. n = -35/2 is a negatuve value. The first term is 72, and each term is \(\frac{1}{3}\) times the previous term. Find the sum of the terms of each geometric sequence. Solutions available . Answer: ERROR ANALYSIS In Exercises 51 and 52, describe and correct the error in finding the sum of the series. . b. a4 = 4(96) = 384 Question 5. Question 9. b. 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. .has a finite sum. . Answer: Question 72. Question 33. Interpret your answer in the context of this situation. Question 3. Begin with a pair of newborn rabbits. COMPLETE THE SENTENCE A. an = 51 + 8n C. 1.08 Answer: Question 47. a5 = a4 5 = -14 5 = -19 Answer: Answer: Write a rule for the nth term of the sequence. 2, \(\frac{3}{2}\), \(\frac{9}{8}\), \(\frac{27}{32}\), . a6 = 3 2065 + 1 = 6196. Question 1. Answer: Answer: Question 33. The value that a drug level approaches after an extended period of time is called the maintenance level. Write a recursive rule for the balance an of the loan at the beginning of the nth month. a. Section 8.1Sequences, p. 410 0.3, 1.5, 7.5, 37.5, 187.5, . February 15, 2021 / By Prasanna. Question 9. \(\sum_{i=1}^{n}\)(3i + 5) = 544 . \(\frac{2}{5}+\frac{4}{25}+\frac{8}{125}+\frac{16}{1625}+\frac{32}{3125}+\cdots\) WHAT IF? Answer: Question 5. .. . . Describe how the structure of the equation presented in Exercise 40 on page 448 allows you to determine the starting salary and the raise you receive each year. -3(n 2) 4(n 2)(3 + n)/2 = -507 7 + 10 + 13 +. Answer: Question 1. Calculate the monthly payment. 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? c. 3x2 14 = -20 b. Answer: Question 12. View step-by-step homework solutions for your homework. Which graph(s) represents an arithmetic sequence? . \(\sum_{n=1}^{\infty}\left(-\frac{1}{2}\right)^{n-1}\) a. Answer: MODELING WITH MATHEMATICS In Exercises 57 and 58, use the monthly payment formula given in Example 6. a1 = 32, r = \(\frac{1}{2}\) Answer: Question 58. 36, 18, 9, \(\frac{9}{2}\), \(\frac{9}{4}\), . MODELING WITH MATHEMATICS Question 4. 301 = 4 + 3n 3 a1 = 4(1) = 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. 1, 4, 7, 10, . Explain. an = 108 Use the sequence mode and the dot mode of a graphing calculator to graph the sequence. f. x2 5x 8 = 0 a6 = -5(a6-1) = -5a5 = -5(-5000) = 25,000. .. \(\frac{2}{3}, \frac{2}{6}, \frac{2}{9}, \frac{2}{12}, \ldots\) . 7x+3=31 Question 73. Question 66. a6 = 96, r = 2 Write a recursive rule that represents the situation. . Students can know the difference between trigonometric functions and trigonometric ratios from here. Answer: Question 26. Answer: Question 36. 441450). WRITING EQUATIONS In Exercises 3944, write a rule for the sequence with the given terms. HOW DO YOU SEE IT? WRITING Answer: Question 58. Enhance your performance in homework, assignments, chapter test, etc by practicing from our . Moores prediction was accurate and is now known as Moores Law. Answer: In Exercises 310, write the first six terms of the sequence. How did understanding the domain of each function help you to compare the graphs in Exercise 55 on page 431? . Then graph the first six terms of the sequence. 11.7, 10.8, 9.9, 9, . an = a1rn-1. REWRITING A FORMULA Answer: Question 3. . b. HOW DO YOU SEE IT? Look back at the infinite geometric series in Exploration 1. Then verify your rewritten formula by funding the sums of the first 20 terms of the geometric sequences in Exploration 1. Let an be your balance n years after retiring. Question 7. \(\sum_{i=1}^{12}\)4 (\(\frac{1}{2}\))i+3 c. A. a3 = 11 Explicit: fn = \(\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\frac{1}{\sqrt{5}}\left(\frac{1-\sqrt{5}}{2}\right)^{n}\), n 1 Work with a partner. Answer: Question 68. Given that, Answer: Vocabulary and Core Concept Check 4, 20, 100, 500, . . Answer: Question 28. Answer: Vocabulary and Core Concept Check 1, 6, 11, 16, . . 7n 28 + 6n + 6n 120 = 455 a1 = 34 USING STRUCTURE a6 = 4( 1,536) = 6,144, Question 24. Question 1. B. an = n/2 Question 23. a18 = 59, a21 = 71 800 = 4 + 2n 2 b. Answer: Question 19. Answer: Justify your answers. If n = 1. \(\sum_{n=1}^{\infty} 8\left(\frac{1}{5}\right)^{n-1}\) WRITING D. an = 35 8n Answer: Write the first six terms of the sequence. . .+ 100 = 23 + 10 Answer: Answer: Find the sum. WHAT IF? Which is different? For what values of n does the rule make sense? Answer: Question 21. Answer: Question 56. . . f(3) = f(3-1) + 2(3) The first 22 terms of the sequence 17, 9, 1, 7, . Answer: Question 27. S = a1/1-r (n 9) (6n + 67) = 0 You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. an = 180(3 2)/3 Each year, the company loses 20% of its current members and gains 5000 new members. Answer: Question 60. . Answer: Question 23. (3n + 13n)/2 + 5n = 544 f(n) = \(\frac{2n}{n+2}\) Sign up. Let us consider n = 2. 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). 1st Edition. \(\sum_{i=1}^{10}\)4(\(\frac{3}{4}\))i1 Year 3 of 8: 117 . . Answer: Question 19. Grounded in solid pedagogy and extensive research, the program embraces Dr. John Hattie's Visible Learning Research. CRITICAL THINKING . \(\frac{1}{6}, \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{2}, \ldots\) A regular polygon has equal angle measures and equal side lengths. Answer: Determine the type of function represented by the table. For a 2-month loan, t= 2, the equation is [L(1 + i) M](1 + i) M = 0. Answer: In Exercises 4148, write an explicit rule for the sequence. Answer: Question 17. Answer: In Exercises 3340, write a rule for the nth term of the geometric sequence. 4 + \(\frac{12}{5}+\frac{36}{25}+\frac{108}{125}+\frac{324}{625}+\cdots\) Answer: Essential Question How can you recognize a geometric sequence from its graph? Answer: Question 11. Use each formula to determine how many rabbits there will be after one year. . a2 = 4(2) = 8 Answer: Write a recursive rule for the sequence. an = 180(4 2)/4 . Answer: Vocabulary and Core Concept Check When an infinite geometric series has a finite sum, what happens to r n as n increases? .Terms of a sequence 375, 75, 15, 3, . Big Ideas Math Book Algebra 2 Answer Key Chapter 2 Quadratic Functions. 2x 3y + z = 4 Answer: Question 60. .. Then find a9. Answer: Question 4. 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. The length2 of the second loop is 0.9 times the length of the first loop. a1 = 4, an = 0.65an-1 h(x) = \(\frac{1}{x-2}\) + 1 \(\sum_{k=1}^{4}\)3k2 c. 2, 4, 6, 8, . \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots\) \(\sum_{i=1}^{n}\)(4i 1) = 1127 an = 180/3 = 60 The top eight runners finishing a race receive cash prizes. Describe what happens to the values in the sequence as n increases. Tell whether the sequence 7, 14, 28, 56, 112, . Explain. 5 + 6 + 7 +. Answer: Question 2. a1 = 12, an = an-1 + 16 Use the pattern of checkerboard quilts shown. Tn = 180(12 2) 8 x 2197 = -125 What is the amount of the last payment? a2 = 2(2) + 1 = 5 . . -5 2 \(\frac{4}{5}-\frac{8}{25}-\cdots\) Use the given values to write an equation relating x and y. He predicted how the number of transistors that could fit on a 1-inch diameter circuit would increase over time. WRITING In Example 6, how does the monthly payment change when the annual interest rate is 5%? 216=3x+18 All the solutions shown in BIM Algebra 2 Answers materials are prepared by math experts in simple methods. Answer: Question 6. Answer: Core Concepts A population of 60 rabbits increases by 25% each year for 8 years. USING EQUATIONS The rule for a recursive sequence is as follows. a2 = 2/2 = 4/2 = 2 Is the sequence formed by the curve radii arithmetic, geometric, or neither? Loan 2 is a 30-year loan with an annual interest rate of 4%. Access the user-friendly solutions . \(3+\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\cdots\) a4 = a + 3d Big Ideas Math . NUMBER SENSE In Exercises 53 and 54, find the sum of the arithmetic sequence. a1 = 34 5, 20, 35, 50, 65, . Suppose the spring has infinitely many loops, would its length be finite or infinite? n = -67/6 is a negatuve value. The variables x and y vary inversely. . Use what you know about arithmetic sequences and series to determine what portion of a hekat each man should receive. Learn how to solve questions in Chapter 2 Quadratic Functions with the help of the Big Ideas Math Algebra 2 Book Answer Key. Answer: A recursive sequence is also called the recurrence sequence it is a sequence of numbers indexed by an integer and generated by solving a recurrence equation. Answer: 8.3 Analyzing Geometric Sequences and Series (pp. . Tell whether the sequence 12, 4, 4, 12, 20, . At each stage, each new branch from the previous stage grows two more branches, as shown. Here is what Gauss did: . Sum = a1(1 r) (The figure shows a partially completed spreadsheet for part (a).). . \(\sum_{i=1}^{20}\)(2i 3) 2x 3 = 1 4x How many seats are in the front row of the theater? . \(\sum_{i=10}^{25}\)i 1, 2, 2, 4, 8, 32, . Make a table that shows n and an for n= 1, 2, 3, 4, 5, 6, 7, and 8. Question 15. A towns population increases at a rate of about 4% per year. \(\sum_{i=1}^{26}\)(4i + 7) Answer: Question 48. Cubing on both sides (3n + 64) (n 17) = 0 3n = 300 Answer: USING STRUCTURE . a1 = the first term of the series What is a rule for the nth term of the sequence? (1/10)n-1 . Let an be the number of skydivers in the nth ring. Your salary is given by the explicit rule an = 35,000(1.04)n-1, where n is the number of years you have worked. a2 = a1 5 = 1-5 = -4 a2 = 64, r = \(\frac{1}{4}\) 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. Step2: Find the sum There are x seats in the last (nth) row and a total of y seats in the entire theater. . Answer: Question 21. This is similar to the linear functions that have the form y=mx +b. Answer: Question 3. The population declines by 10% each decade for 80 years. Since then, the companys profit has decreased by 12% per year. After the first year, your salary increases by 3.5% per year. Find the population at the end of each decade. a1 = 4(1) + 7 = 11. Question 5. Evaluating Recursive Rules, p. 442 MODELING WITH MATHEMATICS Answer: Question 70. \(\left(\frac{9}{49}\right)^{1 / 2}\) Write a conjecture about how you can determine whether the infinite geometric series Use finite differences to find a pattern. |r| < 1, the series does have a limit given by formula of limit or sum of an infinite geometric series 1, 7, 13, 19, . a. tn = arn-1 Given, (11 2i) (-3i + 6) = 8 + x Answer: Question 8. (7 + 12(5)) + (7 + 12(6)) + . 12, 20, 28, 36, . (7 + 12n) = 455 Answer: Question 3. Evaluating a Recursive Rule MODELING WITH MATHEMATICS The diagram shows the bounce heights of a basketball and a baseball dropped from a height of 10 feet. Answer: Question 59. S = 2/(1-2/3) You borrow $10,000 to build an extra bedroom onto your house. . 8x = 2072 c. How long will it take to pay off the loan? \(\sum_{i=1}^{35}\)1 6, 24, 96, 384, . Looking at the race as Zeno did, the distances and the times it takes the person to run those distances both form infinite geometric series. What is the total amount of prize money the radio station gives away during the contest? DRAWING CONCLUSIONS What is the maintenance level of this drug given the prescribed dosage? The loan is secured for 7 years at an annual interest rate of 11.5%. . . Find the total distance flown at 30-minute intervals. The sum of infinite geometric series S = 6. Answer: Question 18. You push your younger cousin on a tire swing one time and then allow your cousin to swing freely. a1 = 25 Answer: Question 12. an = 180(6 2)/6 Describe the pattern, write the next term, and write a rule for the nth term of the sequence. More textbook info . Licensed math educators from the United States have assisted in the development of Mathleaks . WHAT IF? r = a2/a1 . Answer: Question 7. Question 29. Write your answer in terms of n, x, and y. The Sierpinski carpet is a fractal created using squares. HOW DO YOU SEE IT? Write a recursive rule for the sequence and find its first eight terms. M = L\(\left(\frac{i}{1-(1+i)^{-t}}\right)\). Write a rule for the nth term. recursive rule, p. 442, Core Concepts Question 11. a4 = 3 229 + 1 = 688 f(0) = 10 . n = 15. 2: Teachers; 3: Students; . . 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. . Here a1 = 7, a2 = 3, a3 = 4, a5 = -1, a6 = 5. Question 4. MODELING WITH MATHEMATICS Answer: Question 26. Answer: Question 57. Classify the sequence as arithmetic, geometric, or neither. Use a spreadsheet to help you answer the question. BIM Algebra 2 Chapter 8 Sequences and Series Solution Key is given by subject experts adhering to the Latest Common Core Curriculum. Explain. Answer: Question 56. Question 28. . Answer: Question 6. Is your friend correct? WHICH ONE DOESNT BELONG? Answer: In Exercises 1526, describe the pattern, write the next term, and write a rule for the nth term of the sequence. \(\sum_{k=1}^{\infty} \frac{11}{3}\left(\frac{3}{8}\right)^{k-1}\) Answer: Question 69. A sequence is an ordered list of numbers. \(\frac{7}{7^{1 / 3}}\) a1 = 2(1) + 1 = 3 a2 = 3 25 + 1 = 76 . What happens to the population of fish over time? a1 = 34 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. Answer: Question 14. In a skydiving formation with R rings, each ring after the first has twice as many skydivers as the preceding ring. MODELING WITH MATHEMATICS a. Let a1 = 34. Answer: Graph the function. Question 3. q (x) = x 3 6x + 3x 4. USING EQUATIONS FINDING A PATTERN an = \(\frac{1}{4}\)(5)n-1 MODELING WITH MATHEMATICS an = a1 x rn1 .. \(\sum_{i=1}^{6}\)4(3)i1 . Answer: Question 14. C. an = 51 8n How many pieces of chalk are in the pile? Answer: In Exercises 3138, write a rule for the nth term of the arithmetic sequence. f(3) = 15. Answer: 8 rings? . Question 7. FINDING A PATTERN How much money will you save? f(6) = 45. Your friend claims that 0.999 . 3, 6, 9, 12, 15, 18, . a1 = -4, an = an-1 + 26. You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. . n = 11 Answer: Essential Question How can you find the sum of an infinite geometric series? . a5 = 1, r = \(\frac{1}{5}\) a3 = 3 1 = 9 1 = 8 The number of items increases until it stabilizes at 57,500. 2 + \(\frac{2}{6}+\frac{2}{36}+\frac{2}{216}+\frac{2}{1296}+\cdots\) The library can afford to purchase 1150 new books each year. You borrow $2000 at 9% annual interest compounded monthly for 2 years. a26 = 4(26) + 7 = 111. 2x y 3z = 6 4 52 25 = 15 Answer: Question 10. The track has 8 lanes that are each 1.22 meters wide. 3, 12, 48, 192, 768, . b. In a geometric sequence, the ratio of any term to the previous term, called the common ratio, is constant. Answer: Question 68. 4, 8, 12, 16, . 7 7 7 7 = 2401. D. 10,000 a1 = 1 1 = 0 , the common ratio is 2. a. Answer: Sequences and Series Maintaining Mathematical Proficiency Page 407, Sequences and Series Mathematical Practices Page 408, Lesson 8.1 Defining and Using Sequences and Series Page(409-416), Defining and Using Sequences and Series 8.1 Exercises Page(414-416), Lesson 8.2 Analyzing Arithmetic Sequences and Series Page(417-424), Analyzing Arithmetic Sequences and Series 8.2 Exercises Page(422-424), Lesson 8.3 Analyzing Geometric Sequences and Series Page(425-432), Analyzing Geometric Sequences and Series 8.3 Exercises Page(430-432), Sequences and Series Study Skills: Keeping Your Mind Focused Page 433, Sequences and Series 8.1 8.3 Quiz Page 434, Lesson 8.4 Finding Sums of Infinite Geometric Series Page(435-440), Finding Sums of Infinite Geometric Series 8.4 Exercises Page(439-440), Lesson 8.5 Using Recursive Rules with Sequences Page(441-450), Using Recursive Rules with Sequences 8.5 Exercises Page(447-450), Sequences and Series Performance Task: Integrated Circuits and Moore s Law Page 451, Sequences and Series Chapter Review Page(452-454), Sequences and Series Chapter Test Page 455, Sequences and Series Cumulative Assessment Page(456-457), Big Ideas Math Answers Grade 7 Accelerated, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 2 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 1 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 7 Module 2 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 7 Module 3 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 3 Module 2 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 3 Module 1 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 2 Answer Key. f(1) = \(\frac{1}{2}\)f(0) = 1/2 10 = 5 The first term of the series for the parabola below is represented by the area of the blue triangle and the second term is represented by the area of the red triangles. Then graph the first six terms of the sequence. Sn = a1 + a1r + a1r2 + a1r3 + . 7x + 3 = 31 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. Then describe what happens to Sn as n increases. You are buying a new house. . . . . Write the first five terms of the sequence. . Justify your answer. Question 41. Answer: Question 16. Rule for a Geometric Sequence, p. 426 b. . 1 + 0.1 + 0.01 + 0.001 + 0.0001 +. . 216=3(x+6) 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. 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. \(\sum_{i=1}^{\infty} \frac{2}{5}\left(\frac{5}{3}\right)^{i-1}\) How is the graph of f similar? . Employees at the company receive raises of $2400 each year. Ageometric sequencehas a constant ratiobetweeneach pair of consecutive terms. Write a recursive rule for the sequence 5, 20, 80, 320, 1280, . e. x2 = 16 We have included Questions . . Answer: Question 18. a2 = 2 = 1 x 2 = 1 x a1. n = 2 Answer: Question 44. Find both answers. Answer: Question 6. In Example 3, suppose there are nine layers of apples. Answer: Question 8. WRITING a21 = 25, d = \(\frac{3}{2}\) 798 = 2n . Answer: Question 53. a2 =72, a6 = \(\frac{1}{18}\) Answer: Determine whether the graph represents an arithmetic sequence, geometric sequence, or neither. Check out the modules according to the topics from Big Ideas Math Textbook Algebra 2 Ch 3 Quadratic Equations and Complex Numbers Solution Key. . . . . is geometric. Partial Sums of Infinite Geometric Series, p. 436 What do you notice about the graph of an arithmetic sequence? You make a $500 down payment on a $3500 diamond ring. a0 = 162, an = 0.5an-1 Answer: c. World records must be set on tracks that have a curve radius of at most 50 meters in the outside lane. Compare these values to those in your table in part (b). The process involves removing smaller triangles from larger triangles by joining the midpoints of the sides of the larger triangles as shown. Answer: Question 21. A teacher of German mathematician Carl Friedrich Gauss (17771855) asked him to find the sum of all the whole numbers from 1 through 100. Give an example of a real-life situation which you can represent with a recursive rule that does not approach a limit. Writing Rules for Sequences Classify the solution(s) of each equation as real numbers, imaginary numbers, or pure imaginary numbers. a4 = 4/2 = 16/2 = 8 Question 2. Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. 7, 12, 17, 22, . Explain your reasoning. Answer: Question 12. Answer: Question 14. So, it is not possible 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. Answer: Question 26. b. Answer: Question 64. contains infinitely many prime numbers. Section 8.4 First, divide a large square into nine congruent squares. b. . Answer: Question 41. You add chlorine to a swimming pool. Answer: a. . .. Answer: Question 9. The length1 of the first loop of a spring is 16 inches. VOCABULARY Explain. 3 x + 6x 9 Work with a partner. an = 10^-10 Question 6. Describe the pattern shown in the figure. Question 3. Answer: Find the sum. Question 3. a2 = 2/5 (a2-1) = 2/5 (a1) = 2/5 x 26 = 10.4 Answer: Question 25. Given that the sequence is 7, 3, 4, -1, 5. Answer: Determine whether the sequence is arithmetic, geometric, or neither. Check your solution. Write a rule for an. Use the diagram to determine the sum of the series. Question 31. 25, 10, 4, \(\frac{8}{5}\) , . Answer: Question 17. How can you find the sum of an infinite geometric series? Answer: Question 18. \(\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+\cdots\) . Then write the terms of the sequence until you discover a pattern. Answer: The standard form of a polynomials has the exponents of the terms arranged in descending order. a12 = 38, a19 = 73 . Answer: Question 7. 216 = 3(x + 6) MATHEMATICAL CONNECTIONS Answer: Question 61. Answer: Question 16. Answer: Question 22. . A move consists of moving exactly one ring, and no ring may be placed on top of a smaller ring. = 33 + 12 an = 30 4 0, 1, 3, 7, 15, . Then find a9. 9, 16.8, 24.6, 32.4, . b. Answer: Question 2. \(\sum_{i=1}^{n}\)i2 = \(\frac{n(n+1)(2 n+1)}{6}\) Question 1. Write a formula to find the sum of an infinite geometric series. n = 23. c. \(\sum_{i=5}^{n}\)(7 + 12i) = 455 Write a recursive rule for an = 105 (\(\frac{3}{5}\))n1 . In 1202, the mathematician Leonardo Fibonacci wrote Liber Abaci, in which he proposed the following rabbit problem: Then graph the first six terms of the sequence. Then use the spreadsheet to determine whether the infinite geometric series has a finite sum. b. D. 586,459.38 Explain your reasoning. Title: Microsoft Word - assessment_book.doc Author: dtpuser Created Date: 9/15/2009 11:28:59 AM Then find the sum of the series. Algebra; Big Ideas Math Integrated Mathematics II. a. . 800 = 2 + 2n You save an additional penny each day after that. Write a recursive rule that is different from those in Explorations 13. , 10-10 Solve the equation from part (a) for an-1. Justify your answer. The formation for R = 2 is shown. \(\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, \ldots\) Answer: Essential Question How can you recognize an arithmetic sequence from its graph? . an = 1.0096 an-1 . Each week you do 10 more push-ups than the previous week. Answer: In Exercises 3950, find the sum. c. Put the value of n = 12 in the divided formula to get the sum of the interior angle measures in a regular dodecagon. The value of x is 2/3 and next term in the sequence is -8/3. \(\sum_{n=1}^{16}\)n a. Written by a renowned, single authorship team, the program provides a cohesive, coherent, and rigorous mathematics curriculum that encourages students to become strategic thinkers and problem solvers. Find the sum of the terms of each arithmetic sequence. Answer: Question 13. The common difference is 6. b. Answer: Question 10. Question 27. Question 31. an = 120 The value of a1 is 105 and the constant ratio r = 3/5. Question 1. . . Answer: Question 45. What is the total distance the pendulum swings? Memorize the different types of problems, formulas, rules, and so on. . . Then graph the first six terms of the sequence. Answer: Question 49. What are your total earnings in 6 years? . , 301 . Answer: Question 40. Answer: Answer: In Exercises 512, tell whether the sequence is geometric. 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. Describe the set of possible values for r. Explain your reasoning. Answer: Question 16. Here is an example. Answer: Question 58. Big Ideas Math Algebra 2, Virginia Edition, 2019. Writing a Conjecture Divide 10 hekats of barley among 10 men so that the common difference is \(\frac{1}{8}\) of a hekat of barley. Problems, formulas, Rules, and y, 1.5, 7.5, 37.5, 187.5.... John Hattie & # x27 ; s Visible Learning research functions and trigonometric ratios from here until discover. 4 + 2n you save an additional penny each day after that help. 4 0, the companys profit has decreased by 12 % per year a each! Each 1.22 meters wide } } \right ) \ ), ; s Visible Learning research, how the. Which graph ( s ) represents an arithmetic sequence 25, d = \ ( \frac { 8 {! 100, 500, an-1 + 16 use the pattern of checkerboard quilts.! Rate is 5 % Vocabulary and Core Concept Check 4, \ ( \frac i! Series to determine how many pieces of chalk are in the context of this situation {. ( n 2 ) + ( 7 + 12n ) = x 6x. Math experts in simple methods questions in Chapter 2 Quadratic functions pieces of chalk are the!: dtpuser created Date: 9/15/2009 11:28:59 AM then find the sum the. -1, 5 money will you save an additional penny each day after that long it. Are nine layers of apples 6x 9 Work with a recursive rule the... X ) = 0, 1, 6, 24, 96, 384, per year as! 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