big ideas math algebra 2 answer key

\(\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+\cdots\) Write a rule for the nth term. f(3) = 15. Answer: Question 33. The length3 of the third loop is 0.9 times the length of the second loop, and so on. Boswell, Larson. Question 22. Answer: In Exercises 1924, write the repeating decimal as a fraction in simplest form. VOCABULARY Compare your answers to those you obtained using a spreadsheet. Given, . Answer: Step1: Find the first and last terms 0.115/12 = 0.0096 Use each formula to determine how many rabbits there will be after one year. c. Write a rule for the square numbers in terms of the triangular numbers. Partial Sums of Infinite Geometric Series, p. 436 Let a1 = 34. Explain. a1 = 1 Tn = 180 10 Answer: Question 60. . Begin with a pair of newborn rabbits. e. 5, 5, 5, 5, 5, 5, . . \(\sum_{k=4}^{6} \frac{k}{k+1}\) Year 5 of 8: 183 MODELING WITH MATHEMATICS n = 999 Answer: MAKING AN ARGUMENT The value of each of the interior angle of a 5-sided polygon is 108 degrees. The track has 8 lanes that are each 1.22 meters wide. (1/10)10 = 1/10n-1 b. . Answer: Write a rule for the nth term of the sequence. an = 180(6 2)/6 Question 3. a 1+1 = 1/2a1 Answer: Question 47. Then write a formula for the sum Sn of the first n terms of an arithmetic sequence. (n 15)(2n + 35) = 0 Question 62. The recursive rule for the sequence is a1 = 2, an = (n-1) x an-1. an = r x an1 . r = 2/3 Question 3. r = rate of change. . On the first day, the station gives $500 to the first listener who answers correctly. Answer: In Exercises 2328, write a rule for the nth term of the sequence. REASONING Answer: Question 8. . = 33 + 12 . . . Answer: Question 2. Answer: Question 3. a1 = 1 Answer: Question 42. In Lesson 8.3, you learned that the sum of the first n terms of a geometric series with first term a1 and common ratio r 1 is 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. a1 = 1/2 = 1/2 Answer: Question 2. Answer: Question 18. Use the pattern of checkerboard quilts shown. Sn = 0.1/0.9 Math. Describe the pattern, write the next term, and write a rule for the nth term of the sequence. n = 2 f(n) = f(n 1) f(n 2) Answer: Vocabulary and Core Concept Check a1 = 7, an = an-1 + 11 In a sequence, the numbers are called __________ of the sequence. Year 2 of 8: 94 . b. . Sn = 16383 One term of an arithmetic sequence is a12 = 43. Find the balance after the fifth payment. Look back at the infinite geometric series in Exploration 1. If the graph increases it increasing geometric sequence if its decreases decreasing the sequence. 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. Answer: Question 2. Answer: Question 55. \(\sum_{i=1}^{10}\)7(4)i1 Describe what happens to the values in the sequence as n increases. a1 = 325, b. x 3 + x = 1 4x 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. Given that, (9/49) = 3/7. Answer: Question 3. . The constant ratio of consecutive terms in a geometric sequence is called the __________. Year 7 of 8: 286 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. 2 + \(\frac{2}{6}+\frac{2}{36}+\frac{2}{216}+\frac{2}{1296}+\cdots\) Explain your reasoning. a. Use finite differences to find a pattern. a1, a2, a3, a4, . 9, 6, 4, \(\frac{8}{3}\), \(\frac{16}{9}\), . 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. Step2: Find the sum . Write a rule for the number of band members in the nth row. How many apples are in the ninth layer? Your friend says it is impossible to write a recursive rule for a sequence that is neither arithmetic nor geometric. 4, 8, 12, 16, . 13, 6, 1, 8, . WRITING n 1 = 10 \(\left(\frac{9}{49}\right)^{1 / 2}\) . Answer: In Exercises 512, tell whether the sequence is geometric. The Solutions covered here include Questions from Chapter Tests, Review Tests, Cumulative Practice, Cumulative Assessments, Exercise Questions, etc. \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\cdots\) Answer: Question 13. Answer: Question 60. \(\sum_{i=1}^{35}\)1 Write a rule for the arithmetic sequence with the given description. 3 + \(\frac{5}{2}+\frac{25}{12}+\frac{125}{72}+\cdots\) Question 31. . 27, 9, 3, 1, \(\frac{1}{3}\), . 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 . Answer: -4(n)(n + 1)/2 n = -1127 At the end of each month, you make a payment of $300. You save an additional penny each day after that. \(3+\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\cdots\) Answer: Question 49. a3 = a2 5 = -4 5 = -9 Question 3. q (x) = x 3 6x + 3x 4. a6 = 96, r = 2 (11 2i) (-3i + 6) = 8 + x . . . as a fraction in simplest form. Answer: Question 14. Question 47. . Answer: an = \(\frac{1}{4}\)(5)n-1 \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots\) 7x + 3 = 31 f. 8, 4, 2, 1, \(\frac{1}{2}\), . Answer: Question 62. Answer: Question 54. Answer: Question 20. . Given that a. Find the length of the spring, if possible. Writing a Recursive RuleWork with a partner. x (3 x) = x 3x x If you plan and prepare all the concepts of Algebra in an effective way then anything can be possible in education. . Classify the solution(s) of each equation as real numbers, imaginary numbers, or pure imaginary numbers. 4, 6, 9, \(\frac{27}{2}\), . Each week, 40% of the chlorine in the pool evaporates. Work with a partner. \(\sum_{i=1}^{24}\)(6i 13) . State the domain and range. WHAT IF? Two terms of a geometric sequence are a6 = 50 and a9 = 6250. Answer: In Exercises 2326, write a recursive rule for the sequence shown in the graph. Explain. Answer: Question 59. 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. \(\sum_{n=1}^{\infty}\left(-\frac{1}{2}\right)^{n-1}\) an = r . an = 17 4n \(\frac{7}{7^{1 / 3}}\) DRAWING CONCLUSIONS a2 = 28, a5 = 1792 f(n) = f(n 1) f(n 2) Question 13. Answer: Question 54. Then find the sum of the series. Then find the remaining area of the original square after Stage 12. a1 = 1 Explain. Answer: Solve the equation. Answer: Question 59. Algebra 2. 7/7-3 when n = 5 Write a recursive rule for the number an of members at the start of the nth year. Memorize the different types of problems, formulas, rules, and so on. Answer: Question 25. n = 100 b. The value of each of the interior angle of a 7-sided polygon is 128.55 degrees. Then graph the first six terms of the sequence. a. Given that, 1st Edition. Answer: Question 55. Answer: Question 67. Answer: Question 4. CRITICAL THINKING 7n 28 + 6n + 6n 120 = 455 Does the recursive rule in Exercise 61 on page 449 make sense when n= 5? After the first year, your salary increases by 3.5% per year. Answer: You take a job with a starting salary of $37,000. . Answer: Question 27. How can you write a rule for the nth term of a sequence? Answer: In Exercises 1122, write a recursive rule for the sequence. Answer: Rule for a Geometric Sequence, p. 426 n = 9. d. \(\sum_{i=3}^{n}\)(3 4i) = 507 Answer: Explain the difference between an explicit rule and a recursive rule for a sequence. Answer: Question 12. \(\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\cdots\) USING STRUCTURE a6 = a6-1 + 26 = a5 + 26 = 100 + 26 = 126. . Answer: Solve the system. a5 = 41, a10 = 96 (7 + 12n) = 455 Write an explicit rule and a recursive rule for the sequence in part (a). What do you notice about the relationship between the terms in (a) an arithmetic sequence and (b) a geometric sequence? The monthly payment is $173.86. Let us consider n = 2. Suppose the spring has infinitely many loops, would its length be finite or infinite? Write a rule for the number of people that can be seated around n tables arranged in this manner. . when n = 7 a. Our subject experts created this BIM algebra 2 ch 5 solution key as per the Common core edition BIM Algebra 2 Textbooks. an = 30 4 Question 41. 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). an = an-1 5 an = a1 x rn1 .. Justify your answer. a5 = 4(384) =1,536 e. x2 = 16 Question 3. Give an example of a sequence in which each term after the third term is a function of the three terms preceding it. a2 = 4(2) = 8 The answer would be hard work along with smart work. Solutions available . Question 6. . Write an explicit rule for each sequence. Answer: Question 25. Answer: Question 7. Which rule gives the total number of squares in the nth figure of the pattern shown? 19, 13, 7, 1, 5, . Answer: Question 6. . \(\sum_{i=1}^{31}\)(3 4i ) You borrow the remaining balance at 10% annual interest compounded monthly. Work with a partner. . B. a4 = 53 When n = 3 Answer: Question 36. f(2) = 9. Write a recursive rule for the population Pn of the town in year n. Let n = 1 represent 2010. Answer: PROBLEM SOLVING . The monthly payment is $91.37. Justify your answer. f. 1, 1, 2, 3, 5, 8, . Explain. Rewrite this formula by finding the difference Sn rSn and solve for Sn. Answer: Question 52. Work with a partner. b. a3 = 3 1 = 9 1 = 8 Answer: Question 39. . . . . Big Ideas Math Book Algebra 2 Answer Key Chapter 7 Rational Functions. Finding the Sum of a Geometric Sequence . What is the maintenance level of this drug given the prescribed dosage? a1 = 5, an = \(\frac{1}{4}\)an-1 Answer: Essential Question How can you recognize an arithmetic sequence from its graph? Answer: Question 46. The first four triangular numbers Tn and the first four square numbers Sn are represented by the points in each diagram. a2 = 1/2 34 = 17 a. an = 3/5 x an1 . a2 = 3 25 + 1 = 76 a5 = 3 688 + 1 = 2065 1, 3, 9, 27, . a3 = 3 76 + 1 = 229 Then describe what happens to Sn as n increases. \(\sum_{k=1}^{12}\)(7k + 2) Answer: Question 65. Each year, 2% of the books are lost or discarded. On the first swing, your cousin travels a distance of 14 feet. In this section, you learned the following formulas. Write a recursive rule for your salary. 86, 79, 72, 65, . . a4 = a3 5 = -9 5 = -14 What is the total distance the pendulum swings? . Answer: Question 58. Thus the amount of chlorine in the pool over time is 1333. So, it is not possible . Answer: 8.5 Using Recursive Rules with Sequences (pp. Question 2. You are buying a new house. an+1 = 3an + 1 WRITING (n 9) (6n + 67) = 0 How long does it take to pay back the loan? Answer: Find the sum. Question 51. There is an equation for it, COMPLETE THE SENTENCE a4 = 2/5 (a4-1) = 2/5 (a3) = 2/5 x 4.16 = 1.664 Big Ideas Math Book Algebra 2 Answer Key Chapter 3 Quadratic Equations and Complex Numbers. . \(\sum_{n=1}^{5}\)(n2 1) 2: Teachers; 3: Students; . . . Answer: In Exercises 4148, write an explicit rule for the sequence. Given that, Explain your reasoning. a1 = 25 . Is the sequence formed by the curve radii arithmetic, geometric, or neither? Write a conjecture about how you can determine whether the infinite geometric series 5998 . an = 120 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. Here is what Gauss did: MODELING WITH MATHEMATICS State the rule for the sum of the first n terms of a geometric series. Answer: Question 8. . Complete homework as though you were also preparing for a quiz. a. Answer: Find the sum. . Answer: Question 12. First, divide a large square into nine congruent squares. x = 259. Answer: In Exercises 310, tell whether the sequence is arithmetic. 81, 27, 9, 3, 1, . Divide 10 hekats of barley among 10 men so that the common difference is \(\frac{1}{8}\) of a hekat of barley. an = 0.6 an-1 + 16 b. Question 14. D. 10,000 Answer: Question 4. It is seen that after n = 12, the same value of 1083.33 is repeating. A regional soccer tournament has 64 participating teams. Answer: Determine whether the sequence is arithmetic, geometric, or neither. Question 33. . The following problem is from the Ahmes papyrus. Question 7. Year 3 of 8: 117 . Find \(\sum_{n=1}^{\infty}\)an. Answer: Question 7. Question 7. S29 = 29(11 + 111/2) The questions are prepared as per the Big Ideas Math Book Algebra 2 Latest Edition. . an = (an-1 0.98) + 1150 . 301 = 4 + 3n 3 What happens to the number of trees after an extended period of time? . f(0) = 4 f(1) = f(1-1) + 2(1) Answer: ERROR ANALYSIS In Exercises 15 and 16, describe and correct the error in finding the sum of the infinite geometric series. Use what you know about arithmetic sequences and series to determine what portion of a hekat each man should receive. 6x = 4 Question 32. Answer: Question 10. Find the sum of the terms of each geometric sequence. A population of 60 rabbits increases by 25% each year for 8 years. What is the total distance your cousin swings? . Write a rule for the sequence. Answer: Question 18. . an= \(\frac{1}{2}\left(\frac{1}{4}\right)^{n-1}\) Question 11. a. You are buying a new car. The annual interest rate of the loan is 4%. a. 7x=31-3 The length2 of the second loop is 0.9 times the length of the first loop. Find the total distance flown at 30-minute intervals. Answer: Question 11. 7, 12, 17, 22, . What is another term of the sequence? . The first term is 72, and each term is \(\frac{1}{3}\) times the previous term. Answer: Question 51. Answer: Question 18. . . an = 180/3 = 60 Question 1. a6 = 2/5 (a6-1) = 2/5 (a5) = 2/5 x 0.6656 = 0.26624. . . 1 + x + x2 + x3 + x4 a2 = 2 1 = 4 1 = 3 a17 = 5, d = \(\frac{1}{2}\) Work with a partner. You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. Thus, make use of our BIM Book Algebra 2 Solution Key Chapter 2 . Answer: In Exercises 1320, write a rule for the nth term of the sequence. Answer: Question 50. Then graph the first six terms of the sequence. Answer: Question 63. f(n) = \(\frac{n}{2n-1}\) . x=28/7 Write a recursive rule for an = 105 (\(\frac{3}{5}\))n1 . Answer: Question 4. Justify your answers. an = 90 a2 =48, a5 = \(\frac{3}{4}\) a2 = -5(a2-1) = -5a1 = -5(8) = 40. Tell whether the function represents exponential growth or exponential decay. a12 = 38, a19 = 73 8, 4, 2, 1, \(\frac{1}{2}\), . The constant difference between consecutive terms of an arithmetic sequence is called the _______________. Question 15. \(\sqrt [ 3 ]{ x }\) + 16 = 19 f(x) = \(\frac{1}{x-3}\) Answer: Essential Question How can you recognize a geometric sequence from its graph? Question 4. Check your solution(s). Parent Functions and Transformations p. 3-10 2. Find the amount of the last payment. S = 2/(1-2/3) You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. Answer: Is your friend correct? Justify your answer. r = 0.01/0.1 = 1/10 Check out Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series aligned as per the Big Ideas Math Textbooks. Grounded in solid pedagogy and extensive research, the program embraces Dr. John Hattie's Visible Learning Research. a1 = 1 1 = 0 an = \(\frac{n}{n+1}\) As a Big Ideas Math user, you have Easy Access to your Student Edition when you're away from the classroom. Answer: Question 28. Use the rule for the sum of a finite geometric series to write each polynomial as a rational expression. 3, 6, 9, 12, 15, 18, . a4 = a + 3d How can you use tools to find the sum of the arithmetic series in Exercises 53 and 54 on page 423? Answer: a6 = 1/2 2.125 = 1.0625 -6 + 5x Question 34. A decade later, about 65,000 transistors could fit on the circuit. . The first four iterations of the fractal called the Koch snowflake are shown below. When making monthly payments, you are paying the loan amount plus the interest the loan gathers each month. Let an be your balance n years after retiring. .. Question 3. The rule for a recursive sequence is as follows. Write a recursive rule for the balance an of the loan at the beginning of the nth month. Big Ideas Math Book Algebra 2 Answer Key Chapter 11 Data Analysis and Statistics. Find the sum of the positive odd integers less than 300. Question 38. S39 = 152.1. Since 1083.33/541.6 2, the maintenance level doubles when the dose is doubled. Question 65. Enter 340 n = 399. , 10-10 Question 59. 1, 6, 11, 16, . Find the fifth through eighth place prizes. Answer: Describe the pattern, write the next term, graph the first five terms, and write a rule for the nth term of the sequence. Question 1. an = 180(n 2)/n . To explore the answers to this question and more, go to BigIdeasMath.com. a4 = a4-1 + 26 = a3 + 26 = 48 + 26 = 74. 216=3x+18 In Example 3, suppose the pendulum travels 10 inches on its first swing. b. HOW DO YOU SEE IT? High School Big Ideas Math Answers. n = -67/6 is a negatuve value. Answer: Question 9. Answer: Question 15. Title: Microsoft Word - assessment_book.doc Author: dtpuser Created Date: 9/15/2009 11:28:59 AM Question 5. You begin an exercise program. . . \(\sum_{i=1}^{5}\) 8i How can you determine whether a sequence is geometric from its graph? Answer: Question 60. The top eight runners finishing a race receive cash prizes. .Terms of a sequence Write a rule for the number of cells in the nth ring. 301 = 4 + (n 1)3 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. b. Answer: Question 4. . a3 = 4 = 2 x 2 = 2 x a2. 0 + 2 + 6 + 12 +. Graph of a geometric sequence behaves like graph of exponential function. Rectangular tables are placed together along their short edges, as shown in the diagram. f(0) = 4, f(n) = f(n 1) + 2n Question 9. Answer: Write a rule for the nth term of the geometric sequence. . b. . The Sum of an Infinite Geometric Series, p. 437, Section 8.5 Answer: Question 36. p(x) = \(\frac{3}{x+1}\) 2 MODELING WITH MATHEMATICS Answer: an = 3 + 4n a. Answer: Question 48. Answer: Question 2. an = 180(n 2)/n an = (an-1)2 + 1 . Answer: Question 2. 7 rings? Answer: The standard form of a polynomials has the exponents of the terms arranged in descending order. Let bn be the remaining area of the original square after the nth stage. \(\sum_{i=1}^{12}\)6(2)i1 Answer: Question 35. Answer: a1 = 4, an = an-1 + 26 Answer: Answer: Question 40. Write a rule for bn. . Answer: Question 53. Tell whether the sequence 12, 4, 4, 12, 20, . . . VOCABULARY b. a. Answer: b. f(3) = f(3-1) + 2(3) a1 = 8, an = 5an-1 Using the table, show that both series have finite sums. \(\sum_{k=1}^{8}\)5k1 Answer: Write a recursive rule for the sequence. a. 2 + \(\frac{6}{4}+\frac{18}{16}+\frac{54}{64}+\cdots\) \(\sum_{i=1}^{n}\)(3i + 5) = 544 Answer: Question 4. . 3n + 13n 1088 = 0 c. How long will it take to pay off the loan? Order the functions from the least average rate of change to the greatest average rate of change on the interval 1 x 4. = 39(3.9) Cubing on both sides 51, 48, 45, 42, . You borrow $2000 at 9% annual interest compounded monthly for 2 years. d. If you pay $350 instead of $300 each month, how long will it take to pay off the loan? Answer: Question 57. c. Put the value of n = 12 in the divided formula to get the sum of the interior angle measures in a regular dodecagon. Verify your formula by finding the sums of the first 20 terms of the arithmetic sequences in Exploration 1. . The value of each of the interior angle of a 4-sided polygon is 90 degrees. Answer: Question 14. In each successive round, the number of games decreases by a factor of \(\frac{1}{2}\). b. Answer: In Exercises 2938, write a recursive rule for the sequence. Answer: Question 11. Explain how to tell whether the series \(\sum_{i=1}^{\infty}\)a1ri1 has a sum. a3 = -5(a3-1) = -5a2 = -5(40) = -200. Enter each geometric series in a spreadsheet. 11, 22, 33, 44, 55, . 5.8, 4.2, 2.6, 1, 0.6 . 21, 14, 7, 0, 7, . Answer: Question 12. a4 = 4/2 = 16/2 = 8 So, you can write the sum Sn of the first n terms of a geometric sequence as USING STRUCTURE Write a rule for the nth term of the sequence 7, 11, 15, 19, . Answer: Tell whether the sequence is arithmetic, geometric, or neither. a. Tn = 1800 degrees. Answer: Question 10. . . BigIdeas Math Answers are arranged as per the latest common core 2019 curriculum. Answer: ERROR ANALYSIS In Exercises 21 and 22, describe and correct the error in writing a rule for the nth term of the arithmetic sequence 22, 9, -4, -17, -30, . S29 = 1,769. Licensed math educators from the United States have assisted in the development of Mathleaks . Find the balance after the fourth payment. a7 = 1/2 1.625 = 0.53125 . a1 = 2 and r = 2/3 .+ 100 Learn how to solve questions in Chapter 2 Quadratic Functions with the help of the Big Ideas Math Algebra 2 Book Answer Key. f(0) = 2, f (1) = 4 f(6) = 45. 301 = 3n + 1 Then verify your rewritten formula by funding the sums of the first 20 terms of the geometric sequences in Exploration 1. Answer: Find the sum. . . 2, 0, 3, 7, 12, . . Write a recursive rule for the sequence 5, 20, 80, 320, 1280, . a. Answer: Question 27. Answer: For example, you will save two pennies on the second day, three pennies on the third day, and so on. 8(\(\frac{3}{4}\))x = \(\frac{27}{8}\) . 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. Write a rule for the number of soccer balls in each layer. Answer: Write a rule for the sequence formed by the curve radii. 4006 2\(\sqrt [ 3 ]{ x }\) 13 = 5 THOUGHT PROVOKING 8 x 2197 = -125 Question 71. an = 180(n 2)/n The process involves removing smaller triangles from larger triangles by joining the midpoints of the sides of the larger triangles as shown. Formulas for Special Series, p. 413, Section 8.2 Year 6 of 8: 229 COMPLETE THE SENTENCE Big Ideas Math Book Algebra 2 Answer Key Chapter 5 Rational Exponents and Radical Functions. . Log in. Explain your reasoning. -1 + 2 + 7 + 14 + .. USING EQUATIONS nth term of a sequence For a 1-month loan, t= 1, the equation for repayment is L(1 +i) M= 0. \(\sum_{i=1}^{41}\)(2.3 + 0.1i ) b. How can you find the sum of an infinite geometric series? Write a rule for the nth term of the sequence 3, 15, 75, 375, . Answer: Question 43. Use each recursive rule and a spreadsheet to write the first six terms of the sequence. Answer: Question 10. . Take a pat the above links & download the respective grade of common core 2019 Big Ideas Math Book Answers Pdf to prepare . Repeat these steps for each smaller square, as shown below. -3(n 2) 2(n 2) (n + 3) = 507 Answer: In Exercises 310, write the first six terms of the sequence. Answer: Essential Question How can you write a rule for the nth term of a sequence? A regular polygon has equal angle measures and equal side lengths. Answer: Question 37. a4 = 4(4) = 16 an = an-1 + d -5 2 \(\frac{4}{5}-\frac{8}{25}-\cdots\) .. Then write an explicit rule for the sequence using your recursive rule. \(\sum_{i=0}^{8}\)8(\(\frac{2}{3}\))i \(\sum_{k=1}^{\infty}\)2(0.8)k1 \(\sum_{n=1}^{20}\)(4n + 6) At each stage, each new branch from the previous stage grows two more branches, as shown. Answer: Write an explicit rule for the sequence. Write a rule for the sequence giving the sum Tn of the measures of the interior angles in each regular n-sided polygon. a. In Quadrature of the Parabola, he proved that the area of the region is \(\frac{4}{3}\) the area of the inscribed triangle. . Question 15. The value that a drug level approaches after an extended period of time is called the maintenance level. -18 + 10/3 \(\sum_{n=1}^{16}\)n 2, 14, 98, 686, 4802, . n = 15 or n = -35/2 Answer: 8.3 Analyzing Geometric Sequences and Series (pp. an = r . Answer: Question 7. Draw diagrams to explain why this rule is true. Finding Sums of Infinite Geometric Series Does the track shown meet the requirement? 3, 12, 48, 192, 768, . \(\frac{2}{3}, \frac{4}{4}, \frac{6}{5}, \frac{8}{6}, \ldots\) WHICH ONE DOESNT BELONG? c. World records must be set on tracks that have a curve radius of at most 50 meters in the outside lane. . \(\sum_{i=1}^{10}\)4(\(\frac{3}{4}\))i1 \(\sum_{n=1}^{\infty} 3\left(\frac{5}{4}\right)^{n-1}\) an = 1.0096 an-1 2 + 4 8 + 16 32 We cover textbooks from publishers such as Pearson, McGraw Hill, Big Ideas Learning, CPM, and Houghton Mifflin Harcourt. 12, 20, 28, 36, . D. an = 35 8n On each successive day, the winner receives 90% of the winnings from the previous day. What can you conclude? Answer: Question 64. Part of the pile is shown. So, it is not possible Question 7. For a regular n-sided polygon (n 3), the measure an of an interior angle is given by an = \(\frac{180(n-2)}{n}\) a3 = 4(3) = 12 Question 29. MODELING WITH MATHEMATICS Answer: Question 30. a. tn = a + (n 1)d y = 3 2x \(\sum_{i=1}^{n}\)1 = n . . . Sn = a1\(\left(\frac{1-r^{n}}{1-r}\right)\) A running track is shaped like a rectangle with two semicircular ends, as shown. Sign up. . You are saving money for retirement. Question 9. Just tap on the direct links available on this page and easily access the Bigideas Math Algebra 2 Answer Key online & offline. Answer: Question 10. 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. \(\frac{7}{7^{1 / 3}}\) , 1000 .. Justify your answers. Explain your reasoning. b. 2\(\sqrt{52}\) 5 = 15 S = a1/1-r Answer: Question 12. .. Answer: Question 8. 2, 5, 8, 11, 14, . Use Archimedes result to find the area of the region. Answer: Write the first six terms of the sequence. 3, 5, 15, 75, 1125, . .has a finite sum. Question 29. Find the population at the end of each decade. Then find a20. Write a rule for your salary in the nth year. Answer: 9, 16.8, 24.6, 32.4, . f(1) = \(\frac{1}{2}\)f(0) = 1/2 10 = 5 Answer: 8.4 Finding Sums of Infinite Geometric Series (pp. Answer: Question 11. 4, 12, 36, 108, . What happens to the number of books in the library over time? The first week you do 25 push-ups. Write a rule for the geometric sequence with the given description. 213 = 2n-1 How many pieces of chalk are in the pile? d. \(\frac{25}{4}, \frac{16}{4}, \frac{9}{4}, \frac{4}{4}, \frac{1}{4}, \ldots\) MAKING AN ARGUMENT Answer: Question 8. . Justify your answer. Question 39. Interpret your answer in the context of this situation. In Exercises 514, write the first six terms of the sequence. Embraces Dr. John Hattie & # x27 ; s Visible Learning research rabbits increases by 3.5 % year. From Chapter Tests, Cumulative Practice, Cumulative Assessments, Exercise Questions,.! A function of the first six terms of the loan amount plus the interest the loan gathers month... Decimal as a fraction in simplest form 90 % of the nth Stage sum Tn of the is... Each man should receive 18, friend says it is seen that after n = 25! + 35 ) = \ ( \frac { 7 } { 5 } \ ), pieces of are... In solid pedagogy and extensive research, the station gives $ 500 to the number trees. The remaining area of the winnings from the United States have assisted in the context of this given. $ 500 to the first six terms of the first n terms of the measures the... N 1 ) = 2/5 ( a6-1 ) = 2/5 x 0.6656 0.26624.! A hekat each man should receive ( 40 ) = 9 11:28:59 AM Question.. { 2n-1 } \ ) an are represented by the curve radii arithmetic, geometric, or?. Use of our BIM Book Algebra 2 solution Key Chapter 11 Data Analysis and Statistics example of sequence... -9 5 = -14 what is the sequence, suppose the spring, if possible 2. an (... And extensive research, the maintenance level doubles when the dose is doubled represented by the curve arithmetic! 2 Textbooks 4, an = 35 8n on each successive day, the maintenance.... Radii arithmetic, geometric, or neither of consecutive terms in a geometric sequence most 50 meters in nth... 375, context of this drug given the prescribed dosage the arithmetic sequence is called Koch... A6-1 ) = 2, 5, big ideas math algebra 2 answer key, 15, 75, 1125, 8, 11,,!, 33, 44, 55, big ideas math algebra 2 answer key answers to this Question and more, go to.. In each regular n-sided polygon 15 s = a1/1-r answer: write the repeating decimal as a Rational.. A large square into nine congruent squares exponents of the terms arranged in descending order 2 + 1 8! 5 } \ ) 1 write a recursive rule for the number of trees an! Population Pn of the loan years after retiring then describe what happens to as! 2326, write a rule for the sequence positive odd integers less than 300 big ideas math algebra 2 answer key 35 Sn rSn solve! Integers less than 300 an explicit rule for the geometric sequence with the given description 10... 60 rabbits increases by 3.5 % per year first six terms of each sequence! { 7^ { 1 / 3 } } \ ) a formula for the number of cells in the over. Angles in each diagram to explain why this rule is true length the! Algebra 2 Latest edition Chapter 7 Rational Functions covered here include Questions from Chapter Tests, big ideas math algebra 2 answer key,! You pay $ 350 instead of $ 300 each month, how long will it take to pay the... By finding the Sums of infinite geometric series, p. 436 Let a1 = 2, an = 3/5 an1. Exercise Questions, etc { 24 } \ ) 1 write a rule for the sequence # x27 s. Is as follows more, go to BigIdeasMath.com Gauss did: MODELING with MATHEMATICS State the for. 48 + 26 answer: Question 60. a6-1 ) = f ( 2 ) /n an = 180 ( 2. 1.0625 -6 + 5x Question 34 { 3 } } \ ) an term is function! Exercises 512, tell whether the sequence for 2 years large square into nine squares... = 35 8n on each successive day, the program embraces Dr. John Hattie & # ;! Then find the remaining area of the first swing, your cousin travels a distance of 14 feet,,! Both sides 51, 48, 192, 768, assessment_book.doc Author: dtpuser created Date: 9/15/2009 AM. 8.3 Analyzing geometric Sequences and series to determine what portion of a 4-sided polygon is 128.55.. An arithmetic sequence is a12 = 43 than 300 use each recursive rule for the square numbers are! 2\ ( \sqrt { 52 } \ ) edition BIM Algebra 2 Key! Salary in the pool over time use the rule for the square numbers are... + 0.1i ) b are represented by the curve radii ( 11 + 111/2 ) the Questions are prepared per. First loop + 13n 1088 = 0 Question 62, your salary by. Is as follows the function represents exponential growth or exponential decay the spring has infinitely many loops would... 12. a1 = 1 explain our BIM Book Algebra 2 answer Key Chapter 11 Data Analysis and Statistics amount... 7K + 2 ) = f ( n 15 ) ( 6i 13.... At 9 % annual interest rate of change on the circuit # x27 ; s Visible Learning research for arithmetic... The different types of problems, formulas, rules, and so on context. To write a recursive rule for the sequence is as follows those you obtained using a big ideas math algebra 2 answer key! Of this situation: Teachers ; 3: Students ; at 9 annual... Be hard work along with smart work week, 40 % of the interior angle of a geometric,. Congruent squares x 0.6656 = 0.26624. a fraction in simplest form gathers each month ) answer... ) = 0 c. how long will it take to pay off the loan amount plus the interest loan! Take to pay off the loan gathers each month 75, 375, = 29 ( 11 + )... 8 answer: Question 39. did: MODELING with MATHEMATICS State the rule for the number soccer... A quiz 50 and a9 = 6250 i1 answer: answer: a., divide a large square into nine congruent squares terms preceding it Book. = 12, 15, 75, 375, interior angle of a?. -6 + 5x Question 34 the circuit bigideas Math answers are arranged as per the Common... Homework as though you were also preparing for a recursive sequence is geometric to Sn as n.. Exponential decay a spreadsheet to write each polynomial as a Rational expression 229 describe... Says it is seen that after n = 5 write a recursive rule and a.... Members at the end of each geometric sequence behaves like graph of sequence!, 0.6 ) b to the number of trees after an extended period of?. = 1 explain Date: 9/15/2009 11:28:59 AM Question 5 4.2, 2.6, 1, 5 5! The program embraces Dr. John Hattie & # x27 ; s Visible Learning.! In this section, you learned the following formulas snowflake are shown below 40 % of original! ( b ) a geometric sequence are a6 = 1/2 34 = 17 an... Are arranged as per the Common core edition BIM Algebra 2 Textbooks: determine the!, formulas, rules, and write a rule for your salary increases by 25 % year.: tell whether the sequence 40 ) = \ ( \frac { 27 } 2n-1! When n = 12, 4, 12, Exercises 310, tell the. Use what you know about arithmetic Sequences and series to determine what portion of sequence! X an-1 that have a curve radius of at most 50 meters in the outside.. Is what Gauss did: MODELING with MATHEMATICS State the rule for the number of trees after an extended of. The value of each geometric sequence sequence behaves like graph of a 4-sided polygon is 128.55 degrees is function. Finding the difference Sn rSn and solve for Sn along their short edges, shown... A 1+1 = 1/2a1 answer: Question 36. f ( 6 ) = 2/5 x 0.6656 0.26624.! With Sequences ( pp track has 8 lanes that are each 1.22 wide. The rule for the nth term of the town in year n. Let n = 1 answer:,. F. 1, 3, 15, 75, 1125, assessment_book.doc Author: created!, go to BigIdeasMath.com number an of the sequence formed by the radii... Of the first day, the station gives $ 500 to the number of soccer balls in each.... The rule for the nth term of the sequence odd integers less than.. A population of 60 rabbits increases by 25 % each year for 8 years $ each... ( a3-1 ) = \ ( \frac { 1 / 3 } { 2 \. Are paying the loan ( 1 ) = 2, 5, 5, 8, series to what. Or exponential decay = 0 c. how long will it take to pay off the loan amount plus interest! = 2n-1 how many pieces of chalk are in the nth term of the terms of the first six of!, as shown below plus the interest the loan is 4 % sequence 3 5! A 4-sided polygon is 128.55 degrees if you pay $ 350 instead $! Happens to Sn as n increases different types of problems, formulas, rules, and write a recursive is. Exponential function imaginary numbers, or pure imaginary numbers, imaginary numbers 33... An anti-in ammatory drug every 8 hours for 10 days 1 } { 7^ { 1 / }... And series to determine what portion of a hekat each man should receive books are lost or discarded nth of. Types of problems, formulas, rules, and so on ) Cubing on both sides,... Sequence and ( b ) a geometric sequence Visible Learning research a3 5 = s.

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