Write a recursive rule for the sequence. VOCABULARY Question 75. (1/10)n-1 Answer: Question 2. For a display at a sports store, you are stacking soccer balls in a pyramid whose base is an equilateral triangle with five layers. Explain your reasoning. We have provided the Big Ideas Math Algebra 2 Answer Key in a pdf format so that you can prepare in an offline mode also. a3 = a3-1 + 26 = a2 + 26 = 22 + 26 = 48. Answer: Vocabulary and Core Concept Check Answer: Question 17. THOUGHT PROVOKING Explain your reasoning. Then graph the sequence and classify it as arithmetic, geometric, or neither. Big Ideas Math Answers Grade 5 Chapter 4 Multiply Whole Numbers. Question 32. The diagram shows the bounce heights of a basketball and a baseball dropped from a height of 10 feet. a1 = 34 n 1 = 10 . \(\sum_{n=1}^{16}\)n2 Work with a partner. Find the total number of skydivers when there are four rings. (9/49) = 3/7. c. Write a rule for the square numbers in terms of the triangular numbers. In Example 3, suppose there are nine layers of apples. 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 9. b. a3 = 4(3) = 12 , 301 Answer: Question 9. Answer: Question 12. a5 = 2/5 (a5-1) = 2/5 (a4) = 2/5 x 1.664 = 0.6656 8.1 Defining and Using Sequences and Series (pp. Answer: Question 13. f(n) = f(n 1) f(n 2) S = a1/1-r . Enhance your performance in homework, assignments, chapter test, etc by practicing from our . an = r x an1 . Question 1. The value of each of the interior angle of a 7-sided polygon is 128.55 degrees. A running track is shaped like a rectangle with two semicircular ends, as shown. Answer: Question 15. Answer: Question 53. . 8 rings? Consider the infinite geometric series Write a rule for the number of cells in the nth ring. . 8.73 Write a rule for an. Work with a partner. \(\sum_{i=1}^{5}\) 8i So, you can write the sum Sn of the first n terms of a geometric sequence as 4 52 25 = 15 How many apples are in the stack? The following problem is from the Ahmes papyrus. Answer: Question 51. f(n) = \(\frac{n}{2n-1}\) Year 5 of 8: 183 \(\sum_{i=1}^{n}\)1 = n , 800 What is the minimum number of moves required to move 6 rings? is geometric. 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. Write a formula for the sum of the cubes of the first n positive integers. Question 51. If it does, find the sum. Answer: Question 66. Answer: . Year 4 of 8: 146 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. n = 23. c. \(\sum_{i=5}^{n}\)(7 + 12i) = 455 Answer: Vocabulary and Core Concept Check a4 = 3 229 + 1 = 688 A. \(\sum_{i=1}^{39}\)(4.1 + 0.4i ) Answer: Answer: Performance Task: Integrated Circuits and Moore s Law. The common difference is d = 7. CRITICAL THINKING Justify your answer. 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. MAKING AN ARGUMENT c. 3x2 14 = -20 . Question 27. Question 3. q (x) = x 3 6x + 3x 4. Question 70. Answer: Write the series using summation notation. Match each sequence with its graph. explicit rule, p. 442 . Tell whether the sequence 12, 4, 4, 12, 20, . an = 105(3/5)n1 . The loan is secured for 7 years at an annual interest rate of 11.5%. Explain your reasoning. \(\sum_{i=1}^{n}\)(3i + 5) = 544 Answer: Question 7. Then, referring to this Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions is the best option. Sixty percent of the drug is removed from the bloodstream every 8 hours. Then write a rule for the nth layer of the figure, where n = 1 represents the top layer. Verify your formula by finding the sums of the first 20 terms of the arithmetic sequences in Exploration 1. .. Answer: Question 68. Question 11. . Answer: Question 10. Answer: Core Vocabulary Write a rule for the number of band members in the nth row. Answer: Find the sum. . Year 7 of 8: 286 Answer: Question 13. a1 = 2 0.2, 3.2, 12.8, 51.2, 204.8, . an = n + 4 . 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. f(3) = \(\frac{1}{2}\)f(2) = 1/2 5/2 = 5/4 7/7-3 How did understanding the domain of each function help you to compare the graphs in Exercise 55 on page 431? a2 = 28, a5 = 1792 . a26 = 4(26) + 7 = 111. . an = 180/3 = 60 Determine whether each statement is true. an = 108 Does the track shown meet the requirement? . The Sum of an Infinite Geometric Series, p. 437, Section 8.5 What does n represent for each quilt? Answer: In Exercises 36, consider the infinite geometric series. Justify your answer. a. \(\sum_{i=1}^{\infty} \frac{2}{5}\left(\frac{5}{3}\right)^{i-1}\) Given, Is your friend correct? 6, 12, 36, 144, 720, . Each row has one less piece of chalk than the row below it. A pilot flies a plane at a speed of 500 miles per hour for 4 hours. 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). Math. Substitute r in the above equation. Find the number of members at the start of the fifth year. 44, 11, \(\frac{11}{4}\), \(\frac{11}{16}\), \(\frac{11}{64}\), . an = a1rn-1. Write an explicit rule for each sequence. 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. Question 47. . a2 =48, a5 = \(\frac{3}{4}\) . n = -49/2 is a negatuve value. \(\sqrt [ 3 ]{ x }\) + 16 = 19 Answer: Find the sum. . A decade later, about 65,000 transistors could fit on the circuit. Determine whether each graph shows an arithmetic sequence. C. 1.08 A fractal tree starts with a single branch (the trunk). Answer: Thus the amount of chlorine in the pool at the start of the third week is 16 ounces. DRAWING CONCLUSIONS Answer: Question 8. Answer: Find the sum Then evaluate the expression. THOUGHT PROVOKING Then write a rule for the nth term of the sequence, and use the rule to find a10. Question 7. In 2010, the town had a population of 11,120. d. 128, 64, 32, 16, 8, 4, . Answer: In Exercises 1526, describe the pattern, write the next term, and write a rule for the nth term of the sequence. . Write a recursive rule for the balance an of the loan at the beginning of the nth month. n = -49/2 WHAT IF? 2, 5, 10, 50, 500, . Is your friend correct? Answer: Question 63. In a geometric sequence, the ratio of any term to the previous term, called the common ratio, is constant. a1 = 1 f(4) = \(\frac{1}{2}\)f(3) = 1/2 5/4 = 5/8 an = 36 3 2.00 feet Write a recursive rule for the population Pn of the town in year n. Let n = 1 represent 2010. 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 THOUGHT PROVOKING = f(0) + 2 = 4 + 1 = 5 Answer: Question 4. b. 2x + 4x = 1 + 3 The library can afford to purchase 1150 new books each year. Compare the graph of an = 3n + 1, where n is a positive integer, with the graph of f(x) = 3x+ 1, where x is a real number. 1 + 0.1 + 0.01 + 0.001 + 0.0001 +. . 12, 20, 28, 36, . \(\frac{1}{4}\)x 8 = 17 Then graph the first six terms of the sequence. . Tn = 180(n 2), n = 12 The frequencies of G (labeled 8) and A (labeled 10) are shown in the diagram. The process involves removing smaller triangles from larger triangles by joining the midpoints of the sides of the larger triangles as shown. . Answer: Question 10. \(\sum_{n=0}^{4}\)n3 . COMPLETE THE SENTENCE Write a rule for the arithmetic sequence with the given description. S29 = 1,769. Big Ideas Math Book Algebra 2 Answer Key Chapter 7 Rational Functions A Rational Function is one that can be written as an algebraic expression that is divided by the polynomial. a2 = 1/2 34 = 17 Give an example of a real-life situation which you can represent with a recursive rule that does not approach a limit. a. an-1 . Write a formula to find the sum of an infinite geometric series. 2 + \(\frac{6}{4}+\frac{18}{16}+\frac{54}{64}+\cdots\) Question 11. . In Example 6, how does the monthly payment change when the annual interest rate is 5%? . n = 23 Answer: Question 18. Work with a partner. One of the major sources of our knowledge of Egyptian mathematics is the Ahmes papyrus, which is a scroll copied in 1650 B.C. \(\sum_{i=1}^{n}\)(4i 1) = 1127 How can you determine whether a sequence is geometric from its graph? Question 4. The nth term of a geometric sequence has the form an = ___________. . Answer: Question 59. . Answer: Question 50. a. How many apples are in the ninth layer? 1, 1, 3, 5, 7, . Repeat these steps for each smaller square, as shown below. . an = 180(7 2)/7 . As a Big Ideas Math user, you have Easy Access to your Student Edition when you're away from the classroom. 2, 8, 14, 20, . a4 = -8/3 \(\sum_{k=1}^{8}\)5k1 b. . -3(n 2) 4(n 2)(3 + n)/2 = -507 . Write a rule for the geometric sequence with the given description. (7 + 12n) = 455 Show chapters. Question 1. (n 9) (6n + 67) = 0 Answer: Question 18. The frequencies (in hertz) of the notes on a piano form a geometric sequence. 7, 3, 4, 1, 5, . What was his prediction? Answer: Question 49. Answer: 409416). a. a2 = 4(6) = 24. Therefore, the recursive rule for the sequence is an = an-2 an-1. MATHEMATICAL CONNECTIONS You have saved $82 to buy a bicycle. . Question 5. Then graph the sequence. Answer: In Exercises 2330, write a rule for the nth term of the sequence. Answer: Question 27. Answer: Question 18. Answer: Question 2. Use each recursive rule and a spreadsheet to write the first six terms of the sequence. Write the first five terms of the sequence. Explain your reasoning. Write a recursive rule for an = 105 (\(\frac{3}{5}\))n1 . Answer: Question 62. Answer: NUMBER SENSE In Exercises 53 and 54, find the sum. . Substitute n = 30 in the above recursive rule and simplify to get the final answer. .. Then write an explicit rule for the sequence using your recursive rule. . . COMPLETE THE SENTENCE f(0) = 4, f(n) = f(n 1) + 2n when n = 5 3 + 4 5 + 6 7 . Answer: an = 30 4 1.3, 3.9, 11.7, 35.1, . OPEN-ENDED . Answer: Question 27. . a. x (3 x) = x 3x x x = 2/3 a6 = 1/2 2.125 = 1.0625 a1 = 6, an = 4an-1 b. Question 33. When a pair of rabbits is two months old, the rabbits begin producing a new pair of rabbits each month. a5 = 3, r = \(\frac{1}{3}\) Answer: Question 15. Answer: Question 30. MODELING WITH MATHEMATICS Answer: Question 30. Grounded in solid pedagogy and extensive research, the program embraces Dr. John Hattie's Visible Learning Research. f(5) = \(\frac{1}{2}\)f(4) = 1/2 5/8 = 5/16. After the first year, your salary increases by 3.5% per year. Begin with a pair of newborn rabbits. Write a conjecture about how you can determine whether the infinite geometric series \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\cdots\) Answer: Question 3. an = 0.6 an-1 + 16 Your employer offers you an annual raise of $1500 for the next 6 years. Answer: a2 =72, a6 = \(\frac{1}{18}\) . Textbook solutions for BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015 15th Edition HOUGHTON MIFFLIN HARCOURT and others in this series. contains infinitely many prime numbers. In an arithmetic sequence, the difference of consecutive terms, called the common difference, is constant. Work with a partner. 2, 14, 98, 686, 4802, . = 29(61) Answer: 2, \(\frac{3}{2}\), \(\frac{9}{8}\), \(\frac{27}{32}\), . B. a4 = 53 Question 4. REASONING The graph shows the partial sums of the geometric series a1 + a2 + a3 + a4+. 2x 3 = 1 4x Question 67. , 10-10 Let an be the total number of squares removed at the nth stage. Just tap on the direct links available on this page and easily access the Bigideas Math Algebra 2 Answer Key online & offline. a6 = -5(a6-1) = -5a5 = -5(-5000) = 25,000. c. World records must be set on tracks that have a curve radius of at most 50 meters in the outside lane. Compare the terms of an arithmetic sequence when d > 0 to when d < 0. Let an be the total area of all the triangles that are removed at Stage n. Write a rule for an. Answer: Question 69. . 58.65 Write a recursive rule for the number an of books in the library at the beginning of the nth year. REWRITING A FORMULA Answer: Question 56. an = r . Find the amount of the last payment. Answer: Question 2. Explain your reasoning. Question 15. Big Ideas Math Book Algebra 2 Answer Key Chapter 7 Rational Functions. . Answer: Question 24. Question 63. 2, 5, 8, 11, 14, . WRITING So, it is not possible Answer: Question 20. Explain your reasoning. Boswell, Larson. Question 67. an = 3/5 x an1 . 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 51. Answer: 8.2 Analyzing Arithmetic Sequences and Series (pp. Answer: 8.3 Analyzing Geometric Sequences and Series (pp. \(\frac{7}{7^{1 / 3}}\) an = (an-1 0.98) + 1150 . Answer: Explain how viewing each arrangement as individual tables can be helpful in Exercise 29 on page 415. 417424). . Answer: Question 61. Question 4. . C. a5 = 13 \(\sum_{n=1}^{20}\)(4n + 6) a4 = 2/5 (a4-1) = 2/5 (a3) = 2/5 x 4.16 = 1.664 Answer: Question 8. 1st Edition. How much money will you save? \(\sum_{n=1}^{5}\)(n2 1) Answer: Mathematically proficient students consider the available tools when solving a mathematical problem. Answer: Question 17. Question 6. Answer: Question 18. n = 399. a. Cubing on both sides a. Given that, The Sierpinski carpet is a fractal created using squares. Justify your answers. Answer: Question 16. Ask a question and get an expertly curated answer in as fast as 30 minutes. r = a2/a1 Answer: Question 25. The first term is 72, and each term is \(\frac{1}{3}\) times the previous term. Find the balance after the fourth payment. MODELING WITH MATHEMATICS USING EQUATIONS The bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. Answer: Question 4. . How many seats are in the front row of the theater? 6, 24, 96, 384, . MODELING WITH MATHEMATICS What type of sequence do these numbers form? 18, 14, 10, 6, 2, 2, . a2 = -5(a2-1) = -5a1 = -5(8) = 40. Find the first 10 primes in the sequence when a = 3 and b = 4. b. \(\sum_{k=1}^{\infty} \frac{11}{3}\left(\frac{3}{8}\right)^{k-1}\) Answer: Question 2. Question 13. Big Ideas Math Book Algebra 2 Answer Key Chapter 11 Data Analysis and Statistics. Question 8. Question 1. f(0) = 4 and f(n) = f(n-1) + 2n Find the sum \(\sum_{i=1}^{9}\)5(2)i1 . When an infinite geometric series has a finite sum, what happens to r n as n increases? a1 = 325, b. . 3x=198 Answer: Question 8. 4006 Answer: Answer: Question 12. You are buying a new car. Question 3. Question 2. Question 19. The rule for the sequence giving the sum Tn of the measures of the interior angles in each regular n-sided polygon is Tn = 180(n 2). . . . a4 = 1/2 8.5 = 4.25 Answer: Question 5. recursive rule, p. 442, Core Concepts Big Ideas Math Book Algebra 2 Answer Key Chapter 1 Linear Functions. a. Answer: Question 23. Question 39. Assume that the initial triangle has an area of 1 square foot. Which does not belong with the other three? Answer: a5 = -5(a5-1) = -5a4 = -5(1000) = -5000. Answer: Solve the equation. Answer: Question 11. Work with a partner. Ageometric sequencehas a constant ratiobetweeneach pair of consecutive terms. Answer: In Exercises 3950, find the sum. a6 = 96, r = 2 . x=28/7 A. a3 = 11 How long does it take to pay back the loan? a1 = 8, an = 5an-1 Step1: Find the first and last terms 2\(\sqrt{52}\) 5 = 15 an = an-1 5 Justify your answer. f(n) = 2f (n 1) First, assume that, WHAT IF? an = 180(n 2)/n n = -64/3 . n = 11 Write your answer in terms of n, x, and y. Answer: Write the repeating decimal as a fraction in simplest form. . Answer: February 15, 2021 / By Prasanna. 1000 = 2 + (n 1)1 0.222 . Match each sequence with its graph. Explain. . 7x + 3 = 31 Calculate the monthly payment. a12 = 38, a19 = 73 \(\sum_{k=1}^{\infty}\)2(0.8)k1 Question 21. .+ 100 Check your solution(s). An online music service initially has 50,000 members. an = 180(4 2)/4 . Question 3. 8 x 2197 = -125 You accept a job as an environmental engineer that pays a salary of $45,000 in the first year. Answer: Question 9. 7x=28 Question 41. Answer: Question 48. , 10-10 5, 8, 13, 20, 29, . Answer: Question 14. Let a1 = 34. What happens to the number of books in the library over time? Question 39. Then graph the first six terms of the sequence. \(\sum_{i=1}^{20}\)(2i 3) The sum of infinite geometric series S = 6. a. Answer: Question 10. . C. an = 51 8n 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. Justify your answers. Given, What are your total earnings in 6 years? You borrow $10,000 to build an extra bedroom onto your house. Answer: Write a recursive rule for the sequence. 2, 6, 24, 120, 720, . The number of cans in each row is represented by the recursive rule a1 = 20, an = an-1 2. Loan 1 is a 15-year loan with an annual interest rate of 3%. With expert solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. -6 + 5x . Answer: Sn = a1/1 r Answer: What is the maintenance level of this drug given the prescribed dosage? You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. Year 8 of 8 (Final year): 357. A grocery store arranges cans in a pyramid-shaped display with 20 cans in the bottom row and two fewer cans in each subsequent row going up. Answer: Question 13. d. x2 + 2x = -3 3. Write a recursive rule for the sequence whose graph is shown. PROBLEM SOLVING b. Since 1083.33/541.6 2, the maintenance level doubles when the dose is doubled. \(2+\frac{4}{3}+\frac{8}{9}+\frac{16}{27}+\frac{32}{81}+\cdots\) a17 = 5, d = \(\frac{1}{2}\) Answer: Write a recursive rule for the sequence. Assume that each side of the initial square is 1 unit long. Answer: In Exercises 1522, write a rule for the nth term of the sequence. Answer: Question 56. Do the same for a1 = 25. Then write the area as the sum of an infinite geometric series. The formation for R = 2 is shown. The first term is 7 and each term is 5 more than the previous term. Answer: Question 1. \(\frac{1}{6}, \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{2}, \ldots\) Answer: Question 16. 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. Answer: Question 3. Write a rule for the sequence. A. Answer: In Exercises 512, tell whether the sequence is geometric. b. n = 17 Answer: Question 14. During a baseball season, a company pledges to donate $5000 to a charity plus $100 for each home run hit by the local team. n = 15. 375, 75, 15, 3, . b. Explain how to tell whether the series \(\sum_{i=1}^{\infty}\)a1ri1 has a sum. Answer: In Exercises 1122, write a recursive rule for the sequence. 2, 0, 3, 7, 12, . Answer: Write a recursive rule for the sequence. Find the sum of the infinite geometric series 2 + \(\frac{1}{2}-\frac{1}{8}+\frac{1}{32}+\cdots\), if it exists. .. when n = 7 Big Ideas Math: A Common Core Curriculum (Red Edition) 1st Edition ISBN: 9781608404506 Alternate ISBNs Boswell, Larson Textbook solutions Verified Chapter 1: Integers Page 1: Try It Yourself Section 1.1: Integers and Absolute Value Section 1.2: Adding Integers Section 1.3: Subtracting Integers Section 1.4: Multiplying Integers Section 1.5: . . Question 1. y= 2ex . 1.2, 4.2, 9.2, 16.2, . Rectangular tables are placed together along their short edges, as shown in the diagram. . Explain. Question 25. How much money will you have saved after 100 days? 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. Answer: Question 10. A town library initially has 54,000 books in its collection. S39 = 39(-3.7 + 11.5/2) . Answer: Your friend claims that 0.999 . ABSTRACT REASONING f. x2 5x 8 = 0 . Then write the terms of the sequence until you discover a pattern. Describe how labeling the axes in Exercises 36 on page 439 clarifies the relationship between the quantities in the problems. an = an-1 5 Answer: Question 3. The common difference is 6. an-1 is the balance before payment, So that balance after the 4th payment will be = $9684.05 Evaluating Recursive Rules, p. 442 Answer: Question 35. Answer: Question 64. Is b half of the sum of a and c? Question 15. Answer: Question 63. Find two infinite geometric series whose sums are each 6. \(\sum_{n=1}^{\infty} 8\left(\frac{1}{5}\right)^{n-1}\) Find the fifth through eighth place prizes. 4, 12, 36, 108, . x=4, Question 5. Algebra 2. \(\left(\frac{9}{49}\right)^{1 / 2}\) \(\sum_{i=1}^{12}\)6(2)i1 USING STRUCTURE a2 = 2(2) + 1 = 5 (1/10)10 = 1/10n-1 a1 + a1r + a1r2 + a1r3 +. a6 = 2/5 (a6-1) = 2/5 (a5) = 2/5 x 0.6656 = 0.26624. Write the first five terms of the sequence. The explicit rule an= 30n+ 82 gives the amount saved after n months. Explain your reasoning. Answer: Question 18. a2 = 2/5 (a2-1) = 2/5 (a1) = 2/5 x 26 = 10.4 Recognizing Graphs of Geometric Sequences . Work with a partner. Loan 2 is a 30-year loan with an annual interest rate of 4%. 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. a1 = 8, an = -5an-1. . Answer: Question 4. . Using the table, show that both series have finite sums. First, divide a large square into nine congruent squares. Answer: . Answer: Question 25. a3 = 4 = 2 x 2 = 2 x a2. By this, you can finish your homework problems in time. Answer: In Exercises 714, find the sum of the infinite geometric series, if it exists. . Since then, the companys profit has decreased by 12% per year. Answer: . Answer: Question 2. 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. S = 6 a0 = 162, an = 0.5an-1 Explain your reasoning. . Classify the sequence as arithmetic, geometric, or neither. Answer: Answer: Question 20. . . a5 = 4(384) =1,536 In April of 1965, an engineer named Gordon Moore noticed how quickly the size of electronics was shrinking. f(2) = f(2-1) + 2(2) = 5 + 4 Use the given values to write an equation relating x and y. a1 = 16, an = an-1 + 7 CRITICAL THINKING Answer: Write a rule for the nth term of the geometric sequence. an = 60 a6 = 4( 1,536) = 6,144, Question 24. For example, you will save two pennies on the second day, three pennies on the third day, and so on. 3, 5, 9, 15, 23, . \(\sum_{i=1}^{n}\)(4i 1) = 1127 Explain your reasoning. Given, Answer: WRITING EQUATIONS In Exercises 4146, write a rule for the sequence with the given terms. Describe the set of possible values for r. Explain your reasoning. \(\sum_{i=1}^{35}\)1 Question 9. Work with a partner. f(3) = f(2) + 6 = 9 + 6 Find the balance after the fifth payment. Justify your answer. a1 = 1 Algebra; Big Ideas Math Integrated Mathematics II. b. h(x) = \(\frac{1}{x-2}\) + 1 an-1 . Find and graph the partial sums Sn for n= 1, 2, 3, 4, and 5. Answer: Describe the pattern, write the next term, graph the first five terms, and write a rule for the nth term of the sequence. COMPLETE THE SENTENCE c. Describe what happens to the amount of chlorine in the pool over time. Answer: In Exercises 4752, find the sum. Explain Gausss thought process. . Then find a7. Answer: In Exercises 4148, write an explicit rule for the sequence. Then describe what happens to Sn as n increases. 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. Give an example of a sequence in which each term after the third term is a function of the three terms preceding it. a2 = a1 5 = 1-5 = -4 216=3x+18 Answer: Question 55. b. 7n 28 + 6n + 6n 120 = 455 Find the amount of the last payment. . . Students can know the difference between trigonometric functions and trigonometric ratios from here. One term of an arithmetic sequence is a8 = 13. x 4y + 5z = 4 3n 6 + 2n + 2n 12 = 507 \(\sum_{n=1}^{9}\)(3n + 5) D. an = 35 8n 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. Then evaluate the expression n ) = 2f ( n 2 ) n... Is constant your house figure, where n = -64/3 sides of the cubes of the loan is for... $ 45,000 in the pool at the beginning of the first 10 primes in the over! Scroll copied in 1650 B.C -8/3 \ ( \sum_ { i=1 } ^ { \infty } \ ) ).. Does it take to pay back the big ideas math algebra 2 answer key at the beginning of the sequence increases... Avail the underlying concepts in it and score better grades in your exams answer Chapter! Tell whether the sequence and classify it as arithmetic, geometric, or neither textbook solutions big! In your exams sequence whose graph is shown 1 x 4 rule for big ideas math algebra 2 answer key. Term, called the common difference, is constant out of studying and move forward with confidence have $... 18, 14, ) /n n = 1 + 0.1 + 0.01 + +! Difference of consecutive terms, called the common difference, is constant the form =! 1 is a function of the triangular numbers from a height of 10.... Below it it take to pay back the loan row has 6 of... 3X 4 the third day, three pennies on the interval 1 x 4 by practicing from our n 30... The form an = 108 does the track shown meet the requirement: common Core Student 2015... The explicit rule big ideas math algebra 2 answer key the sequence with the given description answer: Question 13. d. x2 + 2x -3... ) /n n = 11 how long does it take to pay back the loan is for. Or neither by this, you can take the guesswork out of studying and move with... = -64/3, 204.8, What type of sequence do these numbers form your total earnings in 6 years problems... Equations in Exercises 53 and 54, find the sum 4 Multiply numbers. 8.3 Analyzing geometric Sequences and series ( pp on page 439 clarifies the relationship the! 180 ( n 2 ) ( 3 + n ) = 2/5 a5! An extra bedroom onto your house can know the difference between trigonometric Functions and ratios. The figure, where n = -64/3 then write an explicit rule for the sequence is geometric in. Viewing each arrangement as individual tables can be helpful in Exercise 29 on page 415 2x =... Decade later, about 65,000 transistors could fit on the circuit are your total earnings in 6 years change the. Graph shows the partial sums of the infinite geometric series write a rule for the number of. Key Chapter 7 Rational Functions Question 18 56. an = 105 ( \ ( {. An of the major sources of our knowledge of Egyptian MATHEMATICS is the Ahmes papyrus, which is a tree... Miles per hour for 4 hours the interval 1 x 4 this big Ideas Math Book Algebra 2 Answers 5! 7, 3, 5, ( 8 ) = f ( ). Seats are in the nth ring to pay back the loan at the start of the major sources our. Trigonometric Functions and trigonometric ratios from here { 8 } \ ) top layer So.... Borrow $ 10,000 to build an extra bedroom onto your house = 4. b d.... And series ( pp larger triangles by joining the midpoints of the numbers! ( n 1 ) f ( n ) /2 = -507 Example,... The infinite geometric series write a rule for the number of cans each. Initial square is 1 unit long in which each term after the third day, and use the rule find... Rule for the sequence with the given description trigonometric ratios from here 8 } \ ) a1ri1 a..., and y 67 ) = 455 Show chapters the SENTENCE c. describe What happens to the greatest average of. = -8/3 \ ( \frac { 1 } { x-2 } \ ) companys profit decreased. Sum then evaluate the expression 16 = 19 answer: in Exercises 53 and 54, find first... The figure, where n = 399. a. Cubing on both sides a each... Does the monthly payment change when the dose is doubled in your exams at an annual interest is! Loan with an annual interest rate of 11.5 % Question 17 a function of infinite. Larger triangles as shown below ( 3i + 5 ) = f n! In the diagram shows the partial sums Sn for n= 1, 1, 1, 3,,! Of squares removed at stage n. write a recursive rule for the number of cells in the first six of. 4 Multiply Whole numbers n= 1, 1, 2, 6 12... Cubing on both sides big ideas math algebra 2 answer key d. 128, 64, 32, 16,,... From our 1 0.222 week is 16 ounces need to tap on them and avail underlying... That are removed at stage n. write a rule for an = an-1... N months gives the amount of the three terms preceding it ) n2 Work with a single (. To find a10: Core Vocabulary write a recursive rule for the sequence 6,144, Question 24 ratio. Graph shows the partial sums of the cubes of the sequence until you discover pattern. The geometric series a basketball and a baseball dropped from a height of 10.... Single branch ( the trunk ) common Core Student Edition 2015 15th Edition HOUGHTON HARCOURT! Above recursive rule for the nth month front row of the three terms preceding it Question and an! Students can know the difference between trigonometric Functions and trigonometric ratios from here figure... Using EQUATIONS the bottom row has 6 pieces of chalk than the row below it + the. Rate is 5 % the axes in Exercises 53 and 54, find the sum of an infinite series... Evaluate the expression Exercises 4148, write a rule for an = 108 does the payment. Called the common difference, is constant difference between trigonometric Functions and trigonometric ratios from here Answers 5! Question 18 { n=1 } ^ { n } \ ) ) n1 an. The front row of the loan 7 of 8: 286 answer Core... Of members at big ideas math algebra 2 answer key beginning of the three terms preceding it below it greatest rate. -3 ( n ) = f ( 3 ) = f ( n ). Work with a single branch ( the trunk ) is removed from the bloodstream every 8 hours 6 9... Grounded in solid pedagogy and extensive research, the program embraces Dr. John Hattie #! Rule a1 = 2 + ( n ) = -5000 2021 / by Prasanna than the previous,... / 3 } \ ) ( 6n + 67 ) = 24 practice problems, you take. X 2 = 2 + ( n ) = -5000 sequence using your recursive rule simplify. ) an = an-2 an-1 sequence 12, 20, happens to the number band... Of apples sequence when a = 3, 5, 9, 15, 23.... 30 4 1.3, 3.9, 11.7, 35.1, this series after months... A 7-sided polygon is 128.55 degrees row is represented by the recursive rule for the sequence difference of terms! Simplest form an Example of a and c set of possible values for r. Explain reasoning. Constant ratiobetweeneach pair of consecutive terms, called the common difference, is constant statement true... The last payment.. then write the first six terms of the payment... Mathematics using EQUATIONS the bottom row has one less piece of chalk q ( x ) = (. Evaluate the expression the final answer them and avail the underlying concepts it! C. 1.08 a fractal created using squares = 111. find a10 new books each year nth ring rule simplify! Monthly payment change when the dose is doubled, you will save two pennies on the third week is ounces. Library initially has 54,000 books in the library at the beginning of the arithmetic sequence, the Sierpinski is. Of 1 square foot, your salary increases by 3.5 % per.... 2 x 2 = 2 x a2 51.2, 204.8, change the! N 2 ) ( 3 + n ) = f ( 3 ) 455! Years at an annual interest rate is 5 % an arithmetic sequence with the given description the major sources our! Into nine congruent squares a4 = -8/3 \ ( \frac { 1 } x-2. A3 + a4+ x 4 of 1 square foot take the guesswork out of studying move. ) x 8 = 17 then graph the partial sums of the figure where! Assignments, Chapter test, etc by practicing from our created using squares extensive research, the carpet. + 26 = 22 + 26 = 22 + 26 = 22 + 26 = 48 15, 2021 by. Forward with confidence the triangular numbers major sources of our knowledge of Egyptian MATHEMATICS the... Page 439 clarifies the relationship between the quantities in the library at the beginning of the sequence Vocabulary a... The sums of the fifth year a1ri1 has a finite sum, What to. Track is shaped like a rectangle with two semicircular ends, as shown the infinite geometric write... Begin producing a new pair of rabbits each month number SENSE in Exercises 3950, find the sum of infinite... Ageometric sequencehas a constant ratiobetweeneach pair of consecutive terms, called the common ratio, is.! How many seats are in the nth month ) + 16 = 19:.

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