MATHEMATICAL CONNECTIONS The first four triangular numbers Tn and the first four square numbers Sn are represented by the points in each diagram. a. Answer: Question 13. a1 = 3, an = an-1 6 when n = 5 Use what you know about arithmetic sequences and series to determine what portion of a hekat each man should receive. A. Explain your reasoning. Question 4. Compare the terms of an arithmetic sequence when d > 0 to when d < 0. Log in. y = 3 2x Write a recursive rule for the number an of members at the start of the nth year. Answer: Question 6. What does n represent for each quilt? The monthly payment is $213.59. How can you determine whether a sequence is geometric from its graph? B. (1/10)10 = 1/10n-1 . Thus, make use of our BIM Book Algebra 2 Solution Key Chapter 2 . f. 1, 1, 2, 3, 5, 8, . . MODELING WITH MATHEMATICS a4 = 1/2 8.5 = 4.25 Answer: Question 11. 12, 6, 0, 6, 12, . . Given that, 16, 9, 7, 2, 5, . Answer: Question 67. Compare the given equation with the nth term Explain your reasoning. Consider the infinite geometric series WHICH ONE DOESNT BELONG? Use the drop-down menu below to select your program. Answer: Question 12. 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. You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. Answer: Question 21. . The questions are prepared as per the Big Ideas Math Book Algebra 2 Latest Edition. Your friend claims the total amount repaid over the loan will be less for Loan 2. Big Ideas Math Book Algebra 2 Answer Key Chapter 7 Rational Functions. Answer: In Exercises 310, tell whether the sequence is arithmetic. Answer: ERROR ANALYSIS In Exercises 27 and 28, describe and correct the error in writing a recursive rule for the sequence 5, 2, 3, -1, 4, . WRITING \(\sum_{n=1}^{\infty} 3\left(\frac{5}{4}\right)^{n-1}\) 417424). an = a1 + (n-1)(d) A running track is shaped like a rectangle with two semicircular ends, as shown. Find both answers. Answer: Question 54. a2 =72, a6 = \(\frac{1}{18}\) Based on the BIM Textbooks, our math professional subject experts explained the chapter-wise questions in the BIM Solution Key. . Answer: Question 18. 3 x + 3(2x 3) 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. Year 7 of 8: 286 Answer: \(\sum_{k=3}^{6}\)(5k 2) Describe the pattern. c. 3, 6, 12, 24, 48, 96, . Answer: Question 8. Big Ideas Math Book Algebra 2 Answer Key Chapter 1 Linear Functions. Describe how labeling the axes in Exercises 36 on page 439 clarifies the relationship between the quantities in the problems. With the help of step-by-step explanative . c. Describe what happens to the amount of chlorine in the pool over time. Answer: Question 13. Year 3 of 8: 117 Answer: Question 6. Answer: Solve the system. A radio station has a daily contest in which a random listener is asked a trivia question. Explain your reasoning. Question 5. . 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. . For a regular n-sided polygon (n 3), the measure an of an interior angle is given by an = \(\frac{180(n-2)}{n}\) Answer: .. Write a rule for the nth term. Answer: Question 13. Question 15. a. 3.1, 3.8, 4.5, 5.2, . MODELING WITH MATHEMATICS Let an be your balance n years after retiring. Find the perimeter and area of each iteration. How many apples are in the ninth layer? Answer: Question 15. . , 800 Answer: Question 20. Question 1. The monthly payment is $173.86. Check out Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series aligned as per the Big Ideas Math Textbooks. Question 5. Answer: Question 18. Answer: Question 56. \(\sum_{i=2}^{8} \frac{2}{i}\) Write an explicit rule and a recursive rule for the sequence in part (a). , 8192 a4 = 4/2 = 16/2 = 8 Question 11. \(\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \frac{1}{162}, \ldots\) What is the amount of the last payment? (n 15)(2n + 35) = 0 Finding Sums of Infinite Geometric Series \(\sum_{k=1}^{8}\)5k1 . Answer: Question 14. Answer: Question 14. . How much money will you save? 5 + 6 + 7 +. Work with a partner. Use each recursive rule and a spreadsheet to write the first six terms of the sequence. a. Explain your reasoning. a3 = 4(24) = 96 Answer: Question 14. . The Sierpinski triangle is a fractal created using equilateral triangles. 7x + 3 = 31 The first 8 terms of the geometric sequence 12, 48, 192, 768, . a. f(6) = f(6-1) + 2(6) = f(5) + 12 a1 = 4, an = 0.65an-1 \(2+\frac{4}{3}+\frac{8}{9}+\frac{16}{27}+\frac{32}{81}+\cdots\) Answer: Question 57. REWRITING A FORMULA First, divide a large square into nine congruent squares. Answer: Question 49. , 10-10 a. Given that, Answer: Question 48. 9, 6, 4, \(\frac{8}{3}\), \(\frac{16}{9}\), . . a1 = 2(1) + 1 = 3 an= \(\frac{1}{2}\left(\frac{1}{4}\right)^{n-1}\) Answer: Question 6. Answer: Question 56. 301 = 4 + (n 1)3 Consider 3 x, x, 1 3x are in A.P. Step2: Find the sum . . If not, provide a counterexample. COMPLETE THE SENTENCE Answer: Write the series using summation notation. Determine whether each graph shows a geometric sequence. You save an additional penny each day after that. . a2 = -5(a2-1) = -5a1 = -5(8) = 40. Find the balance after the fifth payment. Rectangular tables are placed together along their short edges, as shown in the diagram. Answer: Question 2. -1 + 2 + 7 + 14 + .. MODELING WITH MATHEMATICS Answer: Question 56. Answer: Question 33. What logical progression of arguments can you use to determine whether the statement in Exercise 30 on page 440 is true? . a1 = -4, an = an-1 + 26. Answer: Question 6. 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. b. when n = 4 Answer: Question 35. Enter each geometric series in a spreadsheet. DRAWING CONCLUSIONS an-1 is the balance before payment, So that balance after the 4th payment will be = $9684.05 27, 9, 3, 1, \(\frac{1}{3}\), . Question 23. Answer: x 4y + 5z = 4 Work with a partner. b. You and your friend are comparing two loan options for a $165,000 house. b. \(\frac{3^{-2}}{3^{-4}}\) Question 3. How much money will you have saved after 100 days? Answer: Question 39. Justify your answer. The library can afford to purchase 1150 new books each year. Question 3. . Answer: Write the series using summation notation. Answer: Question 6. a. Work with a partner. . Look back at the infinite geometric series in Exploration 1. Year 2 of 8: 94 How many pieces of chalk are in the pile? . Answer: Question 55. Also, the maintenance level is 1083.33 Answer: Question 68. Explain your reasoning. Answer: Question 10. Find the first 10 primes in the sequence when a = 3 and b = 4. WRITING EQUATIONS In Exercises 3944, write a rule for the sequence with the given terms. Answer: Question 51. Question 1. Question 39. Then graph the first six terms of the sequence. . a. 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). 8x = 2197 125 7x=28 2, 5, 8, 11, 14, . 0.3, 1.5, 7.5, 37.5, 187.5, . Question 38. You take out a 5-year loan for $15,000. . Order the functions from the least average rate of change to the greatest average rate of change on the interval 1 x 4. Answer: Question 56. MAKING AN ARGUMENT 6, 12, 36, 144, 720, . Answer: Write a recursive rule for the amount of chlorine in the pool at the start of the nth week. In this section, you learned the following formulas. Answer: Question 8. Then find a9. Answer: Question 19. c. Write an explicit rule for the sequence. a6 = 2/5 (a6-1) = 2/5 (a5) = 2/5 x 0.6656 = 0.26624. What type of relationship do the terms of the sequence show? You want to save $500 for a school trip. Answer: Question 4. Answer: Answer: b. C. 1.08 a. Answer: Question 14. Answer: Write an explicit rule for the sequence. Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series helps you to get a grip on the concepts from surface level to a deep level. 213 = 2n-1 Let a1 = 34. \(\sum_{i=1}^{6}\)2i Is your friend correct? Explain your reasoning. 3x=216-18 HOW DO YOU SEE IT? You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. -5 2 \(\frac{4}{5}-\frac{8}{25}-\cdots\) Begin with a pair of newborn rabbits. , 10-10 During a baseball season, a company pledges to donate $5000 to a charity plus $100 for each home run hit by the local team. Is your friend correct? a. Write a rule for the nth term. View step-by-step homework solutions for your homework. = f(0) + 2 = 4 + 1 = 5 DRAWING CONCLUSIONS Use the diagram to determine the sum of the series. Answer: Question 15. WRITING a4 = a + 3d One of the major sources of our knowledge of Egyptian mathematics is the Ahmes papyrus, which is a scroll copied in 1650 B.C. NUMBER SENSE In Exercises 53 and 54, find the sum of the arithmetic sequence. Answer: Question 37. Explain. THOUGHT PROVOKING A town library initially has 54,000 books in its collection. B. an = 35 + 8n Solve both of these repayment equations for L. Ask a question and get an expertly curated answer in as fast as 30 minutes. Answer: Question 14. Question 31. . Question 1. 1.34 feet Then, referring to this Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions is the best option. e. \(\frac{1}{2}\), 1, 2, 4, 8, . Check your solution(s). What is another term of the sequence? , an, . . Writing a Recursive Rule 1, 2.5, 4, 5.5, 7, . 1000 = n + 1 Answer: In Exercises 310, write the first six terms of the sequence. Your employer offers you an annual raise of $1500 for the next 6 years. MODELING WITH MATHEMATICS a2 = 2/5 (a2-1) = 2/5 (a1) = 2/5 x 26 = 10.4 Write the first six terms of the sequence. a3 = 4(3) = 12 -6 5 (2/3) Explain your reasoning. Write a rule for the geometric sequence with the given description. Answer: Question 2. February 15, 2021 / By Prasanna. Step1: Find the first and last terms 3 + \(\frac{5}{2}+\frac{25}{12}+\frac{125}{72}+\cdots\) 798 = 2n an = 0.6 an-1 + 16 Answer: Question 10. After doing deep research and meets the Common Core Curriculum, subject experts solved the questions covered in Big Ideas Math Book Algebra 2 Solutions Chapter 11 Data Analysis and Statistics in an explanative manner. Describe how doubling each term in an arithmetic sequence changes the common difference of the sequence. 216=3x+18 Answer: Question 69. Answer: Question 70. PROBLEM SOLVING 7, 1, 5, 11, 17, . 3 x + 6x 9 x=66. Write a rule for the nth term of the sequence 7, 11, 15, 19, . \(\sum_{i=1}^{34}\)1 Answer: Question 7. . Answer: Question 22. Algebra 2. Assuming this trend continues, what is the total profit the company can make over the course of its lifetime? What do you notice about the graph of a geometric sequence? Answer: Question 10. If the graph increases it increasing geometric sequence if its decreases decreasing the sequence. Each year, 2% of the books are lost or discarded. . 2x y 3z = 6 Does the track shown meet the requirement? .Terms of a sequence DRAWING CONCLUSIONS .+ 15 Answer: Question 64. f(n) = \(\frac{2n}{n+2}\) . a12 = 38, a19 = 73 a2 = 28, a5 = 1792 Justify your answer. Justify your answer. Answer: Question 62. f(x) = \(\frac{1}{x-3}\) r = 0.01/0.1 = 1/10 The common difference is d = 7. 6, 24, 96, 384, . Question 59. What are your total earnings? Answer: 2, 14, 98, 686, 4802, . Answer: Question 16. We can conclude that an-1 3, 5, 9, 15, 23, . . tn = 8192, a = 1 and r = 2 On January 1, you deposit $2000 in a retirement account that pays 5% annual interest. Answer: Question 49. \(\sum_{i=1}^{5}\) 8i 2x + 3y + 2z = 1 . Answer: Question 11. Big Ideas MATH: A Common Core Curriculum for Middle School and High School Mathematics Written by Ron Larson and Laurie Boswell. Each ratio is 2/3, so the sequence is geometric If it does, find the sum. a4 = 4(4) = 16 \(\frac{1}{20}, \frac{2}{30}, \frac{3}{40}, \frac{4}{50}, \ldots\) a3 = 2/5 (a3-1) = 2/5 (a2) = 2/5 x 10.4 = 4.16 a. e. x2 = 16 So, it is not possible 58.65 a1 = 5, an = \(\frac{1}{4}\)an-1 Thus the amount of chlorine in the pool over time is 1333. The constant ratio of consecutive terms in a geometric sequence is called the __________. n = 23. c. \(\sum_{i=5}^{n}\)(7 + 12i) = 455 MODELING WITH MATHEMATICS a. f. x2 5x 8 = 0 Question 2. Each week you do 10 more push-ups than the previous week. Step2: Find the sum . a1 = 4, an = 2an-1 1 Find the value of x and the next term in the sequence. Then write the area as the sum of an infinite geometric series. an = (an-1)2 10 435440). . Pieces of chalk are stacked in a pile. Question 5. explicit rule, p. 442 Question 3. \(\sum_{i=1}^{n}\)(3i + 5) = 544 \(\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\cdots\) 19, 13, 7, 1, 5, . c. 3x2 14 = -20 . . Boswell, Larson. Sn = a1 + a1r + a1r2 + a1r3 + . Each row has one less piece of chalk than the row below it. What is the approximate frequency of E at (labeled 4)? Answer: Question 8. Answer: Essential Question How can you find the sum of an infinite geometric series? On the first swing, your cousin travels a distance of 14 feet. a1 = 1 a. In a sequence, the numbers are called __________ of the sequence. Boswell, Larson. 3n = 300 an = 180(n 2)/n Question 4. If so, provide a proof. Then write a formula for the sum Sn of the first n terms of an arithmetic sequence. Classify the sequence as arithmetic, geometric, or neither. Answer: In Exercises 3138, write a rule for the nth term of the arithmetic sequence. A. an = 51 + 8n x=198/3 Question 31. \(\frac{1}{6}, \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{2}, \ldots\) Answer: Question 35. You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. 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 \(\sum_{i=1}^{9}\)5(2)i1 . Answer: Question 4. Answer: Question 50. Answer: Question 21. Answer: Question 23. USING STRUCTURE a3 = 1/2 17 = 8.5 Anarithmetic sequencehas a constantdifference between each consecutive pair of terms. Answer: Question 27. The numbers 1, 6, 15, 28, . The curve radius of lane 1 is 36.5 meters, as shown in the figure. 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 . a1 = 1 1 = 0 There is an equation for it, How is the graph of f different from a scatter plot consisting of the points (1, b1), (2, b21 + b2), (3, b1 + b2 + b3), . . Explain. Explain your reasoning. Solutions available . Answer: Question 32. Give an example of a sequence in which each term after the third term is a function of the three terms preceding it. In April of 1965, an engineer named Gordon Moore noticed how quickly the size of electronics was shrinking. 44, 11, \(\frac{11}{4}\), \(\frac{11}{16}\), \(\frac{11}{64}\), .