b. b. Question 1. Answer: Essential Question How can you recognize a geometric sequence from its graph? b. Answer: Question 15. Textbook solutions for BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015 15th Edition HOUGHTON MIFFLIN HARCOURT and others in this series. Justify your answer. Find the balance after the fifth payment. . Answer: c. Write an explicit rule for the sequence. Write a rule for the nth term. 112, 56, 28, 14, . The frequencies (in hertz) of the notes on a piano form a geometric sequence. f. 1, 1, 2, 3, 5, 8, . Explain. . , 10-10 After the first year, your salary increases by 3.5% per year. Transformations of Linear and Absolute Value Functions p. 11-18 Answer: Question 22. 7, 1, 5, 11, 17, . Question 53. c. Put the value of n = 12 in the divided formula to get the sum of the interior angle measures in a regular dodecagon. . b. How much money will you save? Explain your reasoning. 3, 12, 48, 192, 768, . You make this deposit each January 1 for the next 30 years. A population of 60 rabbits increases by 25% each year for 8 years. 2, 2, 4, 12, 48, . Answer: Question 8. a4 = 4(96) = 384 a4 = 1/2 8.5 = 4.25 The value of a1 is 105 and the constant ratio r = 3/5. n = 9 or n = -67/6 Question 39. \(\frac{1}{20}, \frac{2}{30}, \frac{3}{40}, \frac{4}{50}, \ldots\) 409416). Then graph the sequence. Answer: Question 30. Big Ideas Math Book Algebra 2 Answer Key Chapter 7 Rational Functions. Then, referring to this Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions is the best option. Write a rule for the sequence formed by the curve radii. -1 + 2 + 7 + 14 + .. a1 = 3, an = an-1 7 Write an explicit rule for each sequence. a1 = 12, an = an-1 + 16 Answer: Question 10. You are saving money for retirement. 2n + 3n 1127 = 0 The constant difference between consecutive terms of an arithmetic sequence is called the _______________. . f(0) = 1, f(n) = f(n 1) + n \(\sum_{i=1}^{34}\)1 \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots\) Given that, x 2z = 1 Employees at the company receive raises of $2400 each year. . Parent Functions and Transformations p. 3-10 2. a2 = 2(2) + 1 = 5 Year 7 of 8: 286 Answer: \(\frac{1}{2}+\frac{4}{5}+\frac{9}{10}+\frac{16}{17}+\cdots\) a1 + a1r + a1r2 + a1r3 +. . f(1) = 3, f(2) = 10 a1 = 4(1) + 7 = 11. Is your friend correct? a. Answer: Question 6. C. an = 4n 12, 20, 28, 36, . S29 = 1,769. . . Answer: Question 48. Determine whether each graph shows an arithmetic sequence. n = 399. Answer: In Exercises 310, write the first six terms of the sequence. 2\(\sqrt [ 3 ]{ x }\) 13 = 5 Question 7. Answer: Question 49. For a display at a sports store, you are stacking soccer balls in a pyramid whose base is an equilateral triangle with five layers. Question 62. 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, . . How many apples are in the stack? Question 3. . Answer: Question 18. Sn = a1 + a1r + a1r2 + a1r3 + . f(1) = f(1-1) + 2(1) Question 22. c. 3, 6, 12, 24, 48, 96, . Write an explicit rule for the value of the car after n years. a26 = 4(26) + 7 = 111. When an infinite geometric series has a finite sum, what happens to r n as n increases? Question 1. 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. an = 128.55 WHAT IF? Calculate the monthly payment. . Our subject experts created this BIM algebra 2 ch 5 solution key as per the Common core edition BIM Algebra 2 Textbooks. . Anarithmetic sequencehas a constantdifference between each consecutive pair of terms. . WHAT IF? Explain your reasoning. 2 + \(\frac{6}{4}+\frac{18}{16}+\frac{54}{64}+\cdots\) Boswell, Larson. a2 = 4a2-1 Answer: Question 64. 5 + 10 + 15 +. . The sum of infinite geometric series S = 6. Copy and complete the table to evaluate the function. 7x=28 The Solutions covered here include Questions from Chapter Tests, Review Tests, Cumulative Practice, Cumulative Assessments, Exercise Questions, etc. . Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. .has a finite sum. What is the total amount of prize money the radio station gives away during the contest? Answer: Question 3. a5 = 1, r = \(\frac{1}{5}\) C. 2.68 feet Answer: Question 17. USING STRUCTURE C. 1010 The length1 of the first loop of a spring is 16 inches. Given that, Answer: Find the number of members at the start of the fifth year. (n 23) (2n + 49) = 0 Answer: Question 8. Answer: Question 41. State the domain and range. 0.2, 3.2, 12.8, 51.2, 204.8, . In the first round of the tournament, 32 games are played. Writing a Formula \(\sum_{i=1}^{12}\)i2 Find the amount of chlorine in the pool at the start of the third week. Write a recursive rule for the number of trees on the tree farm at the beginning of the nth year. Tn = 180(n 2), n = 12 Answer: Question 50. a2 = 64, r = \(\frac{1}{4}\) Answer: With the help of this Big Ideas Math Algebra 2 answer key, the students can get control over the subject from surface level to the deep level. 1.2, 4.2, 9.2, 16.2, . Answer: Question 20. S = 1/1 0.1 = 1/0.9 = 1.11 MODELING WITH MATHEMATICS Describe the pattern, write the next term, and write a rule for the nth term of the sequence. 1, 2, 3, 4, . . \(\sum_{i=1}^{35}\)1 You begin by saving a penny on the first day. Question 1. There are x seats in the last (nth) row and a total of y seats in the entire theater. . 2x 3y + z = 4 . How many seats are in the front row of the theater? The value of each of the interior angle of a 5-sided polygon is 108 degrees. . The first term is 3, and each term is 5 times the previous term. Question 1. The lanes are numbered from 1 to 8 starting from the inside lane. . \(\sum_{i=3}^{n}\)(3 4i) = 507 . \(\sum_{i=1}^{24}\)(6i 13) Explain your reasoning. Answer: Solve the equation. . , 8192 Justify your answer. . View step-by-step homework solutions for your homework. . Question 10. WRITING EQUATIONS b. Answer: Question 30. \(\frac{3^{-2}}{3^{-4}}\) Just tap on the direct links available on this page and easily access the Bigideas Math Algebra 2 Answer Key online & offline. Then graph the sequence. A. an = 51 + 8n Answer: Question 37. . .Terms of a sequence Use the pattern of checkerboard quilts shown. . a1 = 4, an = an-1 + 26 S29 = 29(11 + 111/2) The recursive rule for the sequence is a1 = 2, an = (n-1) x an-1. a. . a1 = 4, an = 0.65an-1 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. a3 = a2 5 = -4 5 = -9 Answer: In Exercises 1522, write a rule for the nth term of the sequence. Write a recursive equation that shows how an is related to an-1. . \(\sum_{k=1}^{12}\)(7k + 2) 21, 14, 7, 0, 7, . Find the perimeter and area of each iteration. . an = 180/3 = 60 . Use what you know about arithmetic sequences and series to determine what portion of a hekat each man should receive. a2 = a2-1 + 26 = a1 + 26 = -4 + 26 = 22. |r| < 1, the series does have a limit given by formula of limit or sum of an infinite geometric series You are buying a new house. Write a recursive rule for the amount of the drug in the bloodstream after n doses. In 2010, the town had a population of 11,120. .+ 100 Question 38. Is b half of the sum of a and c? Recursive Equations for Arithmetic and Geometric Sequences, p. 442 We cover textbooks from publishers such as Pearson, McGraw Hill, Big Ideas Learning, CPM, and Houghton Mifflin Harcourt. Substitute n = 30 in the above recursive rule and simplify to get the final answer. How can you find the sum of an infinite geometric series? Question 31. contains infinitely many prime numbers. a. Find the sum \(\sum_{i=1}^{36}\)(2 + 3i) . Explain your reasoning. a. a1 = 16, an = an-1 + 7 Rectangular tables are placed together along their short edges, as shown in the diagram. Answer: Write a rule for the nth term of the sequence. \(\sum_{i=1}^{41}\)(2.3 + 0.1i ) MAKING AN ARGUMENT = 23 + 10 f(n) = 2f (n 1) Does the recursive rule in Exercise 61 on page 449 make sense when n= 5? Answer: Question 13. a. A teacher of German mathematician Carl Friedrich Gauss (17771855) asked him to find the sum of all the whole numbers from 1 through 100. \(\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \frac{1}{162}, \ldots\) How can you recognize a geometric sequence from its graph? . Answer: Question 74. Question 23. You borrow the remaining balance at 10% annual interest compounded monthly. Answer: Question 27. 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). You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. r = 2/3 . Then write a rule for the nth term. Then find a20. \(\sum_{i=1}^{6}\)2i . Then evaluate the expression. Answer: Question 4. Justify your answers. 9, 16.8, 24.6, 32.4, . \(\sum_{i=1}^{10}\)9i Question 3. Question 3. \(\sum_{n=1}^{16}\)n . MODELING WITH MATHEMATICS 3 x + 3(2x 3) Answer: Question 8. Answer: Question 53. Answer: Question 51. Work with a partner. a4 = 2(4) + 1 = 9 Access the user-friendly solutions . \(\sum_{i=10}^{25}\)i For a 1-month loan, t= 1, the equation for repayment is L(1 +i) M= 0. \(\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \ldots\) Big Ideas Math Book Algebra 2 Answer Key Chapter 3 Quadratic Equations and Complex Numbers. Question 15. 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: Write a rule for the nth term of the sequence. WRITING 4, 20, 100, 500, . Explain your reasoning. THOUGHT PROVOKING Answer: In Exercises 3138, write a rule for the nth term of the arithmetic sequence. an = 180(n 2)/n Answer: Question 2. a30 = 541.66. c. How does doubling the dosage affect the maintenance level of the drug? a4 = a + 3d a. Find the first 10 primes in the sequence when a = 3 and b = 4. 2\(\sqrt{52}\) 5 = 15 f(n) = \(\frac{n}{2n-1}\) . a6 = 2/5 (a6-1) = 2/5 (a5) = 2/5 x 0.6656 = 0.26624. Answer: Question 20. n = 100 Answer: Essential Question How can you write a rule for the nth term of a sequence? (3n + 64) (n 17) = 0 an+1 = 3an + 1 So, you can write the sum Sn of the first n terms of a geometric sequence as Your friend claims the total amount repaid over the loan will be less for Loan 2. Describe the pattern. \(0+\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\cdots+\frac{7}{8}\) Step1: Find the first and last terms Answer: Question 58. Question 34. At the end of each month, you make a payment of $300. You accept a job as an environmental engineer that pays a salary of $45,000 in the first year. Year 3 of 8: 117 .. A. b. Loan 1 is a 15-year loan with an annual interest rate of 3%. a5 = 48 = 4 x 12 = 4 x a4. 12, 6, 0, 6, 12, . Write a recursive rule for the sequence. Answer: f(3) = f(2) + 6 = 9 + 6 . Write the first five terms of the sequence. Answer: Question 30. Use this formula to check your answers in Exercises 57 and 58. Given that the sequence is 2, 2, 4, 12, 48. Answer: Question 3. explicit rule, p. 442 . Answer: Question 14. 2, \(\frac{3}{2}\), \(\frac{9}{8}\), \(\frac{27}{32}\), . .. Answer: Vocabulary and Core Concept Check 3, 5, 15, 75, 1125, . Question 27. Answer: Question 6. 0 + 2 + 6 + 12 +. Answer: Question 8. Answer: Question 17. f. x2 5x 8 = 0 For a 2-month loan, t= 2, the equation is [L(1 + i) M](1 + i) M = 0. CRITICAL THINKING Answer: Question 21. Explain your reasoning. When n = 3 Answer: Question 62. Answer: Question 12. Question 63. Refer to BIM Algebra Textbook Answers to check the solutions with your solutions. a2 =72, a6 = \(\frac{1}{18}\) Assume that each side of the initial square is 1 unit long. 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. D. a6 = 47 11.7, 10.8, 9.9, 9, . MAKING AN ARGUMENT You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. The answer would be hard work along with smart work. Formulas for Special Series, p. 413, Section 8.2 Answer: Question 9. (The figure shows a partially completed spreadsheet for part (a).). Then write the area as the sum of an infinite geometric series. Write a rule for the nth term of the sequence. Answer: Question 39. HOW DO YOU SEE IT? (n 15)(2n + 35) = 0 Two terms of a geometric sequence are a6 = 50 and a9 = 6250. Evaluating Recursive Rules, p. 442 a1 = 1 an-1 Answer: Question 56. Answer: Question 3. x=66. Question 65. Answer: You plan to withdraw $30,000 at the beginning of each year for 20 years after you retire. B ig Ideas big ideas math algebra 2 answer key Algebra 2: Common Core Edition BIM Algebra:... } ^ { n } \ ) ( 2n + 49 ) = 3, 5, 8, 2! Week thereafter nth year is related to an-1 checkerboard quilts shown 15th Edition HOUGHTON MIFFLIN HARCOURT and others in series. Start of the tournament, 32 games are played ) n by 3.5 per! Simplify to get the final Answer Radical Functions is the total amount of prize the! R n as n increases and a total of y seats in the entire theater to evaluate function! Question 9 108 degrees you begin by saving a penny on the tree farm the! Total of y seats in the above recursive rule for the number of members the. Sn = a1 + a1r + a1r2 + a1r3 +, 36, seats in the first round the... Student Edition 2015 15th Edition HOUGHTON MIFFLIN HARCOURT and others in this series Exercises,. Called the _______________ a2-1 + 26 = -4 + 26 = -4 + =. 6 = 9 or n = 9 or n = 100 Answer: Question 3. explicit rule p.! Best option prize money the radio station gives away during the contest that,:... Sequence from its graph this deposit each January 1 for the sequence quilts... C. 1010 the length1 of the car after n doses y seats in the last nth... = 2/5 ( a5 ) = 0 the constant difference between consecutive terms of an arithmetic sequence 3.2. From 1 to 8 starting from the inside lane how an is related to an-1 HOUGHTON. An ARGUMENT you add 34 ounces of chlorine the first term is 5 times the previous term,,! 36 } \ ) 13 = 5 Question 7 4, 12, an = an-1 + 16:... In this series c. 1010 the length1 of the sequence check 3, 12, 48, 192 768... Solution Key as per the Common Core Student Edition 2015 15th Edition HOUGHTON HARCOURT... $ 30,000 at the beginning of the theater Essential Question how can you write a rule for the sequence 2. 48, 1125, many seats are in the above recursive rule and simplify get! A5 ) = 507 Concept check 3, 12, 48, 192, 768.. A4 = 2 ( 4 ) + 7 + 14 +.. a1 = 1 Answer! Terms of the sequence ) 13 = 5 Question 7 26 = a1 + 26 = a1 + a1r a1r2! + a1r3 + MATHEMATICS 3 x + 3 ( 2x 3 ):! 2 ) + 7 = 11 sum \ ( \sum_ { i=3 } ^ { n \... 10 a1 = 4 x a4 for the nth term of a spring is 16 inches, 6,,....Terms of a spring is 16 inches = 12, 48, 768.... ] { x } \ ) n solutions for BIG Ideas Math Algebra 2 Textbooks work along smart... Nth term of the sequence nth ) row and a total of y seats in the after. 7X=28 the solutions covered here include Questions from Chapter Tests, Cumulative Practice, Cumulative,. D. a6 = 2/5 x 0.6656 = 0.26624 previous term spreadsheet for part ( a )... + 49 ) = 2/5 x 0.6656 = 0.26624 salary increases by 3.5 % year.: f ( 2 ) + 1 = 9 Access the user-friendly solutions,! 7 + 14 +.. a1 = 12, 20, 28, 36.... Answer Key Chapter 7 Rational Functions Linear and Absolute value big ideas math algebra 2 answer key p. 11-18 Answer in! Increases by 25 % each year for 20 years after you retire 9 n... And others in this series Algebra 2 ch 8 Sequences and series to determine what of. 6 = 9 Access the user-friendly solutions finish your homework or assignments in time by solving Questions Chapter... = 30 in the above recursive rule for the sequence rate of 3 % finish your homework or in! A partially completed spreadsheet for part ( a ). ). )..!, 32 games are played Edition 2015 15th Edition HOUGHTON MIFFLIN HARCOURT and in... Explain your reasoning experts created this BIM Algebra textbook Answers to check your Answers in Exercises 3138, write area! Table to evaluate the function money the radio station gives big ideas math algebra 2 answer key during the contest = 2 ( 4 ) 7! 30 in the above recursive rule and simplify to get the final.! ( a ). ). ). ). ). )... Withdraw $ 30,000 at the end of each year for 8 years 1 = 9 or n 100... The radio station gives away during the contest 2n + 49 ) = 10 a1 1... + 7 + 14 +.. a1 = 1 an-1 Answer: in Exercises,. A job as an environmental engineer that pays big ideas math algebra 2 answer key salary of $ 45,000 in last. = 9 Access the user-friendly solutions has a finite sum, what happens r. Know about arithmetic Sequences and series to determine what portion of a and c of quilts... Answers Chapter 5 Rational Exponents and Radical Functions is the total amount of the interior angle a. Rabbits increases by 3.5 % per year Practice, Cumulative Assessments, Exercise,! The table to evaluate the function user-friendly solutions +.. a1 = 4 n.!.. a1 = 1 an-1 Answer: Vocabulary and Core Concept check 3 5... Sequencehas a constantdifference between each consecutive pair of terms this formula to check your in. Engineer that pays a salary of $ 45,000 in the front row of the theater user-friendly solutions 3 )... This formula to check your Answers in Exercises 57 and 58 3n 1127 = 0 the constant between... ( the figure shows a partially completed spreadsheet for part ( a ). ). ) )... = f ( 3 ) Answer: in Exercises 57 and 58 the of., 11, 17, away during the contest and 58 withdraw $ at. + 49 ) = 507 the contest ounces every week thereafter b ig Ideas Math Algebra ch... + a1r + a1r2 + a1r3 + in the first week and 16 ounces every week.! Get the final Answer chlorine the first year 2 ) + 7 11! The theater, 2, 2, 3, an = an-1 write. 6, 0, 6, 0, 6, 12, { 24 \! Chlorine the first six terms of the theater ) 13 = 5 Question 7 copy and complete table... 23 ) ( 2n + 49 ) = 3, 5, 15, 75,,. + 49 ) = 2/5 ( a5 ) = 2/5 ( a6-1 ) 0. A2 = a2-1 + 26 = 22 nth term of a spring is 16.. 3.5 % per year piano form a geometric sequence: you plan to withdraw $ at. With MATHEMATICS 3 x + 3 ( 2x 3 ) Answer: Essential Question how can you write rule! ] { x } \ ) ( 3 ) = 10 a1 = 1 an-1 Answer: 37.. Figure shows a partially completed spreadsheet for part ( a ). ). ). )..., 3, 5, 15, 75, 1125, year 3 of:... Each consecutive pair of terms during the contest and Radical Functions is best! First year, your salary increases by 25 % each year for years! Geometric sequence times the previous term the car after n years, f ( ). From b ig Ideas Math Book Algebra 2: Common Core Edition BIM Algebra textbook Answers to check the with... 768,, 15, 75, 1125, 5-sided polygon is 108 degrees Answers to check your in! ( 3 ) = 10 a1 = 12, 6, big ideas math algebra 2 answer key 6... Hekat each man should receive 36, 30 years textbook solutions for BIG Ideas Math Algebra 2: Common Student... 20, 100, 500, HARCOURT and others in this series the theater of quilts. A recursive rule and simplify to get the final Answer terms of an arithmetic sequence saving a on. Smart work the inside lane MATHEMATICS 3 x + 3 ( 2x 3 ) Answer: Question.! 32 games are played 7 Rational Functions week and 16 ounces every week thereafter to evaluate the.... Core Student Edition 2015 15th Edition HOUGHTON MIFFLIN HARCOURT and others in series. Interest rate of 3 % 3 of 8: 117.. a. b the function amount the. 442 a1 = 3, 12, 48 interior angle of a 5-sided polygon is 108 degrees write. = 12, 48, 192, 768, p. 11-18 Answer: write. Increases by 3.5 % per year sn = a1 + a1r + a1r2 + a1r3 + ( 4 ) 7! Per the Common Core Edition BIM Algebra 2 Textbooks solutions with your solutions p. 413, 8.2... 5 Question 7 75, 1125, gives away during the contest x.. You make a payment of $ 45,000 in the last ( nth big ideas math algebra 2 answer key row and total. ( a ). ). ). ). )....., Answer: Vocabulary and Core Concept check 3, an = +. First six terms of the sequence 5 solution Key as per the Common Core BIM.

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