Then graph the function. 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. 1 + x + x2 + x3 + x4 Your friend claims the total amount repaid over the loan will be less for Loan 2. Answer: Question 64. a2 = a2-1 + 26 = a1 + 26 = -4 + 26 = 22. If n= 2. . (3n + 13n)/2 + 5n = 544 A radio station has a daily contest in which a random listener is asked a trivia question. Answer: Question 21. PROBLEM SOLVING Write an explicit rule for the sequence. 8192 = 1 2n-1 This problem produces a sequence called the Fibonacci sequence, which has both a recursive formula and an explicit formula as follows. 7x+3=31 16, 9, 7, 2, 5, . Answer: Question 38. Tn = 180(n 2), n = 12 Check your solution. Tn = 1800 degrees. 19, 13, 7, 1, 5, . A regional soccer tournament has 64 participating teams. Complete homework as though you were also preparing for a quiz. Answer: Question 69. THOUGHT PROVOKING Answer: Question 2. 1, 1, 3, 5, 7, . 5, 10, 15, 20, . The graph shows the first six terms of the sequence a1 = p, an = ran-1. a2 = 28, a5 = 1792 a. 3x + 6x3 + 12x5 + 24x7 a1 = 4, an = 0.65an-1 7 + 10 + 13 +. Write the first five terms of the sequence. The minimum number an of moves required to move n rings is 1 for 1 ring, 3 for 2 rings, 7 for 3 rings, 15 for 4 rings, and 31 for 5 rings. a3 = 2/5 (a3-1) = 2/5 (a2) = 2/5 x 10.4 = 4.16 2, 4, 6, 8, 10, . Question 2. Answer: Write a rule for the nth term of the arithmetic sequence. 5, 20, 35, 50, 65, . 3 \(\sum_{i=1}^{n}\)(i + 5n) = 544 Question 53. Explain your reasoning. a1 = 4, an = 2an-1 1 Answer: Question 4. Textbook solutions for BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015 15th Edition HOUGHTON MIFFLIN HARCOURT and others in this series. (-3 4(3)) + (-3 4(4)) + . Based on the type of investment you are making, you can expect to earn an annual return of 8% on your savings after you retire. an = 17 4n r = rate of change. when n = 6 x 2z = 1 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. Question 15. State the domain and range. a1 = 4, an = an-1 + 26 WRITING is geometric. 2 + 4 8 + 16 32 . c. 2, 4, 6, 8, . Big Ideas Math Algebra 2, Virginia Edition, 2019. Work with a partner. a. Get a fun learning environment with the help of BIM Algebra 2 Textbook Answers and practice well by solving the questions given in BIM study materials. Explain. 1, 4, 7, 10, . Question 11. Answer: Question 12. . Find two infinite geometric series whose sums are each 6. The first term is 7 and each term is 5 more than the previous term. a. Question 3. 3, 5, 9, 15, 23, . a1 = 3, an = an-1 7 Question 32. A teacher of German mathematician Carl Friedrich Gauss (17771855) asked him to find the sum of all the whole numbers from 1 through 100. a. Question 5. Answer: In Exercises 1526, describe the pattern, write the next term, and write a rule for the nth term of the sequence. Answer: Question 20. \(\sum_{i=1}^{31}\)(3 4i ) Question 39. 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 9. Answer: Question 5. 1, 2.5, 4, 5.5, 7, . The monthly payment is $173.86. A regular polygon has equal angle measures and equal side lengths. \(\sum_{n=1}^{\infty} 8\left(\frac{1}{5}\right)^{n-1}\) Question 61. A quilt is made up of strips of cloth, starting with an inner square surrounded by rectangles to form successively larger squares. an = (an-1)2 + 1 4 + 7 + 12 + 19 + . a12 = 38, a19 = 73 a2 = 4(6) = 24. 2x 3y + z = 4 12, 6, 0, 6, 12, . Answer: Question 24. Answer: Question 8. Answer: Question 69. Question 70. Your friend claims that 0.999 . Answer: Question 3. Answer: Question 64. 435440). \(\sum_{i=1}^{12}\)4 (\(\frac{1}{2}\))i+3 Your friend says it is impossible to write a recursive rule for a sequence that is neither arithmetic nor geometric. Simply tap on the quick links available for the respective topics and learn accordingly. . Work with a partner. Answer: Question 39. WRITING nth term of a sequence You are saving money for retirement. Find and graph the partial sums Sn for n= 1, 2, 3, 4, and 5. Question 1. M = L\(\left(\frac{i}{1-(1+i)^{-t}}\right)\). . Big ideas math algebra 2 student journal answer key pdf. Write a rule for the nth term of the sequence. Answer: Essential Question How can you define a sequence recursively?A recursive rule gives the beginning term(s) of a sequence and a recursive equation that tells how an is related to one or more preceding terms. 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. Answer: Question 23. . 213 = 2n-1 DRAWING CONCLUSIONS ISBN: 9781680330687. \(\frac{1}{20}, \frac{2}{30}, \frac{3}{40}, \frac{4}{50}, \ldots\) Question 9. Find the total number of skydivers when there are four rings. Boswell, Larson. Answer: Question 42. Answer: In Exercises 2326, write a recursive rule for the sequence shown in the graph. Describe the pattern. A towns population increases at a rate of about 4% per year. Students can know the difference between trigonometric functions and trigonometric ratios from here. Answer: Question 21. y = 3 2x Solutions available . Question 3. \(\sum_{i=1}^{39}\)(4.1 + 0.4i ) f(1) = 2, f(2) = 3 .has a finite sum. Algebra 2. an = 90 Find the balance after the fourth payment. b. The nth term of a geometric sequence has the form an = ___________. . a3 = 2(3) + 1 = 7 Answer: In Exercises 2328, write a rule for the nth term of the sequence. x (3 x) = x 3x x Calculate the monthly payment. The first four iterations of the fractal called the Koch snowflake are shown below. . 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. Answer: Question 34. by an Egyptian scribe. Answer: 8.2 Analyzing Arithmetic Sequences and Series (pp. A population of 60 rabbits increases by 25% each year for 8 years. WRITING EQUATIONS In Exercises 3944, write a rule for the sequence with the given terms. The Sum of an Infinite Geometric Series, p. 437, Section 8.5 Answer: Question 20. Answer: Question 4. Given that, If it does, find the sum. Then find a7. \(\sum_{k=1}^{12}\)(7k + 2) Write a rule for bn. Answer: Question 25. Answer: Question 13. Year 1 of 8: 75 . Answer: Question 16. Recognizing Graphs of Arithmetic Sequences a5 = -5(a5-1) = -5a4 = -5(1000) = -5000. Anarithmetic sequencehas a constantdifference between each consecutive pair of terms. MAKING AN ARGUMENT Answer: 8.3 Analyzing Geometric Sequences and Series (pp. -1 + 2 + 7 + 14 + .. . Use each recursive rule and a spreadsheet to write the first six terms of the sequence. On the first swing, your cousin travels a distance of 14 feet. Solve both of these repayment equations for L. . Then graph the first six terms of 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. b. Write a recursive rule that represents the situation. Question 19. . Find \(\sum_{n=1}^{\infty}\)an. a5 = 3 688 + 1 = 2065 The Sum of a Finite Arithmetic Series, p. 420, Section 8.3 Two terms of a geometric sequence are a6 = 50 and a9 = 6250. The common difference is d = 7. Write a recursive rule for the number an of books in the library at the beginning of the nth year. Answer: Question 15. Answer: Mathematically proficient students consider the available tools when solving a mathematical problem. Question 21. Answer: Question 48. Loan 1 is a 15-year loan with an annual interest rate of 3%. How can you write a rule for the nth term of a sequence? . f(n) = \(\frac{n}{2n-1}\) a4 = a3 5 = -9 5 = -14 . 18, 14, 10, 6, 2, 2, . . 0.115/12 = 0.0096 a. a1 = 16, an = an-1 + 7 . Assume that the initial triangle has an area of 1 square foot. You make a $500 down payment on a $3500 diamond ring. The track has 8 lanes that are each 1.22 meters wide. There are x seats in the last (nth) row and a total of y seats in the entire theater. . 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. Sn = 0.1/0.9 We cover textbooks from publishers such as Pearson, McGraw Hill, Big Ideas Learning, CPM, and Houghton Mifflin Harcourt. (Hint: L is equal to M times a geometric series.) THOUGHT PROVOKING e. 5, 5, 5, 5, 5, 5, . Each year, 2% of the books are lost or discarded. One term of an arithmetic sequence is a12 = 43. a. Describe the type of decline. Answer: Question 9. Answer: Question 14. Given that, Then remove the center square. Write a rule for the number of cells in the nth ring. 1, 8, 15, 22, 29, . Explain your reasoning. Answer: . In general most of the curve represents geometric sequences. f(5) = \(\frac{1}{2}\)f(4) = 1/2 5/8 = 5/16. Write a formula for the sum of the cubes of the first n positive integers. About how much greater is the total distance traveled by the basketball than the total distance traveled by the baseball? a3 = 4, r = 2 Classify the solution(s) of each equation as real numbers, imaginary numbers, or pure imaginary numbers. In Example 3, suppose there are nine layers of apples. USING STRUCTURE Moores prediction was accurate and is now known as Moores Law. Use a series to determine how many days it takes you to save $500. A company had a profit of $350,000 in its first year. 2, 2, 4, 12, 48, . First, divide a large square into nine congruent squares. Answer: an = r . . \(\sum_{n=1}^{5}\)(n2 1) 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. Partial Sums of Infinite Geometric Series, p. 436 an= \(\frac{1}{2}\left(\frac{1}{4}\right)^{n-1}\) , 1000 d. \(\frac{25}{4}, \frac{16}{4}, \frac{9}{4}, \frac{4}{4}, \frac{1}{4}, \ldots\) \(\sum_{i=2}^{7}\)(9 i3) What is the 1000th term of the sequence whose first term is a1 = 4 and whose nth term is an = an-1 + 6? , 3n-2, . . Answer: Question 53. Answer: Use the pattern of checkerboard quilts shown. Rectangular tables are placed together along their short edges, as shown in the diagram. . . Answer: Question 33. b. a. Write a recursive rule for each sequence. x + y + 4z =1 Section 1.2: Transformations of Linear and Absolute Value Functions. The value of each of the interior angle of a 4-sided polygon is 90 degrees. Each week, 40% of the chlorine in the pool evaporates. b. Question 7. Answer: Question 50. 1st Edition. Question 3. Finding the Sum of an Arithmetic Sequence 2: Teachers; 3: Students; . MODELING WITH MATHEMATICS The constant difference between consecutive terms of an arithmetic sequence is called the _______________. b. Question 7. Answer: Question 55. The bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. Answer: Consider 3 x, x, 1 3x are in A.P. 1 + 2 + 3 + 4 +. . Explain how to tell whether the series \(\sum_{i=1}^{\infty}\)a1ri1 has a sum. Given that, an = 0.6 an-1 + 16 a1 = 1 Write a recursive rule for the balance an of the loan at the beginning of the nth month. Compare the terms of an arithmetic sequence when d > 0 to when d < 0. an = 0.4 an-1 + 325 a1 = 34 an = 5, an = an-1 \(\frac{1}{3}\) Evaluating a Recursive Rule Question 33. Which rule gives the total number of squares in the nth figure of the pattern shown? Justify your answer. Answer: In Exercises 3950, find the sum. Answer: Question 3. Answer: Solve the equation. 2.3, 1.5, 0.7, 0.1, . Answer: Question 48. Loan 2 is a 30-year loan with an annual interest rate of 4%. Answer: Question 16. The Greek mathematician Zeno said no. b. a1 = 7, an = an-1 + 11 1000 = 2 + n 1 Page 20: Quiz. a5 = 41, a10 = 96 1, 2, 3, 4, . . A move consists of moving exactly one ring, and no ring may be placed on top of a smaller ring. \(\sum_{i=1}^{7}\)16(0.5)t1 . Answer: Question 41. 216=3x+18 Answer: Question 2. Question 30. b. One term of an arithmetic sequence is a8 = 13. Answer: Question 14. Answer: Essential Question How can you recognize a geometric sequence from its graph? 86, 79, 72, 65, . Explain your reasoning. The top eight runners finishing a race receive cash prizes. COMPLETE THE SENTENCE a. . 216=3(x+6) f(0) = 4 and f(n) = f(n-1) + 2n a. Justify your answer. Explain. Match each sequence with its graph. Finding Sums of Infinite Geometric Series Question 4. b. You take out a 5-year loan for $15,000. Answer: Question 56. a7 = 1/2 1.625 = 0.53125 How did understanding the domain of each function help you to compare the graphs in Exercise 55 on page 431? . . HOW DO YOU SEE IT? Question 25. 8(\(\frac{3}{4}\))x = \(\frac{27}{8}\) Question 3. b. Grounded in solid pedagogy and extensive research, the program embraces Dr. John Hattie's Visible Learning Research. The answer would be hard work along with smart work. 1.34 feet S29 = 29(11 + 111/2) Write a recursive rule for the nth hexagonal number. . Explain your reasoning. \(\sum_{i=1}^{12}\)6(2)i1 MODELING WITH MATHEMATICS .Terms of a sequence The variables x and y vary inversely. In 1202, the mathematician Leonardo Fibonacci wrote Liber Abaci, in which he proposed the following rabbit problem: \(\sum_{i=1}^{41}\)(2.3 + 0.1i ) Year 7 of 8: 286 an = 180(n 2)/n a3 = 3/2 = 9/2 Answer: Question 14. Answer: 8.5 Using Recursive Rules with Sequences (pp. Answer: Question 54. 2\(\sqrt [ 3 ]{ x }\) 13 = 5 Question 1. Use the rule for the sum of a finite geometric series to write each polynomial as a rational expression. Balance after the fourth payment, 20, 35, 50, 65, others in this series )... Bottom row has 15 pieces of chalk, and 5, 20, 35,,... And each term is 5 more than the total number of squares in graph., p. 437, Section 8.5 answer: in big ideas math algebra 2 answer key 3944, write a recursive rule the. = ( an-1 ) 2 + 7 + 10 + 13 + angle measures and equal side.. 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