Part of the pile is shown. is geometric. In Example 3, suppose the pendulum travels 10 inches on its first swing. Write a rule for the number of cells in the nth ring. Answer: In Exercises 2328, write a rule for the nth term of the sequence. What is the maintenance level of this drug given the prescribed dosage? Then write a formula for the sum Sn of the first n terms of an arithmetic sequence. . Write a rule for the sequence. The nth term of a geometric sequence has the form an = ___________. Question 27. Solutions available . . Download Big Ideas Math Algebra 1 Answer Key for Free Students who are wondering how to get on the success path of answering all algebra questions in exams with good results? What do you notice about the relationship between the terms in (a) an arithmetic sequence and (b) a geometric sequence? a1 = 12, an = an-1 + 16 In 1965, only 50 transistors fit on the circuit. Find the population at the end of each decade. From this Big Ideas Math Algebra 2 Chapter 7 Rational Functions Answer Key you can learn how to solve problems in different methods. . Answer: Question 15. Answer: Question 28. Answer: Question 4. \(\sum_{i=1}^{24}\)(6i 13) More textbook info . Answer: Question 15. 425432). Answer: Question 69. Question 5. . . 3 \(\sum_{i=1}^{n}\)(i + 5n) = 544 Answer: In Exercises 36, consider the infinite geometric series. an = 128.55 \(\sum_{i=1}^{n}\)i2 = \(\frac{n(n+1)(2 n+1)}{6}\) Tell whether the sequence is geometric. a4 = a4-1 + 26 = a3 + 26 = 48 + 26 = 74. ABSTRACT REASONING Write an explicit rule for the number of cans in row n. Work with a partner. The annual interest rate of the loan is 4.5%. a3 = 16 417424). p(x) = \(\frac{3}{x+1}\) 2 Explain your reasoning. 183 15. In Example 6, how does the monthly payment change when the annual interest rate is 5%? Answer: Question 2. b. \(\sum_{i=1}^{31}\)(3 4i ) A sequence is an ordered list of numbers. nth term of a sequence Question 57. n = -49/2 \(\sum_{k=4}^{6} \frac{k}{k+1}\) One term of an arithmetic sequence is a8 = 13. Show chapters. Year 6 of 8: 229 . Answer: Question 17. Answer: Question 23. . n = -64/3 is a negative value. What does an represent? n = 300/3 Employees at the company receive raises of $2400 each year. a1 = 1/2 = 1/2 7, 3, 4, 1, 5, . VOCABULARY Write a rule for the arithmetic sequence with the given description. Answer: Question 20. a. x + \(\sqrt{-16}\) = 0 \(\sum_{n=1}^{\infty}\left(-\frac{1}{2}\right)^{n-1}\) Answer: Question 28. 2.00 feet Answer: Vocabulary and Core Concept Check Answer: Question 3. a1 = 4, an = an-1 + 26 Justify your answer. Answer: Write the repeating decimal as a fraction in simplest form. Question 1. Answer: Write the series using summation notation. . Answer: Question 7. 1.5, 7.5, 37.5, 187.5, . WRITING EQUATIONS Answer: 8.5 Using Recursive Rules with Sequences (pp. Each ratio is 2/3, so the sequence is geometric Answer: In Exercises 2938, write a recursive rule for the sequence. Find the number of members at the start of the fifth year. an = 180(4 2)/4 USING EQUATIONS Given, Answer: Question 61. a6 = 1/2 2.125 = 1.0625 Answer: Question 11. a4 = a3 5 = -9 5 = -14 a1 = 4(1) + 7 = 11. a. . Then graph the sequence. \(\sum_{i=1}^{n}\)(3i + 5) = 544 Answer: Question 14. The first 8 terms of the geometric sequence 12, 48, 192, 768, . So, you can write the sum Sn of the first n terms of a geometric sequence as Explain how viewing each arrangement as individual tables can be helpful in Exercise 29 on page 415. an = n + 4 Question 31. an = n + 2 a2 = 4a1 . Answer: Question 13. . Find the balance after the fifth payment. b. WHAT IF? f(5) = \(\frac{1}{2}\)f(4) = 1/2 5/8 = 5/16. Find a0, the minimum amount of money you should have in your account when you retire. . b. . The number of cans in each row is represented by the recursive rule a1 = 20, an = an-1 2. .. Then write an explicit rule for the sequence using your recursive rule. \(\frac{7}{7^{1 / 3}}\) Then find a9. Answer: Question 30. . Section 1.4: Solving Linear . Let L be the amount of a loan (in dollars), i be the monthly interest rate (in decimal form), t be the term (in months), and M be the monthly payment (in dollars). For a 1-month loan, t= 1, the equation for repayment is L(1 +i) M= 0. Answer: Question 15. In Lesson 8.3, you learned that the sum of the first n terms of a geometric series with first term a1 and common ratio r 1 is B. an = 0.6 an-1 + 16 Rewrite this formula by finding the difference Sn rSn and solve for Sn. b. Answer: Question 18. Answer: In Exercises 3950, find the sum. 0.3, 1.5, 7.5, 37.5, 187.5, . . \(\frac{1}{4}+\frac{2}{5}+\frac{3}{6}+\frac{4}{7}+\cdots\) . 4 52 25 = 15 13.5, 40.5, 121.5, 364.5, . 0 + 2 + 6 + 12 +. . an = a1 x rn1 .. Write a recursive rule for your salary. An employee at a construction company earns $33,000 for the first year of employment. The monthly payment is $213.59. C. 2.68 feet . In 2010, the town had a population of 11,120. . a2 = 2/5 (a2-1) = 2/5 (a1) = 2/5 x 26 = 10.4 Answer: Question 5. n = 23. c. \(\sum_{i=5}^{n}\)(7 + 12i) = 455 Answer: Question 6. Answer: Question 45. an = 180(6 2)/6 \(\sqrt [ 3 ]{ x }\) + 16 = 19 Answer: Core Vocabulary Find the sum of the infinite geometric series 2 + \(\frac{1}{2}-\frac{1}{8}+\frac{1}{32}+\cdots\), if it exists. Answer: Question 5. Answer: Question 40. Question 65. Question 3. Answer: Find the sum. . Question 2. Year 4 of 8: 146 \(\frac{1}{6}, \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{2}, \ldots\) Answer: Question 46. a, a + b, a + 2b, a + 3b, . . CRITICAL THINKING b. What are your total earnings? WRITING Question 5. Question 19. Describe how doubling each term in an arithmetic sequence changes the common difference of the sequence. . MAKING AN ARGUMENT Answer: f(6) = f(6-1) + 2(6) = f(5) + 12 Answer: Question 66. a. 208 25 = 15 Your friend believes the sum of a series doubles when the common difference of an arithmetic series is doubled and the first term and number of terms in the series remain unchanged. The value of each of the interior angle of a 6-sided polygon is 120 degrees. Question 53. Big Ideas Math Algebra 2 Texas Spanish Student Journal (1 Print, 8 Yrs) their parents answer the same question about each set of four. Answer: Question 46. Work with a partner. . PROBLEM SOLVING The Sum of a Finite Arithmetic Series, p. 420, Section 8.3 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 . Question 41. a1 = 2(1) + 1 = 3 You are saving money for retirement. Explain your reasoning. Our subject experts created this BIM algebra 2 ch 5 solution key as per the Common core edition BIM Algebra 2 Textbooks. \(\sum_{i=1}^{n}\)(4i 1) = 1127 . B. d. If you pay $350 instead of $300 each month, how long will it take to pay off the loan? Answer: Question 2. Question 31. Answer: Question 64. Write a rule for the number of soccer balls in each layer. Your employer offers you an annual raise of $1500 for the next 6 years. Each year, 2% of the books are lost or discarded. a2 = 2/2 = 4/2 = 2 Write a recursive rule for each sequence. Write a recursive rule for the sequence. an = an-1 5 c. 3, 6, 12, 24, 48, 96, . an = 90 Answer: Question 64. as a fraction in simplest form. Algebra; Big Ideas Math Integrated Mathematics II. . Question 27. an = 120 Step1: Find the first and last terms. You borrow the remaining balance at 10% annual interest compounded monthly. Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. Check your solution. Answer: WRITING EQUATIONS In Exercises 4146, write a rule for the sequence with the given terms. Tn = 180(12 2) . This is similar to the linear functions that have the form y=mx +b. \(\sum_{i=1}^{6}\)2i Answer: Question 26. Assume that each side of the initial square is 1 unit long. . \(\sum_{i=2}^{8} \frac{2}{i}\) Given that, Answer: Question 12. \(2+\frac{4}{3}+\frac{8}{9}+\frac{16}{27}+\frac{32}{81}+\cdots\) Write a recursive rule for the sequence 5, 20, 80, 320, 1280, . A town library initially has 54,000 books in its collection. a5 = a5-1 + 26 = a4 + 26 = 74 + 26 = 100. DIFFERENT WORDS, SAME QUESTION Justify your answers. Use the pattern in the equations you solved in part (a) to write a repayment equation for a t-month loan. FINDING A PATTERN Question 32. 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. 5.8, 4.2, 2.6, 1, 0.6 . Write your answer in terms of n, x, and y. x (3 x) = x 3x x MODELING WITH MATHEMATICS f(x) = \(\frac{1}{x-3}\) c. Is your friend correct? Find the length of the spring, if possible. You save an additional penny each day after that. WHAT IF? c. Put the value of n = 12 in the divided formula to get the sum of the interior angle measures in a regular dodecagon. Answer: c. \(\frac{1}{4}, \frac{4}{4}, \frac{9}{4}, \frac{16}{4}, \frac{25}{4}, \ldots\) 8 x 2197 = -125 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. \(\frac{1}{4}\)x 8 = 17 . a. an = an-1 5 6n + 13n 603 = 0 . Answer: Question 65. Refer to BIM Algebra Textbook Answers to check the solutions with your solutions. Answer: Question 54. . Write a recursive equation that shows how an is related to an-1. If it does, then write a rule for the nth term of the sequence and use a spreadsheet to find the sum of the first 20 terms. .. Answer: Question 70. COMPARING METHODS 3x=216-18 The first 22 terms of the sequence 17, 9, 1, 7, . .has a finite sum. Answer: Question 58. Answer: Question 54. . a8 = 1/2 0.53125 = 0.265625 . n = 2 Answer: Question 12. . Look back at the infinite geometric series in Exploration 1. The Sierpinski carpet is a fractal created using squares. a5 = 2/5 (a5-1) = 2/5 (a4) = 2/5 x 1.664 = 0.6656 You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. an = an-1 + d Question 7. Answer: Question 26. We can conclude that -1 + 2 + 7 + 14 + .. . Answer: Question 55. a1 = 2 Answer: In Exercises 4752, find the sum. 3n + 13n 1088 = 0 Question 15. A company had a profit of $350,000 in its first year. 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. x 3 + x = 1 4x Answer: Simplify the expression. a1 = 1 Answer: Question 8. Write a rule for the nth term of the sequence 3, 15, 75, 375, . f(1) = f(1-1) + 2(1) Answer: In Exercises 3340, write a rule for the nth term of the geometric sequence. Answer: Question 45. a3 = 4(3) = 12 \(\sum_{k=3}^{6}\)(5k 2) Answer: Log in. 3x=198 Answer: Step2: Find the sum 2\(\sqrt [ 3 ]{ x }\) 13 = 5 Explain your reasoning. \(\sum_{i=1}^{20}\)(2i 3) \(\sum_{k=1}^{5}\)11(3)k2 Use each recursive rule and a spreadsheet to write the first six terms of the sequence. 1, 4, 7, 10, . Repeat these steps for each smaller square, as shown below. D. a6 = 47 VOCABULARY COMPLETE THE SENTENCE \(\frac{2}{3}, \frac{4}{4}, \frac{6}{5}, \frac{8}{6}, \ldots\) Answer: Question 7. In number theory, the Dirichlet Prime Number Theorem states that if a and bare relatively prime, then the arithmetic sequence Question 61. b. DRAWING CONCLUSIONS Use the rule for the sum of a finite geometric series to write each polynomial as a rational expression. a6 = a5 5 = -19 5 = -24. You begin by saving a penny on the first day. a1 = 3, an = an-1 6 Question 39. Question 8. Justify your answer. . Answer: Question 10. Answer: Recognizing Graphs of Geometric Sequences Question 9. e. \(\frac{1}{2}\), 1, 2, 4, 8, . \(\left(\frac{9}{49}\right)^{1 / 2}\) On each successive swing, your cousin travels 75% of the distance of the previous swing. Answer: Determine the type of function represented by the table. Question 1. c. Use your rule in part (b) to find the sum of the interior angle measures in the Guggenheim Museum skylight, which is a regular dodecagon. . Write a recursive rule for the sequence. Then find y when x = 4. WHAT IF? What can you conclude? Answer: Answer: Vocabulary and Core Concept Check REASONING Answer: Solve the equation. . Question 5. a4 = 2/5 (a4-1) = 2/5 (a3) = 2/5 x 4.16 = 1.664 Work with a partner. A population of 60 rabbits increases by 25% each year for 8 years. Answer: Question 56. A marching band is arranged in rows. Question 5. USING STRUCTURE a. b. Answer: Describe the pattern, write the next term, graph the first five terms, and write a rule for the nth term of the sequence. e. 5, 5, 5, 5, 5, 5, . when n = 4 Answer: Question 25. a1 = 6, an = 4an-1 Match each sequence with its graph. The common difference is 6. How many apples are in the stack? Answer: Question 1. Answer: In Exercises 310, write the first six terms of the sequence. MODELING WITH MATHEMATICS 3x 2z = 8 Answer: Question 3. CRITICAL THINKING Translating Between Recursive and Explicit Rules, p. 444. . The monthly payment is $173.86. Answer: Question 12. .+ 12 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. 800 = 4 + 2n 2 Question 34. Compare these values to those in your table in part (b). a3 = a3-1 + 26 = a2 + 26 = 22 + 26 = 48. = 29(61) Then find the sum of the series. Order the functions from the least average rate of change to the greatest average rate of change on the interval 1 x 4. Answer: Write a rule for the nth term of the sequence. . Answer: Question 47. Answer: Question 4. .. Then find a9. 8, 6.5, 5, 3.5, 2, . Question 13. Answer: Answer: Question 6. \(\sum_{i=1}^{5} \frac{3+i}{2}\) PROBLEM SOLVING a5 = 4(384) =1,536 Graph of a geometric sequence behaves like graph of exponential function. \(\frac{7}{7^{1 / 3}}\) Question 1. 2x y 3z = 6 c. Write an explicit rule for the sequence. Answer: Question 18. 15, 9, 3, 3, 9, . Justify your answer. 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. When n = 3 Answer: Question 28. Mathematical Practices 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. D. an = 2n + 1 Then find a20. x 2z = 1 Question 59. -5 2 \(\frac{4}{5}-\frac{8}{25}-\cdots\) . \(\sum_{i=1}^{\infty} \frac{2}{5}\left(\frac{5}{3}\right)^{i-1}\) 2, 5, 8, 11, 14, . Answer: Question 60. b. Question 9. a2 = 4(2) = 8 \(\sum_{i=1}^{35}\)1 Question 3. WRITING EQUATIONS In Exercises 3944, write a rule for the sequence with the given terms. In a geometric sequence, the ratio of any term to the previous term, called the common ratio, is constant. The questions are prepared as per the Big Ideas Math Book Algebra 2 Latest Edition. 4, 12, 36, 108, . f(0) = 4 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. tn = 8192, a = 1 and r = 2 \(\sum_{n=1}^{\infty} 8\left(\frac{1}{5}\right)^{n-1}\) Find the amount of chlorine in the pool at the start of the third week. . A. 7, 1, 5, 11, 17, . 86, 79, 72, 65, . Explain Gausss thought process. Write a formula to find the sum of an infinite geometric series. c. How long will it take to pay off the loan? The horizontal axes represent n, the position of each term in the sequence. 16, 9, 7, 2, 5, . a. Do the perimeters and areas form geometric sequences? Question 3. a. . \(\sum_{i=5}^{n}\)(7 + 12i) = 455 f(4) = f(3) + 8 = 15 + 8 b. Mathleaks offers learning-focused solutions and answers to commonly used textbooks for Algebra 2, 10th and 11th grade. 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. a1 = 2 and r = 2/3 . Use the pattern of checkerboard quilts shown. 2 + \(\frac{6}{4}+\frac{18}{16}+\frac{54}{64}+\cdots\) Answer: Essential Question How can you recognize an arithmetic sequence from its graph? . Evaluating Recursive Rules, p. 442 a. 301 = 3n + 1 You plan to withdraw $30,000 at the beginning of each year for 20 years after you retire. 2, \(\frac{3}{2}\), \(\frac{9}{8}\), \(\frac{27}{32}\), . Answer: Question 50. Use a spreadsheet to help you answer the question. Answer: Question 62. 7 + 10 + 13 +. . a4 = a + 3d WHAT IF? MATHEMATICAL CONNECTIONS a2 = 4(6) = 24. Compare sequences and series. Answer: Question 33. \(\sum_{n=1}^{16}\)n2 Answer: Question 8. \(\sum_{k=3}^{7}\)(k2 1) Given that, .What is the value of \(\sum_{n=1}^{\infty}\)an ? Compare the terms of a geometric sequence when r > 1 to when 0 < r < 1. Answer: Question 56. Answer: Question 21. 2\(\sqrt{52}\) 5 = 15 The number of cells in successive rings forms an arithmetic sequence. Step1: Find the first and last terms Explain. b. Answer: Before doing homework, review the concept boxes and examples. Answer: The graph shows the partial sums of the geometric series a1 + a2 + a3 + a4+. Find the sum of the terms of each arithmetic 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. A population of 60 rabbits increases by 25% each year for 8 years. Verify your formula by finding the sums of the first 20 terms of the arithmetic sequences in Exploration 1. b. Answer: Question 16. Answer: In Exercises 714, find the sum of the infinite geometric series, if it exists. . an = 180(n 2)/n Question 65. Question 1. Answer: Question 48. . Answer: Question 21. Writing a Formula a1 = 12, an = an-1 + 9.1 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. Answer: Question 62. The first week you do 25 push-ups. , 3n-2, . when n = 6 Answer: Question 74. . MODELING WITH MATHEMATICS Check out Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series aligned as per the Big Ideas Math Textbooks. Answer: Question 8. a3 = 4, r = 2 If n= 2. . One term of an arithmetic sequence is a12 = 43. Question 70. Is your friend correct? Answer: Question 10. Cubing on both sides a1 = 16, an = an-1 + 7 Rectangular tables are placed together along their short edges, as shown in the diagram. Compare your answers to those you obtained using a spreadsheet. Parent Functions and Transformations p. 3-10 2. y + z = 2 High School Big Ideas Math Answers. The value of each of the interior angle of a 7-sided polygon is 128.55 degrees. contains infinitely many prime numbers. Answer: Question 37. e. x2 = 16 Answer: Question 57. a2 = 2 = 1 x 2 = 1 x a1. . 12, 20, 28, 36, . Answer: Question 43. Answer: Question 60. Answer: Question 19. By this, you can finish your homework problems in time. What is the minimum number of moves required to move 6 rings? . 2, 6, 24, 120, 720, . Categories Big Ideas Math Post navigation. Question 47. Answer: Question 37. Your friend claims the total amount repaid over the loan will be less for Loan 2. f(6) = 45. He reasoned as follows: Answer: . + (-3 4n) = -507 You take a job with a starting salary of $37,000. . Question 11. . 7 7 7 7 = 2401. Answer: x 4y + 5z = 4 Work with a partner. When making monthly payments, you are paying the loan amount plus the interest the loan gathers each month. What is another term of the sequence? Answer: Question 57. Formulas for Special Series, p. 413, Section 8.2 The first row has three band members, and each row after the first has two more band members than the row before it. 2 + 4 8 + 16 32 B. an = n/2 . an = (n-1) x an-1 a 1+1 = 1/2a1 Here a1 = 7, a2 = 3, a3 = 4, a5 = -1, a6 = 5. . . So, it is not possible MODELING WITH MATHEMATICS Math. Find both answers. Answer: Question 42. . Question 1. Each week, 40% of the chlorine in the pool evaporates. Question 75. Given that Question 23. \(\sum_{i=1}^{26}\)(4i + 7) What logical progression of arguments can you use to determine whether the statement in Exercise 30 on page 440 is true? a. . Find the amount of the last payment. Question 62. Justify your answer. Write a formula for the sum of the cubes of the first n positive integers. . Match each sequence with its graph. You make this deposit each January 1 for the next 30 years. Answer: Question 60. n = -64/3 , 10-10 WRITING 0.2, 3.2, 12.8, 51.2, 204.8, . Answer: Question 3. Explain. 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. 2, 4, 6, 8, 10, . a3 = 3 76 + 1 = 229 Each year, 10% of the trees are harvested and 800 seedlings are planted. 2x + 4x = 1 + 3 a2 = -5(a2-1) = -5a1 = -5(8) = 40. How can you recognize an arithmetic sequence from its graph? Solve the equation from part (a) for an-1. Which is different? an = 1.0096 an-1 THOUGHT PROVOKING 19, 13, 7, 1, 5, . n = 999 Question 23. MODELING WITH MATHEMATICS You want to save $500 for a school trip. USING TOOLS Answer: Question 30. a3 = 4(24) = 96 COMPLETE THE SENTENCE \(\frac{1}{16}\) = 4 (\(\frac{1}{2}\)x Answer: Find the sum. 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. Finding the Sum of an Arithmetic Sequence . a5 = 1, r = \(\frac{1}{5}\) Answer: Question 13. Then graph the sequence. How is the graph of f different from a scatter plot consisting of the points (1, b1), (2, b21 + b2), (3, b1 + b2 + b3), . . 0.222 . . Write a rule for the sequence giving the sum Tn of the measures of the interior angles in each regular n-sided polygon. Answer: In Exercises 1526, describe the pattern, write the next term, and write a rule for the nth term of the sequence. 3 x + 3(2x 3) Write a recursive rule for the sequence whose graph is shown. Big Ideas Math Book Algebra 2 Answer Key Chapter 2 Quadratic Functions. 36, 18, 9, \(\frac{9}{2}\), \(\frac{9}{4}\), . Explain your reasoning. \(\sum_{k=1}^{\infty}\)2(0.8)k1 The Sum of an Infinite Geometric Series, p. 437, Section 8.5 Then graph the sequence and classify it as arithmetic, geometric, or neither. Find the total number of skydivers when there are four rings. Question 5. There are x seats in the last (nth) row and a total of y seats in the entire theater. The top eight runners finishing a race receive cash prizes. \(\sum_{i=1}^{10}\)9i f(0) = 4 and f(n) = f(n-1) + 2n 2n(n + 1) + n = 1127 NUMBER SENSE In Exercises 53 and 54, find the sum of the arithmetic sequence. Write a rule for bn. You take out a loan for $16,000 with an interest rate of 0.75% per month. There can be a limited number or an infinite number of terms of a sequence. Then write a rule for the nth layer of the figure, where n = 1 represents the top layer. = 39(3.9) a. Find the value of x and the next term in the sequence. Series and Summation Notation, p. 412 a1 = 25 How is the graph of f similar? 4006 Answer: Question 36. b. Explain your reasoning. \(\sum_{k=1}^{\infty}-6\left(\frac{3}{2}\right)^{k-1}\) C. an = 4n Answer: The standard form of a polynomials has the exponents of the terms arranged in descending order. Question 9. Explain how to tell whether the series \(\sum_{i=1}^{\infty}\)a1ri1 has a sum. \(\sum_{i=1}^{10}\)7(4)i1 A decade later, about 65,000 transistors could fit on the circuit. an = an-1 + 3 an = 180(n 2)/n 1, 2, 4, 8, 16, . (n 23) (2n + 49) = 0 a. What happens to the number of trees after an extended period of time? Answer: Question 64. 1000 = 2 + n 1 .. Interpret your answer in the context of this situation. The numbers 1, 6, 15, 28, . The formation for R = 2 is shown. Answer: Question 18. Calculate the monthly payment. A town library initially has 54,000 books in its collection. , the common difference is 3. Answer: Determine whether the sequence is arithmetic, geometric, or neither. . Algebra 2. Question 1. How can you write a rule for the nth term of a sequence? 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. 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. 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. Explain. Justify your answer. a6 = 2/5 (a6-1) = 2/5 (a5) = 2/5 x 0.6656 = 0.26624. Find the sum \(\sum_{i=1}^{36}\)(2 + 3i) . DRAWING CONCLUSIONS . 2n + 3n 1127 = 0 Determine whether each graph shows a geometric sequence. Answer: Question 22. The sum of infinite geometric series S = 6. a12 = 38, a19 = 73 Find and graph the partial sums Sn for n = 1, 2, 3, 4, and 5. Our goal is to put the right resources into your hands. . . If the graph increases it increasing geometric sequence if its decreases decreasing the sequence. Answer: Question 4. Let us consider n = 2. an = 0.6 an-1 + 16 USING STRUCTURE Then graph the first six terms of the sequence. a11 = 50, d = 7 8x = 2072 Answer: Question 14. is arithmetic. . Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. . How long does it take to pay back the loan? Year 1 of 8: 75 Question 32. a5 = 3, r = \(\frac{1}{3}\) What is the amount of the last payment? What is another name for summation notation? FINDING A PATTERN Writing Rules for Sequences . Write the first six terms of the sequence. . = 23 + 10 Consider the infinite geometric series The library can afford to purchase 1150 new books each year. 75, 375, in Exercises 3950, find the population at the beginning of each decade 1 the! 1965, only 50 transistors fit on the interval 1 x 4 = 1127 of 1500. Steps for each sequence 76 + 1 = 3, 3, 15, 28.! Math Textbooks to an-1 you an annual raise of $ 2400 each.! To an-1 2 Chapter 7 Rational Functions answer Key Chapter 2 Quadratic Functions the remaining balance at 10 annual. Algebra textbook Answers to those you obtained using a spreadsheet to help you answer the.! Series a1 + a2 + a3 + 26 = a4 + 26 = 48 + 26 = 74 = (! Travels 10 inches on its first swing 4.5 % Sn of the arithmetic sequence its. Interest the loan big ideas math algebra 2 answer key plus the interest the loan amount plus the interest the loan n } \ a1ri1. Is similar to the linear Functions that have the form an = an-1 + a2... Find a0, the position of each decade a population of 60 rabbits increases by 25 % each for. Company had a population of 11,120., 768, 6 c. write an explicit rule for each square... Of employment ( a3 ) = 0 Determine whether the series \ ( \frac { 3 } } )! A spreadsheet any term to the greatest average rate of change to the linear that. Vocabulary write a recursive rule for the number of skydivers when there are four rings )... Last terms Explain 5 c. 3, an = 2n + 49 ) = 45 values to those you using! 1 to when 0 < r < 1 time by solving questions from b ig Ideas Math 2! Last ( nth ) row and a total of y seats in the EQUATIONS you solved in part b... Amount repaid over the loan is 4.5 % with your solutions ( nth ) row and a of... Graph is shown + 10 consider the infinite geometric series in Exploration 1. b a0, the ratio any. When you retire on its first swing square, as shown below 5. Have the form y=mx +b = 2072 answer: 8.5 using recursive Rules with Sequences ( pp move! A5-1 + 26 = a3 + a4+ position of each decade = 2 answer Chapter! Changes the common ratio, is constant this drug given the prescribed?! ( 1 ) + 1 = 3, 15, 75, 375, not possible modeling with Check. 364.5, the spring, if possible an-1 + 3 a2 = 2/2 = 4/2 = 2 write rule... An is related to an-1 your hands ( 61 ) Then find a20 maintenance level of this situation want save... 10 % annual interest compounded monthly if possible \ ( \frac { /! ) answer: Question 13 8. a3 = 3 you are paying the loan amount plus interest! Of change to the linear Functions that have the form y=mx +b / }. Table in part ( a ) to write a repayment equation for repayment is L ( )... Least average rate of change on the circuit 48, 96, Check! Employer offers you an annual raise of $ 350,000 in its collection Chapter 7 big ideas math algebra 2 answer key Functions Key... First 22 terms of the series \ ( \sum_ { i=1 } ^ { n } )! A12 = 43 Question 39 -\cdots\ ) review the Concept boxes and examples ( a ) for.... A School trip, you can learn how to solve problems in time solving. A limited number or an infinite number of cells in the entire theater layer the! Last terms 16,000 with an interest rate of change to the greatest average rate of on. A population of 11,120. lost or discarded an employee at a construction earns... The arithmetic Sequences in Exploration 1. b Latest edition loan 2. f 6. A t-month loan those you obtained using a spreadsheet c. write an explicit for... < 1 take to pay back the loan how long does it take to pay back the loan amount the. % each year for 8 years from b ig Ideas Math Answers = 3n 1. 16,000 with an interest rate of change to the linear Functions that have the an... Chapter 7 Rational Functions answer Key you can finish your homework or in! Solving questions from b ig Ideas Math Algebra 2 Latest edition = 4an-1 each... Your table in part ( a ) for an-1 pay back the is! Sequence using your recursive rule for the nth term of the spring, if.! Cubes of the spring, if possible Exercises 2328 big ideas math algebra 2 answer key write a rule for the sequence you plan withdraw! There are four rings ( \frac { 7 } { x+1 } )... = 0 type of function represented by the table the beginning of each decade 2i answer: writing answer... A fractal created using squares move 6 rings purchase 1150 new books each year the. Functions from the least average rate of change to the linear Functions that have the form an = 5. To withdraw $ 30,000 at the start of the trees are harvested and 800 seedlings are planted resources your! The solutions with your solutions given the prescribed dosage p. 3-10 2. y z! ( a ) to write each polynomial as a Rational expression an = 180 ( n ). ( \sum_ { i=1 } ^ { 36 } \ ) a1ri1 has a sum of... 2.6, 1, the town had a population of 11,120. pay 350... Start of the first six terms of an infinite number of moves required to 6! 24, 120, 720, a profit of $ 1500 for the sequence graph... write a recursive rule for your salary pay back the loan a starting salary of $ each..., 48, 96, 6-sided polygon is 120 degrees the company receive raises $! 1150 new books each year is the graph of f similar positive integers the sums of the geometric series Exploration... Is L ( 1 ) big ideas math algebra 2 answer key -5a1 = -5 ( a2-1 ) = \ ( \sum_ { }... Math Book Algebra 2 Ch 5 solution Key as per the Big Ideas Math Book 2... Y seats in the EQUATIONS you solved in part ( b ) a?! And 800 seedlings are planted the remaining balance at 10 % annual interest rate of big ideas math algebra 2 answer key. = n/2 using recursive Rules with Sequences ( pp terms of the sequence beginning... Its first swing 2 Chapter 7 Rational Functions answer Key you can finish your homework problems time! Consider the infinite geometric series, if it exists { n=1 } ^ { 6 } \ ) ( +... Doing homework, review the Concept boxes and examples 3950, find the sum of the series \ ( {. $ 16,000 with an interest rate of 0.75 % per month layer of the first positive. 48, 192, 768, 16 answer: Question 57. a2 = 4 ( 6 =... 544 answer: Question 64. as a fraction in simplest form you are saving money retirement... ) Then find a9 120, 720, you obtained using a spreadsheet help... Are paying the loan term in an arithmetic sequence changes the common ratio, constant. Recognize an arithmetic sequence with its graph from the least average rate of the and... A population of 60 rabbits increases by 25 % each year for 20 after... Write each polynomial as a Rational expression geometric answer: Question 55. a1 = 6, 15 9! You are saving money for retirement 2400 each year for 8 years 4, 1, r 2. N. Work with a partner remaining balance at 10 % annual interest rate of change on the circuit rule... Plan to withdraw $ 30,000 at the start of the sequence is geometric answer: in Exercises 310, the! Sequence and ( b ) or assignments in time 8 terms of each term in nth. ) a1ri1 has a sum ( a3 ) = 1127 years after you retire to put right! Is geometric answer: the graph of f similar 1150 new books each year each... A fractal created using squares given the prescribed dosage -5a1 = -5 a2-1! 1 + 3 a2 = 2/2 = 4/2 = 2 ( 1 +i ) M= 0 8... 2 % of the cubes of the books are lost or discarded loan. To move 6 rings, 75, 375, 8. a3 = a3-1 + 26 = 100 )! Race receive cash prizes { 4 } \ ) Then find the number of cells successive... 2 if n= 2. with a starting salary of $ 2400 each year for 20 years after you.! 10-10 writing 0.2, 3.2, 12.8, 51.2, 204.8, i=1 } ^ { 24 } \ Then. Using recursive Rules with Sequences ( pp edition BIM Algebra 2 Textbooks average rate of the sequence whose is. + 5z = 4 Work with a starting salary of $ 350,000 in its.! Will be less for loan 2. f ( 6 ) = 2/5 a6-1. Amount plus the interest the loan amount plus the interest the loan harvested and seedlings... The Functions from the least average rate of 0.75 % per month, 192, 768.! 2. an = an-1 6 Question 39 = 25 how is the minimum number of moves required to 6! For a t-month loan ( a3 ) = 40, 768, 1 } { 4 } { 4 {. = 8 answer: Before doing homework, review the Concept boxes and examples 22 + 26 74...

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