. Which rule gives the total number of green squares in the nth figure of the pattern shown? 9, 16.8, 24.6, 32.4, . Question 11. 18, 14, 10, 6, 2, 2, . 1000 = 2 + (n 1)1 Tell whether the sequence is geometric. WRITING EQUATIONS Given, \(\sum_{i=1}^{10}\)7(4)i1 Check your solution. VOCABULARY Recursive: a1 = 1, a2 = 1, an = an-2 + an-1 Question 71. 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. Your friend says it is impossible to write a recursive rule for a sequence that is neither arithmetic nor geometric. are called hexagonal numbers because they represent the number of dots used to make hexagons, as shown. The first term is 3, and each term is 5 times the previous term. Answer: ERROR ANALYSIS In Exercises 15 and 16, describe and correct the error in finding the sum of the infinite geometric series. 2n(n + 1) + n = 1127 S = 6 Answer: Find the sum. . You are buying a new house. 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. On the first day, the station gives $500 to the first listener who answers correctly. Looking at the race as Zeno did, the distances and the times it takes the person to run those distances both form infinite geometric series. 44, 11, \(\frac{11}{4}\), \(\frac{11}{16}\), \(\frac{11}{64}\), . Answer: Write a rule for the nth term of the sequence. e. 5, 5, 5, 5, 5, 5, . . After the first year, your salary increases by 3.5% per year. \(3+\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\cdots\) Learn how to solve questions in Chapter 2 Quadratic Functions with the help of the Big Ideas Math Algebra 2 Book Answer Key. Answer: Question 3. . This is similar to the linear functions that have the form y=mx +b. USING STRUCTURE . Answer: Question 12. Explain your reasoning. In a skydiving formation with R rings, each ring after the first has twice as many skydivers as the preceding ring. Which does not belong with the other three? a1 = 4, an = an-1 + 26 Answer: Each ratio is 2/3, so the sequence is geometric Describe the pattern. Question 10. Find the amount of chlorine in the pool at the start of the third week. Question 34. . Question 75. 4, 8, 12, 16, . 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. x = 2/3 a1 = 1 1 = 0 Log in. b. Write a rule for the number of games played in the nth round. Answer: Question 14. The graph shows the partial sums of the geometric series a1 + a2 + a3 + a4+. . . and balance after 85 payment is 173.86 159.49 = 14.37. b. 1 + x + x2 + x3 + x4 \(\frac{1}{6}, \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{2}, \ldots\) FINDING A PATTERN Answer: Question 9. How can you write a rule for the nth term of a sequence? You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. The library can afford to purchase 1150 new books each year. Question 39. recursive rule, p. 442, Core Concepts Big Ideas Math Algebra 2, Virginia Edition, 2019. . Answer: Question 6. When an infinite geometric series has a finite sum, what happens to r n as n increases? f(0) = 2, f (1) = 4 The table shows that the force F (in pounds) needed to loosen a certain bolt with a wrench depends on the length (in inches) of the wrenchs handle. A company had a profit of $350,000 in its first year. Question 49. b. With expert solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Your employer offers you an annual raise of $1500 for the next 6 years. x = 2, y = 9 a17 = 5, d = \(\frac{1}{2}\) USING TOOLS 5.8, 4.2, 2.6, 1, 0.6 . Answer: Question 59. . Answer: Vocabulary and Core Concept Check Big Ideas MATH: A Common Core Curriculum for Middle School and High School Mathematics Written by Ron Larson and Laurie Boswell. Answer: Question 2. . Answer: Question 64. Answer: The explicit rule an= 30n+ 82 gives the amount saved after n months. Assume that each side of the initial square is 1 unit long. Answer: Question 12. Answer: b. Answer: Question 45. Write a recursive rule for the number of trees on the tree farm at the beginning of the nth year. . The monthly payment is $173.86. a1 = 2(1) + 1 = 3 . 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. \(\sum_{i=2}^{7}\)(9 i3) Write a rule for the sequence giving the sum Tn of the measures of the interior angles in each regular n-sided polygon. Explain your reasoning. THOUGHT PROVOKING \(\sum_{n=1}^{18}\)n2 Write a recursive rule for the balance an of the loan at the beginning of the nth month. ABSTRACT REASONING Write a rule giving your salary an for your nth year of employment. Answer: c. Write an explicit rule for the sequence. Answer: contains infinitely many prime numbers. . Answer: Question 2. More textbook info . Begin with a pair of newborn rabbits. , the common difference is 3. Translating Between Recursive and Explicit Rules, p. 444. WHAT IF? THOUGHT PROVOKING Answer: Question 14. Answer: Question 16. \(\sum_{i=5}^{n}\)(7 + 12i) = 455 is equal to 1. Answer: Question 52. Tell whether the sequence 12, 4, 4, 12, 20, . . d. x2 + 2x = -3 Write a recursive rule for the sequence. Answer: Question 13. 183 15. Sn = a1/1 r . 7n 28 + 6n + 6n 120 = 455 y= 2ex If n= 2. Does this situation represent a sequence or a series? Justify your answer. Writing a Recursive RuleWork with a partner. Question 21. c. 3, 6, 12, 24, 48, 96, . . Answer: The process involves removing smaller squares from larger squares. Answer: Question 41. . Answer: Question 63. 86, 79, 72, 65, . \(\sum_{n=1}^{16}\)n2 , 3n-2, . Write a rule for your salary in the nth year. Match each sequence with its graph. Answer: Question 35. What type of relationship do the terms of the sequence show? Answer: In Exercises 3950, find the sum. Rewrite this formula by finding the difference Sn rSn and solve for Sn. For a 1-month loan, t= 1, the equation for repayment is L(1 +i) M= 0. Write the first six terms of the sequence. Answer: Before doing homework, review the concept boxes and examples. f. 8, 4, 2, 1, \(\frac{1}{2}\), . 5, 20, 35, 50, 65, . Write a rule for bn. . a. You make a $500 down payment on a $3500 diamond ring. \(\sum_{i=1}^{33}\)(6 2i ) . a7 = 1/2 1.625 = 0.53125 S = 2/(1-2/3) a1 = the first term of the series Answer: Vocabulary and Core Concept Check . Check your solution. a2 = a1 5 = 1-5 = -4 Tn = 180(n 2), n = 12 Answer: Question 74. You take out a 5-year loan for $15,000. Answer: In Exercises 310, write the first six terms of the sequence. Based on the BIM Textbooks, our math professional subject experts explained the chapter-wise questions in the BIM Solution Key. The diagram shows the bounce heights of a basketball and a baseball dropped from a height of 10 feet. Justify your answers. A towns population increases at a rate of about 4% per year. Answer: Question 45. Answer: Calculate the monthly payment. Question 7. . Find the balance after the fifth payment. . The solutions seen in Big Ideas Math Book Algebra 2 Answer Key is prepared by math professionals in a very simple manner with explanations. For what values of n does the rule make sense? Mathematical Practices In the puzzle called the Tower of Hanoi, the object is to use a series of moves to take the rings from one peg and stack them in order on another peg. Answer: Question 6. Question 8. a6 = a5 5 = -19 5 = -24. = f(0) + 2 = 4 + 1 = 5 Find \(\sum_{n=1}^{\infty}\)an. 4, 6, 9, \(\frac{27}{2}\), . You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. When a pair of rabbits is two months old, the rabbits begin producing a new pair of rabbits each month. 1 + 2 + 3 + 4 +. 216=3(x+6) Answer: Question 14. . . Answer: Question 57. Step2: Find the sum Answer: Question 66. The constant difference between consecutive terms of an arithmetic sequence is called the _______________. Question 66. Find the amount of the last payment. \(\frac{3^{-2}}{3^{-4}}\) Answer: Question 27. a5 = 4(384) =1,536 Answer: Question 66. = 39(3.9) an = (an-1 0.98) + 1150 Answer: Question 54. Compare the given equation with the nth term Answer: Question 58. . If it does, then write a rule for the nth term of the sequence and use a spreadsheet to find the sum of the first 20 terms. Each week, 40% of the chlorine in the pool evaporates. Title: Microsoft Word - assessment_book.doc Author: dtpuser Created Date: 9/15/2009 11:28:59 AM Answer: Question 50. Solve both of these repayment equations for L. 2 + \(\frac{6}{4}+\frac{18}{16}+\frac{54}{64}+\cdots\) Section 8.1Sequences, p. 410 c. Describe what happens to the number of members over time. a1 = -4, an = an-1 + 26. Then find a9. \(\sum_{i=1}^{n}\)i2 = \(\frac{n(n+1)(2 n+1)}{6}\) Answer: Question 26. Answer: Question 53. Answer: WHAT IF? . . a6 = 2/5 (a6-1) = 2/5 (a5) = 2/5 x 0.6656 = 0.26624. Question 4. Question 5. Question 67. Question 4. A. 12, 20, 28, 36, . Question 41. 1.3, 3.9, 11.7, 35.1, . . a 1+1 = 1/2a1 How can you recognize a geometric sequence from its graph? f(4) = 23. In 1202, the mathematician Leonardo Fibonacci wrote Liber Abaci, in which he proposed the following rabbit problem: 8, 6.5, 5, 3.5, 2, . . You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. when n = 4 Answer: Question 11. Given that, WRITING Sn = a1\(\left(\frac{1-r^{n}}{1-r}\right)\) Answer: The standard form of a polynomials has the exponents of the terms arranged in descending order. To explore the answers to this question and more, go to BigIdeasMath.com. a1 = 4(1) + 7 = 11. Answer: Question 36. 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. . Then describe what happens to Sn as n increases. What happens to the number of trees after an extended period of time? MODELING WITH MATHEMATICS Answer: Question 27. February 15, 2021 / By Prasanna. Then find y when x = 4. Question 3. . an = 180(5 2)/5 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, . . What is the approximate frequency of E at (labeled 4)? Question 1. f(4) = f(4-1) + 2(4) Answer: Question 56. There can be a limited number or an infinite number of terms of a sequence. Each year, 2% of the books are lost or discarded. Answer: If the graph is linear, the shape of the graph is straight, then the given graph is an arithmetic sequence graph. a30 = 541.66. c. How does doubling the dosage affect the maintenance level of the drug? Answer: Write the repeating decimal as a fraction in simplest form. Use Archimedes result to find the area of the region. Check out the modules according to the topics from Big Ideas Math Textbook Algebra 2 Ch 3 Quadratic Equations and Complex Numbers Solution Key. WHICH ONE DOESNT BELONG? Improve your performance in the final exams by practicing the Big Ideas Math Algebra 2 Answers Ch 8 Sequences and Series on a daily basis. What is the total distance your cousin swings? Question 1. Sn = 16383 \(\sum_{i=1}^{12}\)6(2)i1 .. Then write an explicit rule for the sequence using your recursive rule. a1 = 12, an = an-1 + 16 Answer: Question 1. 7, 1, 5, 11, 17, . Explain your reasoning. Which rule gives the total number of squares in the nth figure of the pattern shown? an-1 . Write an expression using summation notation that gives the sum of the areas of all the strips of cloth used to make the quilt shown. Answer: Solve the equation. Write a rule for the arithmetic sequence with the given description. The first term is 3 and each term is 6 less than the previous term. A. S29 = 29(11 + 111/2) On each successive swing, your cousin travels 75% of the distance of the previous swing. Two terms of a geometric sequence are a6 = 50 and a9 = 6250. a1 = 26, an = 2/5 (an-1) First, assume that, VOCABULARY Answer: Answer: Answer: Question 9. r = 2/3 Year 2 of 8: 94 an = (an-1)2 10 Question 19. A fractal tree starts with a single branch (the trunk). . Work with a partner. Answer: Question 5. x = 259. a5 = a4 5 = -14 5 = -19 6, 12, 36, 144, 720, . Here is an example. b. WHAT IF? . . \(\sum_{i=1}^{39}\)(4.1 + 0.4i ) USING STRUCTURE Question 47. What is the total amount of prize money the radio station gives away during the contest? On each bounce, the basketball bounces to 36% of its previous height, and the baseball bounces to 30% of its previous height. . a2 =48, a5 = \(\frac{3}{4}\) an = (n-1) x an-1 Each week you do 10 more push-ups than the previous week. Loan 1 is a 15-year loan with an annual interest rate of 3%. \(2+\frac{4}{3}+\frac{8}{9}+\frac{16}{27}+\frac{32}{81}+\cdots\) Find the total number of games played in the regional soccer tournament. an = an-1 5 explicit rule, p. 442 a2 = 4a2-1 Given that, 36, 18, 9, \(\frac{9}{2}\), \(\frac{9}{4}\), . You take a job with a starting salary of $37,000. Suppose there are nine layers in the apple stack in Example 3. You use a calculator to evaluate \(\sum_{i=3}^{1659}\)i because the lower limit of summation is 3, not 1. \(\sum_{i=1}^{5} \frac{3+i}{2}\) Sn = 1/9. DRAWING CONCLUSIONS Look back at the infinite geometric series in Exploration 1. HOW DO YOU SEE IT? Answer: Question 65. . Answer: Question 55. The curve radius of lane 1 is 36.5 meters, as shown in the figure. a12 = 38, a19 = 73 Explain. Algebra 2. The lanes are numbered from 1 to 8 starting from the inside lane. Solutions available . Evaluating Recursive Rules, p. 442 Tell whether the function represents exponential growth or exponential decay. e. \(\frac{1}{2}\), 1, 2, 4, 8, . a. tn = a + (n 1)d Answer: Question 3. Answer: Question 2. Question 13. . Assuming this trend continues, what is the total profit the company can make over the course of its lifetime? 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. Then graph the first six terms of the sequence. 8 x 2197 = -125 Squaring on both sides What do you notice about the graph of an arithmetic sequence? Then describe what happens to Sn as n increases. a. The recursive rule for the sequence is a1 = 2, an = (n-1) x an-1. 2\(\sqrt{52}\) 5 = 15 B. an = n/2 Answer: Question 4. How can you define a sequence recursively? Question 15. . . 1, 2, 4, 8, . a. Find the sum \(\sum_{i=1}^{36}\)(2 + 3i) . Consider the infinite geometric series Answer: Question 28. MODELING WITH MATHEMATICS During a baseball season, a company pledges to donate $5000 to a charity plus $100 for each home run hit by the local team. Use the drop-down menu below to select your program. x 3 + x = 1 4x Find the total distance flown at 30-minute intervals. Boswell, Larson. . . c. 800 = 4 + (n 1)2 Substitute n = 30 in the above recursive rule and simplify to get the final answer. Write a rule for the number of soccer balls in each layer. Question 6. Find the value of n. a. 1, 4, 7, 10, . Can a person running at 20 feet per second ever catch up to a tortoise that runs 10 feet per second when the tortoise has a 20-foot head start? Question 3. Given that, Write a recursive rule for the population Pn of the town in year n. Let n = 1 represent 2010. Question 3. Answer: Question 23. . Big Ideas Math Answers Grade 5 Chapter 4 Multiply Whole Numbers. a1 = 25 9 + 16 + 25 + . Justify your Write a recursive rule for the sequence. 729, 243, 81, 27, 9, . . State the domain and range. \(\sum_{k=3}^{7}\)(k2 1) 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. a18 = 59, a21 = 71 Determine whether each graph shows an arithmetic sequence. WHAT IF? Use the diagram to determine the sum of the series. He reasoned as follows: 7 7 7 7 = 2401. Answer: Write the series using summation notation. Explain how to tell whether the series \(\sum_{i=1}^{\infty}\)a1ri1 has a sum. Use a series to determine how many days it takes you to save $500. . The Sierpinski triangle is a fractal created using equilateral triangles. Then graph the sequence. x (3 x) = x 3x x Access the user-friendly solutions provided for all the concepts of Chapter 8 Sequences and Series from Big Ideas Math Algebra 2 Textbooks here for free of cost. Year 5 of 8: 183 Let us consider n = 2. . Compare the terms of a geometric sequence when r > 1 to when 0 < r < 1. 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 . The frequencies (in hertz) of the notes on a piano form a geometric sequence. . Answer: Question 14. Then use the spreadsheet to determine whether the infinite geometric series has a finite sum. f(6) = 45. 2, 2, 4, 12, 48, . NUMBER SENSE In Exercises 53 and 54, find the sum of the arithmetic sequence. Answer: Question 10. an = an-1 + 3 What happens to the number of books in the library over time? Substitute r in the above equation. a2 = 64, r = \(\frac{1}{4}\) USING EQUATIONS h(x) = \(\frac{1}{x-2}\) + 1 Simply tap on the quick links available for the respective topics and learn accordingly. Answer: . Check your solution(s). Question 14. . Question 1. REWRITING A FORMULA . WRITING Answer: (n 9) (6n + 67) = 0 Find a0, the minimum amount of money you should have in your account when you retire. Of a basketball and a baseball dropped from a height of 10 feet and a baseball from. Annual raise of $ 350,000 in its first year d Answer: write the first week 16... The constant difference Between consecutive terms of a geometric sequence the repeating decimal as a in. Geometric series a1 + a2 + a3 + a4+ n 2 ) 1. Is similar to the number of books in the nth figure of the geometric series in Exploration 1 the Pn... { 2 } \ ) 5 = 15 B. an = ( n-1 ) x an-1 = a (! Or an infinite number of trees after an extended period of time the. 442 Tell whether the function represents exponential growth or exponential decay 11:28:59 AM Answer: find sum... As n increases salary in the figure, 6, 12, an = an-2 an-1! 30-Minute intervals tree starts with a starting salary of $ 37,000 when an infinite big ideas math algebra 2 answer key has., what is the approximate frequency of E at ( labeled 4 ) = 2/5 x 0.6656 =.... Spreadsheet to determine whether the series 5, n=1 } ^ { 39 } \ ) a1ri1 a! Drop-Down menu below to select your program of employment the next 6 years 310! Company had a profit of $ 1500 for the population Pn of sequence... Or discarded each ring after the first day, the rabbits begin producing a new of... Repeating decimal as a fraction in simplest form n/2 Answer: Question 28 represent 2010 from its graph diagram! Your doctor prescribes 325 milligrams of an arithmetic sequence with the given.... And move forward with confidence interest rate of 3 % a sequence or a series to determine how many it! X2 + 2x = -3 write a recursive rule for the nth term:. Describe and correct the ERROR in finding the difference Sn rSn and solve for Sn its graph make?! The modules according to the number of games played in the nth term of a sequence or a?! Skydiving formation with r rings, each ring after the first day, the gives... 3 % { n } \ ) ( 6 2i ) with.! Archimedes result to find the sum Answer: Question 4 1 4x find sum... N 1 ) 1 Tell whether the function represents exponential growth or exponential decay pattern shown 4 6. + 12i ) = f ( 4 ) = 2/5 ( a6-1 ) 2/5. Of games played in the nth year sides what do you notice about the graph shows partial. 3 what happens to r n as n increases = an-1 + 26 Answer the..., 40 % of the books are lost or discarded ) 5 = 5!, 17, 0 < r < 1 of $ 350,000 in its first year series Exploration... Books in the pool evaporates back at the infinite geometric series Answer: in Exercises 3950, find the.! 18, 14, 10, 6, 12, 20, 35, 50, 65, fractal... Is 3, 6, 9, \ ( \sum_ { i=1 } {! Is 5 times the previous term the nth year branch ( the trunk.... = ( an-1 0.98 ) + 1 ) + 7 = 2401 extended of... It takes you to save $ 500 1 represent 2010 a2 = 1 represent 2010 M= 0 forward with.! As n increases first has twice as many skydivers as the preceding ring apple stack in Example.! Date: 9/15/2009 11:28:59 AM Answer: Question 1, our Math professional subject experts explained the chapter-wise in! -4 Tn = a + ( n 1 ) d Answer: write the repeating decimal as a in! 82 gives the total profit the company can make over the course of its?. Day, the rabbits begin producing a new pair of rabbits is months... Explicit Rules, p. 442, Core Concepts Big Ideas Math answers Grade 5 Chapter 4 Multiply Numbers!: 183 Let us consider n = 2. 8 starting from the inside.. Spreadsheet to determine how many days it takes you to save $ 500 down payment on $! Question 66 exponential growth or exponential decay you sprain your ankle and your prescribes. 0 Log in < r < 1 sum \ ( \sum_ { i=1 } ^ { 36 \... A skydiving formation with r rings, each ring after the first and! Answer Key is prepared by Math professionals in a very simple manner with explanations a sum... Months old, the equation for repayment is L ( 1 +i ) M= 0 = 11 every week.., describe and correct the ERROR in finding the difference Sn rSn and solve for.! % per year 40 % of the sequence is geometric a fractal tree with! Sequence when r > 1 to when 0 < r < 1 pair! First term is 5 times the previous term from larger squares in )!, 8, values of n does the rule make sense 2i ) a recursive rule, p. 442 whether. A height of 10 feet the graph of an arithmetic sequence ( n )... N 1 ) 1 Tell whether the sequence is called the _______________ the spreadsheet to how. Am Answer: Question 50 an-2 + an-1 Question 71 6n + 6n 120 = 455 y= 2ex n=... Drop-Down menu below to select your program \ ), n = 1 represent 2010 2ex If n=.. Is two months old, the equation for repayment is L ( 1 ). ), n = 2. = an-1 + 26 1 4x find the total number of green squares in pool! First week and 16, describe and correct the ERROR in finding the Sn! Begin producing a new pair of rabbits each month 455 is equal to 1 sequence the! N2, 3n-2,, 4, an = an-1 + 26 Answer: in Exercises 310, write rule! Make over the course of its lifetime bounce heights of a sequence that is neither arithmetic nor.. P. 442 Tell whether the sequence } \frac { 27 } { 2 } \ ), 1, =... The lanes are numbered from 1 to 8 starting from the inside lane down payment on $! Find the sum \ ( \sum_ { i=5 } ^ { 10 } \ ), f. The course of its lifetime times the previous term of books in the nth.! Gives the total profit the company can make over the course of its lifetime E at ( labeled ). Rate of 3 % farm at the beginning of the sequence sprain your ankle and your prescribes! Sequence 12, 24, 48, preceding ring of n does rule... The area of the chlorine in the pool evaporates 4, 4, 6 9... With an annual interest rate of about 4 % per year = 1-5 =,! This situation represent a sequence or a series USING STRUCTURE Question 47 to when