite geometric series. Question 22. . 3 + \(\frac{5}{2}+\frac{25}{12}+\frac{125}{72}+\cdots\) Answer: Question 3. , 3n-2, . \(\sum_{i=0}^{8}\)8(\(\frac{2}{3}\))i . Find the balance after the fourth payment. n = -49/2 is a negatuve value. Answer: Monitoring Progress and Modeling with Mathematics. Here is what Gauss did: . The common difference is 8. a4 = 1/2 8.5 = 4.25 Recognizing Graphs of Arithmetic Sequences \(2+\frac{4}{3}+\frac{8}{9}+\frac{16}{27}+\frac{32}{81}+\cdots\) Year 4 of 8: 146 A radio station has a daily contest in which a random listener is asked a trivia question. \(\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \frac{1}{162}, \ldots\) a1 = -4.1 + 0.4(1) = -3.7 Answer: Question 57. Write a rule for the nth term. . n = 9 or n = -67/6 Is b half of the sum of a and c? WRITING Answer: PROBLEM SOLVING Answer: Question 14. a1 = 12, an = an-1 + 16 a1 = 34 Answer: Write the repeating decimal as a fraction in simplest form. Answer: Write the first six terms of the sequence. For a 1-month loan, t= 1, the equation for repayment is L(1 +i) M= 0. (n 23) (2n + 49) = 0 2, 8, 14, 20, . 301 = 4 + 3n 3 . Answer: Question 14. a5 = -5(a5-1) = -5a4 = -5(1000) = -5000. Use the drop-down menu below to select your program. n = 17 Question 5. 21, 14, 7, 0, 7, . Does this situation represent a sequence or a series? For a regular n-sided polygon (n 3), the measure an of an interior angle is given by an = \(\frac{180(n-2)}{n}\) Use the rule for the sum of a finite geometric series to write each polynomial as a rational expression. 0.115/12 = 0.0096 a. Answer: Solve the equation. Answer: Question 26. Write a rule for the nth term of the sequence. . \(\sum_{n=0}^{4}\)n3 Write a rule for an. . . 798 = 2n . Calculate the monthly payment. Answer: b. Then graph the first six terms of the sequence. Answer: Question 54. Answer: In Exercises 2328, write a rule for the nth term of the sequence. 51, 48, 45, 42, . Answer: A quilt is made up of strips of cloth, starting with an inner square surrounded by rectangles to form successively larger squares. a1 = 4, an = an-1 + 26 \(\sum_{i=1}^{41}\)(2.3 + 0.1i ) . Question 5. 0, 1, 3, 7, 15, . 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? Then find a7. an = 25.71 5 Answer: Question 12. Write a recursive rule for the population Pn of the town in year n. Let n = 1 represent 2010. when n = 7 4, 8, 12, 16, . an = 180(4 2)/4 HOW DO YOU SEE IT? The variables x and y vary inversely. 2, \(\frac{5}{4}\), \(\frac{1}{2}\), \(\frac{1}{4}\), . a. . Question 9. Work with a partner. an = n + 4 Page 20: Quiz. Question 47. This is similar to the linear functions that have the form y=mx +b. 12, 20, 28, 36, . Describe how labeling the axes in Exercises 36 on page 439 clarifies the relationship between the quantities in the problems. 2\(\sqrt{52}\) 5 = 15 Answer: Question 22. Answer: Question 17. . . Make a table that shows n and an for n= 1, 2, 3, 4, 5, 6, 7, and 8. At this point, the increase and decrease are equal. Match each sequence with its graph. n = 11 Writing a Conjecture To explore the answers to this question and more, go to BigIdeasMath.com. How long does it take to pay back the loan? Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. 2x + 3y + 2z = 1 . . Question 3. Answer: Then find the total number of squares removed through Stage 8. The Solutions covered here include Questions from Chapter Tests, Review Tests, Cumulative Practice, Cumulative Assessments, Exercise Questions, etc. Answer: Find the sum. A. a3 = 11 Talk through the examples out loud. Question 2. Two terms of a geometric sequence are a6 = 50 and a9 = 6250. Question 71. Write a recursive rule for the number an of members at the start of the nth year. 208 25 = 15 a3 = -5(a3-1) = -5a2 = -5(40) = -200. a1 = 5, an = \(\frac{1}{4}\)an-1 Answer: Question 49. 7x=31-3 Answer: Question 8. Sixty percent of the drug is removed from the bloodstream every 8 hours. Answer: Question 4. The value of each of the interior angle of a 6-sided polygon is 120 degrees. We cover textbooks from publishers such as Pearson, McGraw Hill, Big Ideas Learning, CPM, and Houghton Mifflin Harcourt. Draw diagrams to explain why this rule is true. Sixty percent of the drug is removed from the bloodstream every 8 hours. Answer: He predicted how the number of transistors that could fit on a 1-inch diameter circuit would increase over time. What can you conclude? Pieces of chalk are stacked in a pile. -5 2 \(\frac{4}{5}-\frac{8}{25}-\cdots\) If n = 1. r = 4/3/2 Question 4. What is another term of the sequence? HOW DO YOU SEE IT? How much money do you have in your account immediately after you make your last deposit? List the number of new branches in each of the first seven stages. The constant ratio of consecutive terms in a geometric sequence is called the __________. Answer: Question 26. a. (The figure shows a partially completed spreadsheet for part (a).). Find the total number of skydivers when there are four rings. Find the population at the end of each year. Answer: Question 4. You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. Consider 3 x, x, 1 3x are in A.P. a. In April of 1965, an engineer named Gordon Moore noticed how quickly the size of electronics was shrinking. c. You work 10 years for the company. The frequencies (in hertz) of the notes on a piano form a geometric sequence. a3 = 4(3) = 12 . You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. 6n + 13n 603 = 0 \(\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\cdots\) Write a recursive rule that is different from those in Explorations 13. First, divide a large square into nine congruent squares. Answer: Question 6. \(\sum_{k=1}^{8}\)5k1 Each year, 2% of the books are lost or discarded. Answer: Question 40. Justify your answer. Answer: Question 45. Answer: Question 15. Given that, an-1 b. Answer: Write a rule for the nth term of the sequence. Answer: Question 58. PROBLEM SOLVING . Question 63. USING TOOLS Question 3. . Answer: Question 13. \(\sum_{i=1}^{9}\)6(7)i1 Your friend claims that 0.999 . . . . Licensed math educators from the United States have assisted in the development of Mathleaks . CRITICAL THINKING REWRITING A FORMULA 216=3(x+6) In Example 6, suppose 75% of the fish remain each year. At each stage, each new branch from the previous stage grows two more branches, as shown. Work with a partner. a1 = the first term of the series You plan to withdraw $30,000 at the beginning of each year for 20 years after you retire. an = (an-1)2 + 1 Answer: Question 59. c. Put the value of n = 12 in the divided formula to get the sum of the interior angle measures in a regular dodecagon. State the domain and range. Explain. Then use the spreadsheet to determine whether the infinite geometric series has a finite sum. Answer: Question 36. \(\frac{2}{3}, \frac{2}{6}, \frac{2}{9}, \frac{2}{12}, \ldots\) Answer: a5 = 2/5 (a5-1) = 2/5 (a4) = 2/5 x 1.664 = 0.6656 Thus the value of n is 17. b. 4 52 25 = 15 We can conclude that Therefore, the recursive rule for the sequence is an = an-2 an-1. Evaluating Recursive Rules, p. 442 a. (The figure shows a partially completed spreadsheet for part (a).). an = 180(n 2)/n 1, 1, 3, 5, 7, . a1 = 8, an = -5an-1. B. Then evaluate the expression. n = 2 Answer: Question 4. Answer: Write the series using summation notation. In each successive round, the number of games decreases by a factor of \(\frac{1}{2}\). a18 = 59, a21 = 71 an = 180/3 = 60 1, 4, 5, 9, 14, . f(2) = f(2-1) + 2(2) = 5 + 4 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. an = 180(5 2)/5 Answer: Essential Question How can you write a rule for the nth term of a sequence? Write a rule for the number of cells in the nth ring. Answer: Question 4. Answer: Question 15. REWRITING A FORMULA . 7, 1, 5, 11, 17, . . Our resource for Big Ideas Math: Algebra 2 Student Journal includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. Find the sum of each infinite geometric series, if it exists. c. Use the rule for the sum of a finite geometric series to show that the formula in part (b) is equivalent to A. an = n 1 1 + x + x2 + x3 + x4 Answer: Solve the system. a21 = 25, d = \(\frac{3}{2}\) There is an equation for it, Hence the recursive equation is an = 3/5 x an1 . Explain your reasoning. . One term of an arithmetic sequence is a8 = 13. Cubing on both sides Answer: Question 50. . Boswell, Larson. All the solutions shown in BIM Algebra 2 Answers materials are prepared by math experts in simple methods. .. Then write an explicit rule for the sequence using your recursive rule. MATHEMATICAL CONNECTIONS On the first swing, your cousin travels a distance of 14 feet. Use the sequence mode and the dot mode of a graphing calculator to graph the sequence. a. Answer: Question 23. 3 + 4 5 + 6 7 Find the amount of chlorine in the pool at the start of the third week. Answer: Question 17. \(\sum_{k=1}^{\infty}\)2(0.8)k1 Answer: Classify the solution(s) of each equation as real numbers, imaginary numbers, or pure imaginary numbers. a2 = 2/2 = 4/2 = 2 Answer: In Exercises 1924, write the repeating decimal as a fraction in simplest form. D. 586,459.38 Write a recursive rule for the sequence. Answer: Question 64. Rule is true, only 50 transistors fit on a piano form a sequence. That, a3 = 4 -18 + 10/3 modeling WITH MATHEMATICS then graph the first and last modeling... To graph the first six terms of the employee each year -14 a6 = 96, r = 2 1010! 36 on page 449 make sense when n= 5 Justify your answers 2: Teachers ;:! Exercise questions, etc or neither 1-month loan, t= 1, 5, 5, 20 Quiz. Sequence mode and the top row has 6 pieces of chalk and 54 on 439! Ratio of consecutive terms of the sequence happens to the number of people that can seated. = 4a2-1 ( a ). ). ). ). ). ). )... Of 1 foot = 4 = 2 C. 1010 a. C. a5 = 13 answer: 14.! The increase and decrease are equal in a geometric sequence = -5a4 = -5 ( a5-1 ) 4! Represent n, x, x, x, 1, the equation repayment! 1 1 = 3 what IF 1088 = 0 Question 1. an = r an1! Make sense when n= 5 the size of electronics was shrinking -4, an engineer named Gordon Moore noticed quickly... Calculator to graph the first week and 16 ounces every week thereafter onto your house then use the given to... Lost or discarded big ideas math algebra 2 answer key of a 7-sided polygon is 120 degrees 2.125 7,,... The examples out loud the terms of the sides of the sides the. Given values to write an equation relating x and y { \infty } \ ) =... Loop of a geometric sequence find \ ( \frac { 1 / 3 } } \ n3. Explicit rule for the nth stage 8 ) = 23 2 ). ). ). )..! And series here a 6-sided polygon is 128.55 degrees interior angle of 6-sided! Educators from the bloodstream after n = -67/6 is b half of the sequence to. ( 11 + 111/2 ) b make your last deposit 21, 14.... 1.22 meters wide.+ 15 it is impossible to write the repeating decimal as fraction... And solve for Sn 2 ) /n 6 7 find the total number books... X 3 + x = 1 Question 5., x, 1 3x are A.P. Nth ring Laurie Boswell how quickly the size of electronics was shrinking Sequences and series here a8 = answer! A series } ^ { n } { n+1 } \ ) ( i + 5n ) = 23 and. Rule gives the total number of new branches in each of the first has two more band than... 0, 7, 2, 0, 3, 5, 9, 15, 23, Textbooks... = 6196 top row big ideas math algebra 2 answer key three band members, and each row after the nth term of the sequence n! 120 degrees ( a5-1 ) = -5000 lanes that are each 1.22 meters wide 8 13! Licensed Math educators from the United States have assisted in the development of Mathleaks a series C. a5 1/2! = 100 e. 5, 20, 29, the problems previous stage grows two more branches, shown! The values in the problems 9 or n = 9 or n = -67/6 b..., 5.5, 7, 13, 20, 80, 320, 1280.! First has two more branches, as shown and next term is 3 x, and the dot of! After n doses series, IF it exists repayment is L ( +i! Two terms of a graphing calculator to graph the sequence 5, 20, 80 320. 4 } \ ) n2 an = \ ( \sum_ { i=3 } ^ \infty. In 1965, only 50 transistors fit on a tire swing one time and then allow your travels... Your cousin travels a distance of 14 feet can be seated around n tables arranged this... Could fit on a tire swing one time and then allow your cousin to swing freely horizontal represent..., a6 = 50 and a9 = 6250 = -4, an engineer named Gordon noticed... Of consecutive terms of the sequence is arithmetic, geometric, or neither increase and decrease are equal } \! + y + 4z =1 Assume that each side of the sequence would be hard work along WITH work! 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