Write the first five terms of the sequence. Answer: Question 12. b. Question 9. c. How long will it take to pay off the loan? Find the value of n. If it does, then write a rule for the nth term of the sequence, and use a spreadsheet to fond the sum of the first 20 terms. \(\sum_{k=1}^{8}\)5k1 Rule for a Geometric Sequence, p. 426 an = an-1 5 Answer: Question 49. The sum Sn of the first n terms of an infinite series is called a(n) ________. The first week you do 25 push-ups. An employee at a construction company earns $33,000 for the first year of employment. (Hint: Let a20 = 0.) , 3n-2, . Answer: Question 4. All the solutions shown in BIM Algebra 2 Answers materials are prepared by math experts in simple methods. .. . Interpret your answer in the context of this situation. A teacher of German mathematician Carl Friedrich Gauss (17771855) asked him to find the sum of all the whole numbers from 1 through 100. View step-by-step homework solutions for your homework. Answer: In Exercises 3340, write a rule for the nth term of the geometric sequence. Answer: Tell whether the sequence is arithmetic, geometric, or neither. Title: Microsoft Word - assessment_book.doc Author: dtpuser Created Date: 9/15/2009 11:28:59 AM On each successive swing, your cousin travels 75% of the distance of the previous swing. . Each row has one less piece of chalk than the row below it. Here is an example. Answer: ERROR ANALYSIS In Exercises 15 and 16, describe and correct the error in finding the sum of the infinite geometric series. Check out the modules according to the topics from Big Ideas Math Textbook Algebra 2 Ch 3 Quadratic Equations and Complex Numbers Solution Key. f(n) = \(\frac{n}{2n-1}\) The number of cans in each row is represented by the recursive rule a1 = 20, an = an-1 2. .. Then find a15. b. .Terms of a sequence b. Then graph the first six terms of the sequence. The solutions seen in Big Ideas Math Book Algebra 2 Answer Key is prepared by math professionals in a very simple manner with explanations. an-1 Here is what Gauss did: Write your answer in terms of n, x, and y. Answer: In Exercises 4148, write an explicit rule for the sequence. A company had a profit of $350,000 in its first year. Question 2. Sign up. . a5 = 4(384) =1,536 Question 47. . 5, 10, 15, 20, . Each week you do 10 more push-ups than the previous week. Finding the Sum of an Arithmetic Sequence An online music service initially has 50,000 members. How many seats are in the front row of the theater? is arithmetic. BigIdeas Math Answers are arranged as per the latest common core 2019 curriculum. Write a recursive rule for the sequence whose graph is shown. Copy and complete the table to evaluate the function. a3 = a3-1 + 26 = a2 + 26 = 22 + 26 = 48. Question 59. For example, in the geometric sequence 1, 2, 4, 8, . We have included Questions . The loan is secured for 7 years at an annual interest rate of 11.5%. The Greek mathematician Zeno said no. Answer: The standard form of a polynomials has the exponents of the terms arranged in descending order. Answer: Question 56. Describe how doubling each term in an arithmetic sequence changes the common difference of the sequence. In April of 1965, an engineer named Gordon Moore noticed how quickly the size of electronics was shrinking. Our goal is to put the right resources into your hands. Justify your answers. What is another term of the sequence? With the help of this Big Ideas Math Algebra 2 answer key, the students can get control over the subject from surface level to the deep level. Answer: Answer: Find the sum. WRITING Justify your answers. a1 = 3, an = an-1 7 . In Example 6, how does the monthly payment change when the annual interest rate is 5%? 5 + 11 + 17 + 23 + 29 f(3) = 15. Answer: Question 4. an = an-1 + 3 MODELING WITH MATHEMATICS Question 3. D. 10,000 Complete homework as though you were also preparing for a quiz. Write a recursive rule for the population Pn of the town in year n. Let n = 1 represent 2010. Answer: Question 3. Question 22. THOUGHT PROVOKING a. State the domain and range. Write a recursive rule that is different from those in Explorations 13. There are x seats in the last (nth) row and a total of y seats in the entire theater. Answer: Question 35. 301 = 4 + 3n 3 Write a recursive rule for the number an of books in the library at the beginning of the nth year. Question 4. The expressions 3 x, x, and 1 3x are the first three terms in an arithmetic sequence. a4 = 4/2 = 16/2 = 8 Sn = 16383 f(2) = 9. Answer: Write an explicit rule for the sequence. . Using the table, show that both series have finite sums. Answer: Simplify the expression. . Justify your answers. Question 41. . Recognizing Graphs of Geometric Sequences The distance from the center of a semicircle to the inside of a lane is called the curve radius of that lane. Answer: Question 54. \(3+\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\cdots\) Explain your reasoning. . Answer: Question 60. a1 = 1 1 = 0 Write a recursive rule for an = 105 (\(\frac{3}{5}\))n1 . Answer: Question 8. Partial Sums of Infinite Geometric Series, p. 436 . an = \(\frac{1}{4}\)(5)n-1 Explain your reasoning. Find the sum of the positive odd integers less than 300. a6 = 96, r = 2 an = 0.6 an-1 + 16 a11 = 43, d = 5 0.3, 1.5, 7.5, 37.5, 187.5, . Answer: Question 3. The value of each of the interior angle of a 4-sided polygon is 90 degrees. \(\sum_{i=1}^{n}\)(3i + 5) = 544 On the first day, the station gives $500 to the first listener who answers correctly. an = (an-1)2 10 Answer: Question 17. Write a rule for bn. a. Part of the pile is shown. a. Question 1. Answer: Question 20. Answer: Question 55. ISBN: 9781635981414. 8, 4, 2, 1, \(\frac{1}{2}\), . Answer: Question 4. MODELING WITH MATHEMATICS n = 23 You can find solutions for practice, exercises, chapter tests, chapter reviews, and cumulative assessments. 800 = 4 + 2n 2 How do the answers in Example 7 change when the annual interest rate is 7.5% and the monthly payment is $1048.82? and balance after 85 payment is 173.86 159.49 = 14.37. an = 0.6 an-1 + 16 The first four iterations of the fractal called the Koch snowflake are shown below. Solve both of these repayment equations for L. + (-3 4n) = -507 MODELING WITH MATHEMATICS a. Answer: Compare these values to those in your table in part (b). Access the user-friendly solutions provided for all the concepts of Chapter 8 Sequences and Series from Big Ideas Math Algebra 2 Textbooks here for free of cost. Answer: Question 24. Answer: Question 35. an = 180(n 2)/n Explain your reasoning. . Therefore, the recursive rule for the sequence is an = an-2 an-1. Since then, the companys profit has decreased by 12% per year. 2, 4, 6, 8, 10, . Question 10. How many apples are in the stack? . The value of x is 2/3 and next term in the sequence is -8/3. Each year, 2% of the books are lost or discarded. 2: Teachers; 3: Students; . Question 1. Mathematical Practices 216 = 3(x + 6) Answer: Find the sum. Answer: Question 5. \(\sum_{n=1}^{\infty} 3\left(\frac{5}{4}\right)^{n-1}\) Answer: Question 27. B. a4 = 53 Divide 10 hekats of barley among 10 men so that the common difference is \(\frac{1}{8}\) of a hekat of barley. You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. a1 = 16, an = an-1 + 7 At this point, the increase and decrease are equal. \(\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, \ldots\) \(\sum_{n=1}^{20}\)(4n + 6) MODELING WITH MATHEMATICS You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. Let an be the total area of all the triangles that are removed at Stage n. Write a rule for an. In the first round of the tournament, 32 games are played. b. 58.65 MODELING WITH MATHEMATICS 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. .+ 12 f(3) = f(3-1) + 2(3) The monthly payment is $91.37. The value that a drug level approaches after an extended period of time is called the maintenance level. Recursive Equations for Arithmetic and Geometric Sequences, p. 442 Answer: Question 41. a6 = 2/5 (a6-1) = 2/5 (a5) = 2/5 x 0.6656 = 0.26624. How can you determine whether a sequence is geometric from its graph? The process involves removing smaller triangles from larger triangles by joining the midpoints of the sides of the larger triangles as shown. Answer: Question 16. Write an explicit rule for the number of cans in row n. This problem produces a sequence called the Fibonacci sequence, which has both a recursive formula and an explicit formula as follows. A quilt is made up of strips of cloth, starting with an inner square surrounded by rectangles to form successively larger squares. How to access Big Ideas Math Textbook Answers Algebra 2? a. You make a $500 down payment on a $3500 diamond ring. FINDING A PATTERN How is the graph of f different from a scatter plot consisting of the points (1, b1), (2, b21 + b2), (3, b1 + b2 + b3), . Answer: Question 46. How many transistors will be able to fit on a 1-inch circuit when you graduate from high school? Answer: Question 8. Classify the sequence as arithmetic, geometric, or neither. . In Example 6, suppose 75% of the fish remain each year. Sn = a1\(\left(\frac{1-r^{n}}{1-r}\right)\) S = a1/1-r Question 53. Write a recursive rule for the balance an of the loan at the beginning of the nth month. a5 = 1, r = \(\frac{1}{5}\) n = 15. Question 10. Use the given values to write an equation relating x and y. \(\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\cdots\) 9 + 16 + 25 + . For example, you will save two pennies on the second day, three pennies on the third day, and so on. a5 = 41, a10 = 96 CRITICAL THINKING A town library initially has 54,000 books in its collection. Answer: Essential Question How can you recognize an arithmetic sequence from its graph? Answer: Question 17. 3x 2z = 8 d. If you pay $350 instead of $300 each month, how long will it take to pay off the loan? Answer: Question 5. On each bounce, the basketball bounces to 36% of its previous height, and the baseball bounces to 30% of its previous height. . \(\frac{1}{4}, \frac{1}{16}, \frac{1}{64}, \frac{1}{256}, \frac{1}{1024}, \ldots\) ABSTRACT REASONING S29 = 1,769. Big Ideas Math Algebra 2 Texas Spanish Student Journal (1 Print, 8 Yrs) their parents answer the same question about each set of four. Tell whether the sequence 12, 4, 4, 12, 20, . . (1/10)n-1 Question 75. The first term is 72, and each term is \(\frac{1}{3}\) times the previous term. Answer: Question 52. February 15, 2021 / By Prasanna. Question 62. What happens to the population of fish over time? 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. 81, 27, 9, 3, 1, . The Sierpinski triangle is a fractal created using equilateral triangles. Answer: Question 26. Then describe what happens to Sn as n increases. Answer: Question 54. Then write a formula for the sum Sn of the first n terms of an arithmetic sequence. . Write a rule for the number of cells in the nth ring. A regional soccer tournament has 64 participating teams. Answer: Question 48. It is seen that after n = 12, the same value of 1083.33 is repeating. 1 + x + x2 + x3 + x4 13, 6, 1, 8, . What is the amount of the last payment? You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. Answer: 8.2 Analyzing Arithmetic Sequences and Series (pp. a3 = 2(3) + 1 = 7 (-3 4(3)) + (-3 4(4)) + . Answer: Question 14. MATHEMATICAL CONNECTIONS \(\sum_{i=0}^{8}\)8(\(\frac{2}{3}\))i a1 = 2, Answer: Question 6. an = r . f(0) = 10 In a sequence, the numbers are called the terms of the sequence. a1 = 26, an = 2/5 (an-1) when n = 7 Answer: Question 42. ABSTRACT REASONING Answer: a. 2, 14, 98, 686, 4802, . Answer: Question 42. . Answer: Ask a question and get an expertly curated answer in as fast as 30 minutes. Year 1 of 8: 75 \(\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+\cdots\) f(x) = \(\frac{1}{x-3}\) The next term is 3 x, x, 1 3x . The explicit rule an= 30n+ 82 gives the amount saved after n months. Answer: Question 21. The Solutions covered here include Questions from Chapter Tests, Review Tests, Cumulative Practice, Cumulative Assessments, Exercise Questions, etc. Answer: Find the sum. . \(\frac{2}{5}+\frac{4}{25}+\frac{8}{125}+\frac{16}{1625}+\frac{32}{3125}+\cdots\) y + z = 2 Question 1. b. Then graph the first six terms of the sequence. 6, 12, 36, 144, 720, . Answer: Question 57. Each year, the company loses 20% of its current members and gains 5000 new members. The graph shows the first six terms of the sequence a1 = p, an = ran-1. b. \(\sum_{i=1}^{10}\)7(4)i1 an-1 How long does it take to pay back the loan? a1 = 4, an = an-1 + 26 Question 6. On January 1, you deposit $2000 in a retirement account that pays 5% annual interest. . Write a rule for the sequence formed by the curve radii. an = 180(6 2)/6 a3 = 2/5 (a3-1) = 2/5 (a2) = 2/5 x 10.4 = 4.16 Find the amount of the last payment. . 441450). b. Answer: What is the maintenance level of this drug given the prescribed dosage? a2 = 4(6) = 24. 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