big ideas math algebra 2 answer key

301 = 4 + 3n 3 409416). You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. Question 47. Therefore, the recursive rule for the sequence is an = an-2 an-1. . Answer: Question 6. In 1965, only 50 transistors fit on the circuit. Answer: Mathematically proficient students consider the available tools when solving a mathematical problem. Each week, 40% of the chlorine in the pool evaporates. , 1000 . an = 180(n 2)/n Question 1. a. a5 = a4 5 = -14 5 = -19 Answer: Compare these values to those in your table in part (b). . Then write the terms of the sequence until you discover a pattern. $\sum_{i=1}^{\infty} \frac{2}{5}\left(\frac{5}{3}\right)^{i-1}$ When making monthly payments, you are paying the loan amount plus the interest the loan gathers each month. WHAT IF? Answer: Question 4. Answer: Question 2. There is an equation for it, $\sum_{i=10}^{25}$i 1, 2, 3, 4, . Which is different? Question 15. contains infinitely many prime numbers. Answer: Write a recursive rule for the sequence. The first 19 terms of the sequence 9, 2, 5, 12, . . Given that, Compare your answers to those you obtained using a spreadsheet. The value of each of the interior angle of a 6-sided polygon is 120 degrees. . Explain your reasoning. * Ask an Expert *Response times may vary by subject and . $\frac{1}{10}, \frac{3}{20}, \frac{5}{30}, \frac{7}{40}, \ldots$ $\sum_{k=1}^{12}$(7k + 2) Explain. Answer: Question 2. . $\sum_{n=1}^{16}$n Answer: Question 9. Answer: Question 45. a1 = 4(1) + 7 = 11. 4 52 25 = 15 $\sum_{n=1}^{\infty} 3\left(\frac{5}{4}\right)^{n-1}$ For a display at a sports store, you are stacking soccer balls in a pyramid whose base is an equilateral triangle with five layers. Domestic bees make their honeycomb by starting with a single hexagonal cell, then forming ring after ring of hexagonal cells around the initial cell, as shown. Suppose there are nine layers in the apple stack in Example 3. Answer: The lanes are numbered from 1 to 8 starting from the inside lane. Answer: Question 51. a3 = 3 1 = 9 1 = 8 . 7x=28 an = n + 2 Work with a partner. a. b. , 10-10 The common difference is d = 7. Question 65. Question 7. Additionally, much of Mathleak's content is free to use. $\sqrt [ 3 ]{ x }$ + 16 = 19 How many cells are in the honeycomb after the ninth ring is formed? If n= 2. Answer: Question 8. a11 = 50, d = 7 Sixty percent of the drug is removed from the bloodstream every 8 hours. Write a rule for the number of games played in the nth round. $0+\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\cdots+\frac{7}{8}$ A theater has n rows of seats, and each row has d more seats than the row in front of it. f(0) = 4 Answer: ERROR ANALYSIS In Exercises 51 and 52, describe and correct the error in finding the sum of the series. Answer: Question 4. Explain your reasoning. To the astonishment of his teacher, Gauss came up with the answer after only a few moments. a6 = a6-1 + 26 = a5 + 26 = 100 + 26 = 126. A decade later, about 65,000 transistors could fit on the circuit. a. Answer: 8.4 Finding Sums of Infinite Geometric Series (pp. a2 = 2 1 = 4 1 = 3 From this Big Ideas Math Algebra 2 Chapter 7 Rational Functions Answer Key you can learn how to solve problems in different methods. $\sum_{i=1}^{12}$6(2)i1 Write an equation that relates and F. Describe the relationship. 3 x + 6x 9 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. The solutions seen in Big Ideas Math Book Algebra 2 Answer Key is prepared by math professionals in a very simple manner with explanations. (3n + 13n)/2 + 5n = 544 Employees at the company receive raises of $2400 each year. when n = 4 7 + 10 + 13 +. Answer: Answer: Question 14. 1000 = n + 1 . n 1 = 10 an = 108 Then graph the sequence and classify it as arithmetic, geometric, or neither. 112, 56, 28, 14, . Question 31. Justify your answers. Answer: Question 21. Answer: Question 3. Answer: In Exercises 1924, write the repeating decimal as a fraction in simplest form. Answer: Question 46. So, it is not possible a1 = 25 Answer: Question 63. tn = 8192, a = 1 and r = 2 . (11 2i) (-3i + 6) = 8 + x a1 = -4, an = an-1 + 26. . Take a pat the above links & download the respective grade of common core 2019 Big Ideas Math Book Answers Pdf to prepare . For example, in the geometric sequence 1, 2, 4, 8, . an = 180(7 2)/7 Question 31. (The figure shows a partially completed spreadsheet for part (a).). Use what you know about arithmetic sequences and series to determine what portion of a hekat each man should receive. Answer: Question 12. Answer: Question 18. x = 2/3 Learn how to solve questions in Chapter 2 Quadratic Functions with the help of the Big Ideas Math Algebra 2 Book Answer Key. a1, a2, a3, a4, . Answer: Question 40. Then verify your formula by checking the sums you obtained in Exploration 1. MODELING WITH MATHEMATICS Use a series to determine how many days it takes you to save $500. Repeat these steps for each smaller square, as shown below. $\frac{1}{2}+\frac{4}{5}+\frac{9}{10}+\frac{16}{17}+\cdots$ Write a rule for bn. f(5) = 33. f(5) = $\frac{1}{2}$f(4) = 1/2 5/8 = 5/16. when n = 6 OPEN-ENDED Draw diagrams to explain why this rule is true. 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, . Answer: The Solutions covered here include Questions from Chapter Tests, Review Tests, Cumulative Practice, Cumulative Assessments, Exercise Questions, etc. partial sum, p. 436 . x + y + 4z =1 Then graph the sequence. So, it is not possible (The figure shows a partially completed spreadsheet for part (a).). 3 $\sum_{i=1}^{n}$(i + 5n) = 544 How to access Big Ideas Math Textbook Answers Algebra 2? . Answer: Question 67. Answer: Question 57. . 8($\frac{3}{4}$)x = $\frac{27}{8}$ Question 6. . Answer: Determine whether the graph represents an arithmetic sequence, geometric sequence, or neither. You are buying a new car. a2 = 1/2 34 = 17 Then describe what happens to Sn as n increases. THOUGHT PROVOKING 13, 6, 1, 8, . Write your answer in terms of n, x, and y. Answer: Question 18. Question 15. FINDING A PATTERN Work with a partner. FINDING A PATTERN Based on the BIM Textbooks, our math professional subject experts explained the chapter-wise questions in the BIM Solution Key. . Find two infinite geometric series whose sums are each 6. Question 31. What is another term of the sequence? Answer: Question 2. Section 1.3: Modeling with Linear Functions. an = 3/5 x an1 . Given, a1 = 3, an = an-1 6 . Answer: Question 26. Question 10. 2n + 5n 525 = 0 What happens to the number of trees after an extended period of time? = 33 + 12 a4 = -8/3 . D. a6 = 47 f(3) = 15. r = 0.01/0.1 = 1/10 Question 1. Answer: Question 56. f(6) = f(6-1) + 2(6) = f(5) + 12 Answer: Question 30. n = -67/6 is a negatuve value. Explain your reasoning. 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. . c. 3x2 14 = -20 This problem produces a sequence called the Fibonacci sequence, which has both a recursive formula and an explicit formula as follows. r = 2/3 The track has 8 lanes that are each 1.22 meters wide. What was his prediction? (7 + 12n) = 455 12, 20, 28, 36, . Answer: Since then, the companys profit has decreased by 12% per year. The number of cells in successive rings forms an arithmetic sequence. 3 + $\frac{5}{2}+\frac{25}{12}+\frac{125}{72}+\cdots$ Use the pattern in the equations you solved in part (a) to write a repayment equation for a t-month loan. . Question 39. Answer: Question 52. a1 = 5, an = $\frac{1}{4}$an-1 Divide 10 hekats of barley among 10 men so that the common difference is $\frac{1}{8}$ of a hekat of barley. Answer: Question 18. $\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\cdots$ Answer: Question 56. 0.115/12 = 0.0096 7x=31-3 Question 34. a3 = 2(3) + 1 = 7 . Question 4. C. 2.68 feet Big Ideas Math Algebra 2 Solutions | Big Ideas Math Answers Algebra 2 PDF. A running track is shaped like a rectangle with two semicircular ends, as shown. All the solutions shown in BIM Algebra 2 Answers materials are prepared by math experts in simple methods. For a regular n-sided polygon (n 3), the measure an of an interior angle is given by an = $\frac{180(n-2)}{n}$ How much money will you save? Write a conjecture about how you can determine whether the infinite geometric series $\sum_{i=1}^{10}$9i Answer: Question 4. Compare the terms of an arithmetic sequence when d > 0 to when d < 0. A doctor prescribes 325 milligram of an anti-inflammatory drug every 8 hours for 10 days and 60% of the drug is removed from the bloodstream in every 8 hours. an = 180(3 2)/3 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. a3 = 2/5 (a3-1) = 2/5 (a2) = 2/5 x 10.4 = 4.16 a1 = 1 Answer: Question 57. Answer: Question 60. More textbook info . a1 = 25 Explain your reasoning. ISBN: 9781680330687. $2+\frac{4}{3}+\frac{8}{9}+\frac{16}{27}+\frac{32}{81}+\cdots$ The loan is secured for 7 years at an annual interest rate of 11.5%. (n 9) (6n + 67) = 0 Substitute r in the above equation. a5 = 41, a10 = 96 The first 8 terms of the geometric sequence 12, 48, 192, 768, . Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. Answer: Question 13. Answer: Question 73. Answer: Question 30. Use each formula to determine how many rabbits there will be after one year. The Sierpinski carpet is a fractal created using squares. 2, 6, 24, 120, 720, . Answer: Find the sum. Each year, 2% of the books are lost or discarded. . a1 = 34 WRITING THOUGHT PROVOKING by an Egyptian scribe. . $\sum_{i=1}^{39}$(4.1 + 0.4i ) Explain your reasoning. . a. Boswell, Larson. Each year, 2% of the books are lost or discarded. The following problem is from the Ahmes papyrus. Write are cursive rule for the amount you have saved n months from now. The length1 of the first loop of a spring is 16 inches. b. . Sixty percent of the drug is removed from the bloodstream every 8 hours. The graph shows the partial sums of the geometric series a1 + a2 + a3 + a4+. Just tap on the direct links available on this page and easily access the Bigideas Math Algebra 2 Answer Key online & offline. 1, $\frac{1}{3}$, $\frac{1}{3}$, 1, . Students can know the difference between trigonometric functions and trigonometric ratios from here. Answer: Answer: Question 54. 1, 1, 3, 5, 7, . Describe the type of decline. n = 9. d. $\sum_{i=3}^{n}$(3 4i) = 507 b. n = 3 Describe what happens to the values in the sequence as n increases. 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 Then verify your rewritten formula by funding the sums of the first 20 terms of the geometric sequences in Exploration 1. FINDING A PATTERN . 216=3x+18 The sum of infinite geometric series S = 6. How many apples are in the stack? Thus, make use of our BIM Book Algebra 2 Solution Key Chapter 2 . Let us consider n = 2 CRITICAL THINKING . At this point, the increase and decrease are equal. Use a spreadsheet to help you answer the question. Question 8. 6 + 36 + 216 + 1296 + . a18 = 59, a21 = 71 . Rule for a Geometric Sequence, p. 426 Work with a partner. Big Ideas Math Book Algebra 2 Answer Key Chapter 3 Quadratic Equations and Complex Numbers. CRITICAL THINKING an = a1rn-1. (Hint: L is equal to M times a geometric series.) $\sum_{i=5}^{n}$(7 + 12i) = 455 Tell whether the sequence is geometric. Answer: Tell whether the sequence is arithmetic, geometric, or neither. Answer: Question 29. Answer: Question 10. Answer: Solve the system. In Exercises 514, write the first six terms of the sequence. Write a rule for the nth term of the sequence. . Work with a partner. Find and graph the partial sums Sn for n = 1, 2, 3, 4, and 5. Question 19. Question 7. 216 = 3(x + 6) . Is your friend correct? x 4y + 5z = 4 b. Question 39. Write a recursive rule for the number of trees on the tree farm at the beginning of the nth year. The function is not a polynomial function because the term 2x -2 has an exponent that is not a whole number. REWRITING A FORMULA Answer: Write the series using summation notation. Answer: Essential Question How can you find the sum of an infinite geometric series? . DIFFERENT WORDS, SAME QUESTION 0.3, 1.5, 7.5, 37.5, 187.5, . are called hexagonal numbers because they represent the number of dots used to make hexagons, as shown. . a2 = 2/5 (a2-1) = 2/5 (a1) = 2/5 x 26 = 10.4 Explain your reasoning. REWRITING A FORMULA MAKING AN ARGUMENT 4, 20, 100, 500, . Answer: Question 8. a. tn = arn-1 3, 5, 7, 9, . . Question 1. . MAKING AN ARGUMENT Answer: In Exercises 3138, write a rule for the nth term of the arithmetic sequence. Answer: Find the sum. . Answer: Question 13. Answer: Question 2. c. 800 = 4 + (n 1)2 How did understanding the domain of each function help you to compare the graphs in Exercise 55 on page 431? What is the total amount of prize money the radio station gives away during the contest? For example, you will save two pennies on the second day, three pennies on the third day, and so on. Answer: Question 19. 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. When n = 3 Math. You borrow $10,000 to build an extra bedroom onto your house. Answer: b. . Answer: MODELING WITH MATHEMATICS Answer: Question 11. 7, 1, 5, 11, 17, . a1 = 1 Answer: NUMBER SENSE In Exercises 53 and 54, find the sum. Part of the pile is shown. Boswell, Larson. Answer: Question 18. MATHEMATICAL CONNECTIONS c. Match each sequence with its graph. $\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+\cdots$ f(n) = 4 + 2f(n 1) f (n 2) . Title: Microsoft Word - assessment_book.doc Author: dtpuser Created Date: 9/15/2009 11:28:59 AM How long does it take to pay back the loan? Answer: Question 4. Write a recursive rule for the amount of chlorine in the pool at the start of the nth week. Apart from the Quadratic functions exercises, you can also find the exercise on the Lesson Focus of a Parabola. B. a4 = 53 Let an be the total number of squares removed at the nth stage. Answer: Question 2. 7 7 7 7 = 2401. Answer: Question 42. The sum Sn of the first n terms of an infinite series is called a(n) ________. A. a1 = 1 Explain your reasoning. $\sum_{i=3}^{n}$(3 4i) = 507 Tn = 1800 degrees. Given that Page 20: Quiz. Find the amount of the last payment. . Refer to BIM Algebra Textbook Answers to check the solutions with your solutions. If not, provide a counterexample. Justify your answer. $3+\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\cdots$ First, assume that, . Answer: Question 14. 2 + $\frac{2}{6}+\frac{2}{36}+\frac{2}{216}+\frac{2}{1296}+\cdots$ . a1 = 2, Sn = 16383 Question 3. c. You work 10 years for the company. You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. Answer: Question 50. . Explain your reasoning. Question 3. Then write a rule for the nth term. Answer: Question 3. an = r . You accept a job as an environmental engineer that pays a salary of $45,000 in the first year. Answer: WRITING EQUATIONS In Exercises 4146, write a rule for the sequence with the given terms. 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). .. = 23 + 10 S = 6 b. 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. Then find a9. Answer: Question 40. an= $\frac{1}{2}\left(\frac{1}{4}\right)^{n-1}$ a1 = 4, an = 2an-1 1 Find the amount of the last payment. Answer: Question 27. Answer: Question 57. Big Ideas Math Book Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions Trignometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Answer: Question 6. The number of items increases until it stabilizes at 57,500. Question 3. . Question 63. What are your total earnings in 6 years? $\sum_{n=1}^{16}$n2 Answer: Question 6. Sn = a1/1 r a4 = a + 3d COMPLETE THE SENTENCE a1 = 12, an = an-1 + 16 USING TOOLS What is the total distance your cousin swings? COMPLETE THE SENTENCE The annual interest rate of the loan is 4.5%. Write a rule for the nth term of the sequence 7, 11, 15, 19, . Find the balance after the fourth payment. Answer: Question 7. . b. Answer: Question 4. D. 10,000 Tn = 180(12 2) Assume that each side of the initial square is 1 unit long. What is the 873rd term of the sequence whose first term is a1 = 0.01 and whose nth term is an = 1.01an-1? $\sum_{k=1}^{\infty}-6\left(\frac{3}{2}\right)^{k-1}$ n = 9 or n = -67/6 a1 = 26, an = $\frac{2}{5}$an-1. Consider the infinite geometric series What are your total earnings? Question 21. $\sum_{i=1}^{12}$4 ($\frac{1}{2}$)i+3 Answer: Question 51. 1000 = 2 + n 1 an = 180/3 = 60 8 rings? Tell whether the sequence 12, 4, 4, 12, 20, . Answer: . . Find a0, the minimum amount of money you should have in your account when you retire. Answer: Question 36. Explain. Describe the set of possible values for r. Explain your reasoning. Answer: 8.2 Analyzing Arithmetic Sequences and Series (pp. Sn = 1(16384 1) 1/2-1 Tell whether the sequence is arithmetic. In each successive round, the number of games decreases by a factor of $\frac{1}{2}$. In a sequence, the numbers are called __________ of the sequence. 2x 3y + z = 4 MATHEMATICAL CONNECTIONS 0.1, 0.01, 0.001, 0.0001, . . Find both answers. A teacher of German mathematician Carl Friedrich Gauss (17771855) asked him to find the sum of all the whole numbers from 1 through 100. a2 = -5(a2-1) = -5a1 = -5(8) = 40. How much money do you have in your account immediately after you make your last deposit? 58.65 Question 4. Answer: Question 20. . Answer: Essential Question How can you write a rule for the nth term of a sequence? Answer: Question 2. n = 17 a1 = 12, an = an-1 + 9.1 a5 = 3 688 + 1 = 2065 WRITING EQUATIONS Each year, the company loses 20% of its current members and gains 5000 new members. The formation for R = 2 is shown. $\frac{7}{7^{1 / 3}}$ -6 + 10/3 Answer: Question 72. Answer: If the graph is linear, the shape of the graph is straight, then the given graph is an arithmetic sequence graph. C. a5 = 13 PROBLEM SOLVING Order the functions from the least average rate of change to the greatest average rate of change on the interval 1 x 4. Answer: Write the series using summation notation. Question 4. Answer: Question 54. 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. How many seats are in the front row of the theater? Write a recursive rule for the sequence whose graph is shown. In general most of the curve represents geometric sequences. What happens to the population of fish over time? . Sn = 1/9. B. -6 + 5x A. a3 = 11 Answer: Question 24. 2, 2, 4, 12, 48, . 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. . An online music service initially has 50,000 members. b. . You borrow $2000 at 9% annual interest compounded monthly for 2 years. Answer: Question 68. Sn = 0.1/0.9 Given, Sn = a1 + a1r + a1r2 + a1r3 + . Answer: Question 64. Explain your reasoning. Formulas for Special Series, p. 413, Section 8.2 Answer: Use the drop-down menu below to select your program. Answer: Question 6. a. Question 61. a1 = 4(1) = 4 Answer: In Exercises 36, consider the infinite geometric series. 1 + 0.1 + 0.01 + 0.001 + 0.0001 +. Answer: Question 66. You want to save $500 for a school trip. Answer: Question 35. Answer: Question 48. . . What can you conclude? 16, 9, 7, 2, 5, . The first four iterations of the fractal called the Koch snowflake are shown below. Answer: Question 10. Big ideas math algebra 2 student journal answer key pdf. a2 = 28, a5 = 1792 Write a recursive rule for the amount of the drug in the bloodstream after n doses. Answer: Question 20. Answer: The graph shows the first six terms of the sequence a1 = p, an = ran-1. Is your friend correct? Is the sequence formed by the curve radii arithmetic, geometric, or neither? In 1202, the mathematician Leonardo Fibonacci wrote Liber Abaci, in which he proposed the following rabbit problem: Answer: Question 22. Question 10. The degree of a polynomial is the highest exponent of a term. $\sum_{i=2}^{8} \frac{2}{i}$ Answer: Question 14. In Example 6, how does the monthly payment change when the annual interest rate is 5%? One term of an arithmetic sequence is a8 = 13. 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. . Find the fifth through eighth place prizes. THOUGHT PROVOKING 5, 10, 15, 20, . . a1 = 6, an = 4an-1 d. x2 + 2x = -3 Explain your reasoning. Answer: Question 8. Answer: 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 . What happens to the number of books in the library over time? Answer: Determine whether the sequence is arithmetic, geometric, or neither. f(4) = f(4-1) + 2(4) a5 = 48 = 4 x 12 = 4 x a4. Answer: Given that the sequence is 2, 2, 4, 12, 48. Answer: Question 14. Question 9. REASONING C. an = 4n . . . Answer: n = -49/2 is a negatuve value. Answer: Write the first six terms of the sequence. . 2$\sqrt [ 3 ]{ x }$ 13 = 5 5.8, 4.2, 2.6, 1, 0.6 . a2 = 64, r = $\frac{1}{4}$ 6, 12, 36, 144, 720, . $\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, \ldots$ 0, 1, 3, 7, 15, . Classify the solution(s) of each equation as real numbers, imaginary numbers, or pure imaginary numbers. $\sum_{k=1}^{\infty}$2(0.8)k1 Write the first five terms of the sequence. c. How long will it take to pay off the loan? $\frac{1}{4}, \frac{1}{16}, \frac{1}{64}, \frac{1}{256}, \frac{1}{1024}, \ldots$ .? Use this formula to check your answers in Exercises 57 and 58. Answer: Question 33. Answer: Vocabulary and Core Concept Check Compare the graph of an = 5(3)n1, where n is a positive integer, to the graph of f(x) = 5 3x1, where x is a real number. an = $\frac{n}{n+1}$ 1, 6, 11, 16, . . Justify your answer. We have included Questions . Question 5. Then write the area as the sum of an infinite geometric series. Answer: Question 25. 3x 2z = 8 . . Answer: Question 26. Explain. Access the user-friendly solutions . COMPLETE THE SENTENCE a. . WRITING EQUATIONS In Exercises 3944, write a rule for the sequence with the given terms. a2 = 30, r = $\frac{1}{2}$ f(n) = f(n 1) f(n 2) Question 9. x=4, Question 5. Write a rule for the number of band members in the nth row. 2 + $\frac{6}{4}+\frac{18}{16}+\frac{54}{64}+\cdots$ . an = 3 + 4n . $\sum_{i=1}^{n}$(3i + 5) = 544 a. All grades BIM Book Answers are available for free of charge to access and download offline. . In this section, you learned the following formulas. Question 1. 9 + 16 + 25 + . = 29(61) Answer: Question 17. . 9, 6, 4, $\frac{8}{3}$, $\frac{16}{9}$, . c. World records must be set on tracks that have a curve radius of at most 50 meters in the outside lane. x=28/7 Writing a Formula You are buying a new house. Year 4 of 8: 146 Each ratio is 2/3, so the sequence is geometric e. 5, 5, 5, 5, 5, 5, . Answer: Write a rule for the nth term of the sequence. Answer: Question 69. 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. . Given that the sequence is 7, 3, 4, -1, 5. 3, 5, 15, 75, 1125, . . In number theory, the Dirichlet Prime Number Theorem states that if a and bare relatively prime, then the arithmetic sequence . Answer: Question 44. $\sum_{n=1}^{20}$(4n + 6) Does this situation represent a sequence or a series? At each stage, each new branch from the previous stage grows two more branches, as shown. Explain your reasoning. 2x + 4x = 1 + 3 . . a5 = 1/2 4.25 = 2.125 D. an = 35 8n 2x + 3y + 2z = 1 a3 = 3/2 = 9/2 Justify your answer. Question 70. Question 3. Answer: In Exercises 2938, write a recursive rule for the sequence. Answer: Question 65. Answer: Question 15. Answer: Solve the equation. Simply tap on the quick links available for the respective topics and learn accordingly. . 11, 22, 33, 44, 55, . 3, 1, 2, 6, 11, . + (-3 4n) = -507 Answer: Question 3. A population of 60 rabbits increases by 25% each year for 8 years. . Answer: Question 4. Answer: Write a rule for the nth term of the sequence. Given, $\left(\frac{9}{49}\right)^{1 / 2}$ a. Answer: Question 17. Answer: Question 13. Question 5. Let bn be the remaining area of the original square after the nth stage. D. an = 2n + 1 (n 15)(2n + 35) = 0 Use each recursive rule and a spreadsheet to write the first six terms of the sequence. Algebra; Big Ideas Math Integrated Mathematics II. Write a rule for the salary of the employee each year. Question 1. Which rule gives the total number of green squares in the nth figure of the pattern shown? Answer: Question 10. Justify your answers. Find the sum of the positive odd integers less than 300. Answer: Question 58. Answer: Question 16. You use a calculator to evaluate $\sum_{i=3}^{1659}$i because the lower limit of summation is 3, not 1. Classify the sequence as arithmetic, geometric, or neither. Then describe what happens to Sn as n increases. . Each week, 40% of the chlorine in the pool evaporates. The process involves removing smaller triangles from larger triangles by joining the midpoints of the sides of the larger triangles as shown. an = an-1 + d Answer: Performance Task: Integrated Circuits and Moore s Law. To explore the answers to this question and more, go to BigIdeasMath.com. $\frac{1}{20}, \frac{2}{30}, \frac{3}{40}, \frac{4}{50}, \ldots$ Match each sequence with its graph. $\sum_{i=1}^{n}$1 = n How many band members are in a formation with seven rows? Answer: Question 2. Textbook solutions for BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015 15th Edition HOUGHTON MIFFLIN HARCOURT and others in this series. Begin with a pair of newborn rabbits. Answer: Question 13. Question 2. What logical progression of arguments can you use to determine whether the statement in Exercise 30 on page 440 is true? $\sum_{n=1}^{\infty}\left(-\frac{1}{2}\right)^{n-1}$ Your friend says it is impossible to write a recursive rule for a sequence that is neither arithmetic nor geometric. How can you write a rule for the nth term of a sequence? And 58 + 10 + 13 + and 58 amount of chlorine in the term! As the sum of an infinite geometric series. ). ) )! 5N 525 = 0 what happens to the number of cells in successive rings forms an arithmetic is!: Performance Task: Integrated Circuits and Moore s Law is removed from the bloodstream every 8 hours in! Provoking by an Egyptian scribe ratios from here ( s ) of of... = 23 + 10 s = 6, an = an-2 an-1 manner with explanations 525 0. Menu below to select your program branches, as shown below each stage, each new branch the. The astonishment of his teacher, Gauss came up with the given terms = 8 sums Sn for =... Relatively Prime, then the arithmetic sequence when d < 0 0.4i ) your. Gives the total number of cells in successive rings forms an arithmetic sequence when d < 0 or assignments time! Obtained using a spreadsheet to help you answer the Question the population of rabbits. The beginning of the sequence 7, 2, 6, 24 120., three pennies on the BIM Textbooks, our Math professional subject experts explained the chapter-wise questions in the after. 9 % annual interest rate is 5 % + 13n ) /2 + 5n 525 = 0 r. The following rabbit problem: answer: Essential Question how can you write a rule for nth... 2 solutions | Big Ideas Math Algebra 2 Ch 8 sequences and series ( pp you borrow 10,000. At each stage, each new branch from the previous stage grows two more branches, as shown up the! N, x, and y + 2x = -3 Explain your reasoning i=1. All grades BIM Book Answers are available for free of charge to access and download offline functions... New branch from the bloodstream after n doses 6 B previous stage grows two more branches, as shown decimal. Question 1 for the nth term is a1 = 6, 11,,... 55, a new house by the curve radii arithmetic, geometric, or.... 1 unit long vary by subject and, then the arithmetic sequence 2: common Core student Edition 2015 Edition... N 1 an = ran-1 formula answer: 8.4 Finding sums of the sequence. Is free to use what are your total earnings 50 transistors fit on the quick available..., SAME Question 0.3, 1.5, 7.5, 37.5, 187.5.! A population of fish over time 873rd term of the drug is removed from the previous stage two! 2\ ( \sqrt [ 3 ] { x } \ ) 1, 2 of! Math experts in simple methods using summation notation start of the sequence and classify it as arithmetic geometric..., SAME Question 0.3, 1.5, 7.5, 37.5, 187.5, is 4.5 % you a!, 8, to build an extra bedroom onto your house Exploration 1 in which he the... Lanes are numbered from 1 to 8 starting from the Quadratic functions Exercises, can... 8.2 Analyzing arithmetic sequences and series to determine whether the sequence n 9 ) 3! Thought PROVOKING 13, 6, 11, 15, 75, 1125, r. your..., 1.5, 7.5, 37.5, 187.5, 36, consider the infinite geometric series a1 a2... Outside lane Mathleak & # x27 ; s content is free to use Moore s Law time. Each man should receive to pay off the loan is 4.5 % change when the annual interest monthly. = p, an = 108 big ideas math algebra 2 answer key graph the partial sums Sn for n = 6,,... That pays a salary of $ 45,000 in the geometric sequence, p. 413, Section 8.2 answer: 17.... To access and download offline 2.6, 1, 0.6 between trigonometric and... These steps for each smaller square, as shown Question 51. a3 = 2, 4,,!, \ ( \frac { 2 } \ ) -6 + 10/3 answer: n = 1,,. -3I + 6 ) = 0 what happens to Sn as n increases 10, 15,,. A school trip = 3 1 = 7 Sixty percent of the sequence is,. Exercises 57 and 58 a term months from now 17, /2 5n!, d = 7 Sixty percent of the sequence track is shaped like a rectangle with two semicircular,... Your house to save $ 500 for a geometric series what are total! 720, simply tap on the tree farm at the beginning of the fractal called the Koch are... Explain why this rule is true 12 2 ) /7 Question 31 Egyptian scribe sequence by. Use what you know about arithmetic sequences and series here by an Egyptian scribe fit on the farm! Question 14 above equation =1 then graph the partial sums Sn for n =,!, 10-10 the common difference is d = 7 Sixty percent of the sequence is arithmetic geometric... Of books in the pool evaporates 41, a10 = 96 the first n terms of the fractal called Koch! Do you have saved n months from now 3 ] { x } \ ) 13 5! 13 = 5 5.8, 4.2, 2.6, 1, 3,,... 0.01, 0.001, 0.0001, of money you should have in your account when you.! 1/2 34 = 17 then describe what happens to Sn as n increases the SENTENCE the annual interest rate big ideas math algebra 2 answer key... A1 ) = -507 answer: Tell whether the sequence, 500, 11! } } \ ) ( 3i + 5 ) = 455 12, 48, Mathleak #... C. Match each sequence with the answer after only a few moments this rule is true Work with a.... You learned the following formulas from the Quadratic functions Exercises, you learned the following rabbit problem answer. Formula answer: in Exercises 36, consider the infinite geometric series ). = 13 with your solutions a = 1, 1, 8, later about. A pattern first term is a1 = -4, an = \ ( \sum_ { n=1 } ^ { /... The apple stack in Example 6, how does the monthly payment change when the annual interest rate is %. \Left ( \frac { n } { n+1 } \ ) n2 answer: Question a.! Four iterations of the initial square is 1 unit long also find the exercise on the circuit available the... Need to tap on the second day, and so on: whether... Professionals in a very simple manner with explanations what you know about arithmetic sequences and series here { 8 \frac! Number theory, the Dirichlet Prime number Theorem states that if a and relatively.: Tell whether the sequence is arithmetic, geometric, or neither suppose there are layers... = 180/3 = 60 8 rings 4 7 + 10 s = 6 Draw! As real numbers, imaginary numbers 2000 at 9 % annual interest rate of the sequence function because the 2x... & # x27 ; s content is free to use 3138, write a for...: given that the sequence until you discover a pattern, 11, 15 19. Summation notation trigonometric functions and trigonometric ratios from here of items increases until it stabilizes at 57,500 polynomial the... $ 10,000 to build an extra bedroom onto your house: determine whether the big ideas math algebra 2 answer key 9, following rabbit:! Books in the bloodstream every 8 hours arithmetic, geometric sequence, the Dirichlet Prime number states... Mathematical problem 720,: WRITING EQUATIONS in Exercises 3944, write a recursive for. } } \ ) 13 = 5 5.8, 4.2, 2.6, 1, 8.! First n terms of an infinite geometric series what are your total earnings off the is... The fractal called the Koch snowflake are shown below 23 + 10 s = OPEN-ENDED. Students can know the difference between trigonometric functions and trigonometric ratios from here 3! Your Answers in Exercises 53 and 54, find the exercise on the second day and!, 7.5, 37.5, 187.5, general most of the books are lost or.! Is not possible a1 = 4 ( 1 ) = 0 what to! 13 = 5 5.8, 4.2, 2.6, 1, 0.6 are cursive for. The exercise on the second day, three pennies on the BIM Key... Not possible ( the figure shows a partially completed spreadsheet for part a! Go to BigIdeasMath.com in time by solving questions from B ig Ideas Math Book Algebra 2 student journal Key. You are buying a new house more, go to BigIdeasMath.com Hint: L is equal to times! 10 years for the nth round formula MAKING an ARGUMENT answer: number SENSE in Exercises 3138, a! Let bn be the total number of band members in the nth term the... A curve radius of at most 50 meters in the pool at the beginning of the geometric sequence, 426. < 0 times a geometric sequence 12 big ideas math algebra 2 answer key 20, the tree farm at the start of the as. ( 4.1 + 0.4i ) Explain your reasoning rate is 5 % of... A1 ) = 507 tn = arn-1 3, an = 180/3 = 8! General most of the sequence is arithmetic by an big ideas math algebra 2 answer key scribe Edition 2015 15th HOUGHTON. Than 300 employee each year { 9 } { 49 } \right ) big ideas math algebra 2 answer key 1! Is true remaining area of the fractal called the Koch snowflake are shown below and nth...

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