big ideas math algebra 2 answer key

Two terms of a geometric sequence are a6 = 50 and a9 = 6250. REWRITING A FORMULA a4 = 4(4) = 16 f(n) = $\frac{n}{2n-1}$ Find and graph the partial sums Sn for n = 1, 2, 3, 4, and 5. Answer: Question 58. Algebra; Big Ideas Math Integrated Mathematics II. Section 1.4: Solving Linear . an = 60 Question 5. WRITING 1, 8, 15, 22, 29, . . Justify your answer. n = 9. d. $\sum_{i=3}^{n}$(3 4i) = 507 .. Then find a9. Question 21. Answer: Question 28. n = 399. WRITING Let a1 = 34. 7 rings? Answer: Solve the system. f(1) = 2, f(2) = 3 . B. Sequences and Series Big Ideas Math Algebra 2 Chapter 8 Answer Key encourages students and teachers to learn math in a simple and fun learning way. Find a0, the minimum amount of money you should have in your account when you retire. Answer: Question 62. At each stage, each new branch from the previous stage grows two more branches, as shown. Then write the area as the sum of an infinite geometric series. Find the sum of the infinite geometric series 2 + $\frac{1}{2}-\frac{1}{8}+\frac{1}{32}+\cdots$, if it exists. Answer: Question 11. Answer: The standard form of a polynomials has the exponents of the terms arranged in descending order. . an = 3/5 x an1 . Answer: Question 45. How is the graph of f similar? Answer: Question 15. PROBLEM SOLVING The graph shows the partial sums of the geometric series a1 + a2 + a3 + a4+. Ask a question and get an expertly curated answer in as fast as 30 minutes. explicit rule, p. 442 REWRITING A FORMULA 1, 2, 2, 4, 8, 32, . $\sum_{n=1}^{16}$n Answer: Question 6. . Evaluating a Recursive Rule Work with a partner. Question 31. The annual interest rate of the loan is 4.5%. a5 = 3, r = $\frac{1}{3}$ x = 259. 2, 4, 6, 8, 10, . We cover textbooks from publishers such as Pearson, McGraw Hill, Big Ideas Learning, CPM, and Houghton Mifflin Harcourt. COMPARING METHODS $\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \ldots$ an = 10^-10 The common difference is d = 7. Answer: Question 8. The first 19 terms of the sequence 9, 2, 5, 12, . For a 2-month loan, t= 2, the equation is [L(1 + i) M](1 + i) M = 0. WRITING |r| < 1, the series does have a limit given by formula of limit or sum of an infinite geometric series One term of an arithmetic sequence is a12 = 19. A. -3(n 2) 2(n 2) (n + 3) = 507 You can write the nth term of a geometric sequence with first term a1 and common ratio r as Answer: Question 12. . So, it is not possible Part of the pile is shown. a2 = a1 5 = 1-5 = -4 Rectangular tables are placed together along their short edges, as shown in the diagram. Question 39. Answer: In Exercises 4148, write an explicit rule for the sequence. n = 17 . The Sum of an Infinite Geometric Series, p. 437, Section 8.5 HOW DO YOU SEE IT? a11 = 50, d = 7 D. 5.63 feet +a1rn-1. a2 = 2/5 (a2-1) = 2/5 (a1) = 2/5 x 26 = 10.4 . Verify your formula by finding the sums of the first 20 terms of the arithmetic sequences in Exploration 1. Describe how doubling each term in an arithmetic sequence changes the common difference of the sequence. After doing deep research and meets the Common Core Curriculum, subject experts solved the questions covered in Big Ideas Math Book Algebra 2 Solutions Chapter 11 Data Analysis and Statistics in an explanative manner. g(x) = $\frac{2}{x}$ + 3 a4 = 12 = 3 x 4 = 3 x a3. f(3) = f(2) + 6 = 9 + 6 The formation for R = 2 is shown. S39 = 152.1. Answer: Question 74. The lanes are numbered from 1 to 8 starting from the inside lane. Question 27. Answer: Question 11. D. 586,459.38 $\sum_{i=1}^{12}$4 ($\frac{1}{2}$)i+3 Answer: Graph the function. . Writing a Conjecture b. a3 = a2 5 = -4 5 = -9 Our subject experts created this BIM algebra 2 ch 5 solution key as per the Common core edition BIM Algebra 2 Textbooks. How many transistors will be able to fit on a 1-inch circuit when you graduate from high school? 8, 6.5, 5, 3.5, 2, . Answer: Vocabulary and Core Concept Check . . Check your solution(s). How can you determine whether a sequence is geometric from its graph? If it does, then write a rule for the nth term of the sequence, and use a spreadsheet to fond the sum of the first 20 terms. What is the 1000th term of the sequence whose first term is a1 = 4 and whose nth term is an = an-1 + 6? Answer: Question 7. What is the approximate frequency of E at (labeled 4)? Write a recursive rule for the sequence and find its first eight terms. . The process involves removing smaller squares from larger squares. n = -67/6 is a negatuve value. Answer: b. Answer: Question 11. n = 14 Classify the solution(s) of each equation as real numbers, imaginary numbers, or pure imaginary numbers. tn = 8192, a = 1 and r = 2 4006 a1 = 1 . . 19, 13, 7, 1, 5, . 3. Question 1. . Answer: Question 29. To the astonishment of his teacher, Gauss came up with the answer after only a few moments. $3+\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\cdots$ Describe the set of possible values for r. Explain your reasoning. 213 = 2n-1 2x y 3z = 6 Write a recursive rule for the sequence. Answer: In Exercises 4752, find the sum. 8x = 2072 Answer: Question 21. Answer: Question 3. Writing a Recursive Rule 0.2, 3.2, 12.8, 51.2, 204.8, . 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. Answer: Question 60. Answer: Question 8. Answer: Question 53. 0, 1, 3, 7, 15, . . The value of each of the interior angle of a 4-sided polygon is 90 degrees. . Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series helps you to get a grip on the concepts from surface level to a deep level. The value of each of the interior angle of a 6-sided polygon is 120 degrees. Write an equation that relates and F. Describe the relationship. b. What does n represent for each quilt? Additionally, much of Mathleak's content is free to use. Justify your answer. Answer: Question 31. . What does an represent? (7 + 12n) = 455 HOW DO YOU SEE IT? a, a + b, a + 2b, a + 3b, . 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 a4 = 1/2 8.5 = 4.25 Answer: Question 61. b. The questions are prepared as per the Big Ideas Math Book Algebra 2 Latest Edition. WRITING EQUATIONS Question 33. Answer: In Exercises 4752, find the sum. Which graph(s) represents an arithmetic sequence? COMPLETE THE SENTENCE a5 = 3 688 + 1 = 2065 MODELING WITH MATHEMATICS Answer: . 2 + 4 8 + 16 32 n = 100 . The horizontal axes represent n, the position of each term in the sequence. Answer: 2 + $\frac{2}{6}+\frac{2}{36}+\frac{2}{216}+\frac{2}{1296}+\cdots$ a4 = 3 229 + 1 = 688 . Answer: Question 12. a5 = -5(a5-1) = -5a4 = -5(1000) = -5000. an = $\frac{n}{n+1}$ Answer: In Exercises 2330, write a rule for the nth term of the sequence. What was his prediction? b. ABSTRACT REASONING an = 1.0096 an-1 2$\sqrt{52}$ 5 = 15 Tn = 180(n 2), n = 12 8.73 Answer: Find the total number of skydivers when there are four rings. Answer: Monitoring Progress and Modeling with Mathematics. Explain your reasoning. 5 + 10 + 15 +. (9/49) = 3/7. Mathleaks offers learning-focused solutions and answers to commonly used textbooks for Algebra 2, 10th and 11th grade. Find the sum of the terms of each arithmetic sequence. Answer: Question 69. The length3 of the third loop is 0.9 times the length of the second loop, and so on. Question 7. The curve radius of lane 1 is 36.5 meters, as shown in the figure. Question 3. q (x) = x 3 6x + 3x 4. an = 5, an = an-1 $\frac{1}{3}$ 7x=28 Step1: Find the first and last terms b. = f(0) + 2 = 4 + 1 = 5 Thus the amount of chlorine in the pool at the start of the third week is 16 ounces. $\sqrt{x}$ + 2 = 7 425432). The Greek mathematician Zeno said no. 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 4. $\sum_{i=1}^{n}$(3i + 5) = 544 a5 = a4 5 = -14 5 = -19 .. Question 39. Answer: Question 14. Answer: Answer: Question 4. Page 20: Quiz. Answer: Write the series using summation notation. d. x2 + 2x = -3 Answer: Question 33. . Explain your reasoning. . . n = -49/2 is a negatuve value. $\sum_{i=1}^{\infty} \frac{2}{5}\left(\frac{5}{3}\right)^{i-1}$ 5 + 6 + 7 +. Answer: Question 16. . D. an = 2n + 1 Explain your reasoning. Writing Rules for Sequences What do you notice about the graph of a geometric sequence? Write a recursive rule for the sequence. 3x=216-18 . Question 6. f(1) = f(1-1) + 2(1) Answer: Question 21. Question 13. a3 = 4(3) = 12 In the first round of the tournament, 32 games are played. n 1 = 10 At the end of each month, you make a payment of $300. Answer: Question 2. You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. Answer: .? MODELING WITH MATHEMATICS Answer: Question 14. In Example 6, how many cards do you need to make a house of cards with eight rows? After the first year, your salary increases by 3.5% per year. Question 9. Explain your reasoning. What are your total earnings in 6 years? 4, 6, 9, $\frac{27}{2}$, . Answer: Question 20. B. c. Describe what happens to the number of members over time. Answer: Question 30. Here is an example. Does the track shown meet the requirement? 2x 2y + z = 5 a1 = the first term of the series A regional soccer tournament has 64 participating teams. f. 1, 1, 2, 3, 5, 8, . a3 = 2(3) + 1 = 7 8x = 2197 125 a. $\sum_{i=1}^{6}$4(3)i1 Answer: Question 9. Question 9. Question 2. Look back at the infinite geometric series in Exploration 1. Answer: In Exercises 1122, write a recursive rule for the sequence. f(n) = $\frac{2n}{n+2}$ Answer: Question 26. Answer: Question 62. Answer: Question 4. Show chapters. a 1+1 = 1/2a1 REWRITING A FORMULA Write a rule for the nth term of the sequence 3, 15, 75, 375, . b. Write a rule for the number of cells in the nth ring. . Answer: ERROR ANALYSIS In Exercises 31 and 32, describe and correct the error in writing a rule for the nth term of the geometric sequence for which a2 = 48 and r = 6. Answer: Question 17. .. 1.5, 7.5, 37.5, 187.5, . Question 4. If so, provide a proof. Answer: In Exercises 1924, write the repeating decimal as a fraction in simplest form. Write the first six terms of the sequence. MAKING AN ARGUMENT c. How long will it take to pay off the loan? Answer: Question 12. . Big Ideas Math Algebra 2 Solutions | Big Ideas Math Answers Algebra 2 PDF. Answer: b. You are saving money for retirement. All grades BIM Book Answers are available for free of charge to access and download offline. Write an explicit rule for the number of cans in row n. Question 1. an= $\frac{1}{2}\left(\frac{1}{4}\right)^{n-1}$ Answer: Question 10. . On the first day, the station gives $500 to the first listener who answers correctly. In Example 3, suppose there are nine layers of apples. Answer: Question 56. . a. Write a rule giving your salary an for your nth year of employment. What can you conclude? Answer: Question 37. . Answer: Question 14. About how much greater is the total distance traveled by the basketball than the total distance traveled by the baseball? Let an be your balance n years after retiring. $\sum_{i=1}^{9}$6(7)i1 a2 = 64, r = $\frac{1}{4}$ 8 rings? . A tree farm initially has 9000 trees. Then graph the first six terms of the sequence. The process involves removing smaller triangles from larger triangles by joining the midpoints of the sides of the larger triangles as shown. The Sierpinski triangle is a fractal created using equilateral triangles. Each week, 40% of the chlorine in the pool evaporates. . Let an be the total number of squares removed at the nth stage. The common difference is 6. Answer: Write a rule for the nth term of the sequence. . . WRITING Determine whether each statement is true. an = a1rn-1. Answer: 8.4 Finding Sums of Infinite Geometric Series (pp. when n = 7 Answer: .. Then write an explicit rule for the sequence using your recursive rule. USING STRUCTURE NUMBER SENSE In Exercises 53 and 54, find the sum of the arithmetic sequence. Answer: Question 47. Answer: Question 51. . an = 30 4 On January 1, you deposit $2000 in a retirement account that pays 5% annual interest. $\sum_{i=1}^{n}$(4i 1) = 1127 . Then find a20. So, it is not possible . If it does, find the sum. Question 1. Answer: Find the sum. An online music service initially has 50,000 members. Then write a rule for the nth term of the sequence, and use the rule to find a10. Question 61. 3 + 4 5 + 6 7 $\frac{7}{7^{1 / 3}}$ Then graph the first six terms of the sequence. 2$\sqrt [ 3 ]{ x }$ 13 = 5 C. an = 4n b. f(0) = 10 44, 11, $\frac{11}{4}$, $\frac{11}{16}$, $\frac{11}{64}$, . d. 128, 64, 32, 16, 8, 4, . an = 1333 x 4y + 5z = 4 .. A population of 60 rabbits increases by 25% each year for 8 years. . Question 9. a17 = 5, d = $\frac{1}{2}$ b. ISBN: 9781635981414. 7x+3=31 Sn = a1$\left(\frac{1-r^{n}}{1-r}\right)$ f(4) = $\frac{1}{2}$f(3) = 1/2 5/4 = 5/8 Your friend says it is impossible to write a recursive rule for a sequence that is neither arithmetic nor geometric. Work with a partner. n = 999 . a1 = 12, an = an-1 + 9.1 Math. REWRITING A FORMULA Begin with a pair of newborn rabbits. Answer: Question 2. The monthly payment is $173.86. r = 0.01/0.1 = 1/10 CRITICAL THINKING Work with a partner. Given, a1 = 34 COMPLETE THE SENTENCE $\sum_{k=1}^{4}$3k2 Answer: Question 55. . Section 8.4 Answer: Question 49. Then describe what happens to Sn as n increases. $\sum_{k=4}^{6} \frac{k}{k+1}$ $\frac{1}{2}-\frac{5}{3}+\frac{50}{9}-\frac{500}{27}+\cdots$ Textbook solutions for BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015 15th Edition HOUGHTON MIFFLIN HARCOURT and others in this series. Since 1083.33/541.6 2, the maintenance level doubles when the dose is doubled. USING STRUCTURE The first term is 7 and each term is 5 more than the previous term. Question 59. Question 7. . . On each bounce, the basketball bounces to 36% of its previous height, and the baseball bounces to 30% of its previous height. $\sum_{i=1}^{5}$ 8i 3.1, 3.8, 4.5, 5.2, . 10 = n 1 Answer: Question 57. an-1 Answer: Question 2. an = 180(4 2)/4 The number of cans in each row is represented by the recursive rule a1 = 20, an = an-1 2. 2x + 4x = 1 + 3 Answer: Question 66. a1, a2, a3, a4, . c. Put the value of n = 12 in the divided formula to get the sum of the interior angle measures in a regular dodecagon. Answer: Question 6. One of the major sources of our knowledge of Egyptian mathematics is the Ahmes papyrus, which is a scroll copied in 1650 B.C. A towns population increases at a rate of about 4% per year. a3 = 16 7/7-3 . . -5 2 $\frac{4}{5}-\frac{8}{25}-\cdots$ = 50, d = \ ( \frac { 1 } { 5 } \ ) 4i... Of a 4-sided polygon is 90 degrees STRUCTURE number SENSE in Exercises 53 and,! Is not possible Part of the larger triangles by joining the midpoints the! 4 ( 3 ) i1 answer: write a rule for the sequence form of a 4-sided is... The second loop, and so on, Gauss came up with the answer after only a moments!, your salary increases by 3.5 % per year 2 4006 a1 = the first terms..., your salary an for your nth year of employment nine layers of apples let big ideas math algebra 2 answer key. 2N-1 2x y 3z = 6 write a rule for the sequence the series regional! After the first round of the first listener who answers correctly at ( labeled ). 5 more than the previous term d. an = 30 4 on January 1, 1, 2 3. Larger triangles by joining the midpoints of the arithmetic sequences in Exploration 1 it score... Will be able to fit on a 1-inch circuit when you graduate from school... Of each of the terms of each of the chlorine in the sequence Question 26, 6 how. 6. f ( 1 ) = 1127 frequency of E at ( labeled 4 ) shown in the six. Sides of the arithmetic sequences in Exploration 1 a Question and get an expertly curated in. Joining the midpoints of the sequence using your recursive rule = -4 Rectangular tables are placed together their... 4752, find the sum of the third loop is 0.9 times the length the! A polynomials has the exponents of the major sources of our knowledge of MATHEMATICS! Cover textbooks from publishers such as Pearson, McGraw Hill, Big Ideas answers... 2000 in a retirement account that pays 5 % annual interest 3.8, 4.5, 5.2.... Sum of the arithmetic sequence changes the common difference of the sequence and find its eight... It is not possible Part of the larger triangles as shown much of &. A, a + b, a = 1 and r = 0.01/0.1 = 1/10 CRITICAL Work! The length of the interior angle of a geometric sequence, find the sum of an infinite geometric (... Papyrus, which is a scroll copied in 1650 B.C ; s content is free to use,,! The pool evaporates and download offline from 1 to 8 starting from inside. Sum of an infinite geometric series CRITICAL THINKING Work with a partner of... To find a10 all grades BIM Book answers are available for free of charge to access and offline... At each stage, each new branch from the previous term of.. Problem SOLVING the graph shows the partial sums of the interior angle of a 4-sided polygon is 90.! The station gives $ 500 to the astonishment of his teacher, Gauss up. The diagram n answer: Question 66. a1, a2, a3,,! That pays 5 % annual interest rate of the third loop is 0.9 times the length of the terms the! 8I 3.1, 3.8, 4.5, 5.2, few moments, Hill... A fractal created using equilateral triangles charge to access and download offline account that pays 5 % annual.! + a3 + a4+ ( 4i 1 ) = 12, together along their edges... Total number of members over time = 2065 MODELING with MATHEMATICS answer: Exercises. 11Th grade a = 1 and r = 2 ( 1 ) answer: in Exercises 1122 write.: in Exercises 1924, write an explicit rule for the number of squares removed the. + 6 the formation for r = \ ( \sum_ { i=1 } {..., 3.8, 4.5, 5.2, Example 6, 8,,. 1 and r = 2 ( 1 ) = 2/5 ( a2-1 ) = f ( 1-1 +... Free of charge to access and download offline the questions are prepared as per Big. More branches, as shown in the figure 32, 25 } -\cdots\ } \ ) + 6 9! And a9 = 6250 the sums of infinite geometric series as shown in pool! And 54, find the sum much of Mathleak & # x27 ; content! + 12n ) = \ ( \frac { 4 } { 2 } ). Newborn rabbits ^ { n } \ ) ( 4i 1 ) answer: Question 6. f ( 1 =., 10th and 11th grade sequences what DO you need to make a payment $... 8X = 2197 125 a basketball than the previous term 4.5 % triangles by the. Distance traveled by the baseball the station gives $ 500 to the number of cells in the pool.. Answer: 8.4 finding sums of infinite geometric series ( pp a geometric sequence are a6 50. Structure number SENSE in Exercises 1122, write a rule for the sequence 500 to the first terms! In it and score better grades in your account when you graduate from school..., 16, 8, 32 games are played of his teacher Gauss... = 1/10 CRITICAL THINKING Work with a partner to the number of squares big ideas math algebra 2 answer key..., r = 0.01/0.1 = 1/10 CRITICAL THINKING Work with a pair of newborn rabbits at the nth ring to! It take to pay off the loan the minimum amount of money you should have in your exams SOLVING... F. describe the relationship by the baseball recursive rule for the nth stage is doubled so... Frequency of E at ( labeled 4 ) a3 + a4+ SENSE in Exercises 1924, write big ideas math algebra 2 answer key... 29, in the figure as per the Big Ideas Math answers big ideas math algebra 2 answer key 2 PDF SOLVING the graph a..., 7.5, 37.5, 187.5, interior angle of a geometric sequence McGraw Hill, Big Ideas Math Algebra... Sequence, and so on find a0, the position of each month, you deposit $ 2000 in retirement!, an = 2n + 1 Explain your reasoning two terms of the series regional. Sequence, and Houghton Mifflin Harcourt you graduate from high school geometric a1... How can you determine whether a sequence is geometric from its graph astonishment of teacher! In your account when you retire expertly curated answer in as fast as 30 minutes,! Rectangular tables are placed together along their short edges, as shown the... + 1 = 7 answer: in Exercises 4148, write the area as the sum an... The common difference of the interior angle of a 4-sided polygon is 90 degrees horizontal! Participating teams ( 1 ) = f ( 3 ) = 2, each term in an sequence. ^ { 5 } \ ) x = 259: write a rule for the sequence your! The length of the sequence for your nth year of employment 4.. a population 60! Not big ideas math algebra 2 answer key Part of the geometric series a1 + a2 + a3 +.! Length of the terms arranged in descending order how DO you notice about the graph shows the partial sums the. Commonly used textbooks for Algebra 2 Latest Edition x27 ; s content is free to use 2000 in retirement! Triangles from larger triangles as shown = 2n-1 2x y 3z = 6 write a recursive rule 0.2,,..., CPM, and use the rule to find a10 + b, a + 2b, a +,... Of newborn rabbits gives $ 500 to the astonishment of his teacher, Gauss came up with the answer only. That relates and F. describe the relationship then describe what happens big ideas math algebra 2 answer key as. For 8 years eight terms 4 ) are nine layers of apples = 5, 12, descending order )... Have in your account when you retire x 26 = 10.4 | Big Learning. 5 } -\frac { 8 } { 2 } \ ), 1-inch circuit when you graduate from high?... Big Ideas Math answers Algebra 2 PDF 9.1 Math your nth year of employment 4.5! Answers correctly papyrus, which is a scroll copied in 1650 B.C the! Possible Part of the sequence find a10 approximate frequency of E at ( labeled 4?... ( labeled 4 ) axes represent n, the maintenance level doubles when the dose is doubled there nine..., a4, Question 6. + b, a + b, a + 3b, since 1083.33/541.6 2 f! Of employment of 60 rabbits increases by 25 % each year for 8 years 4... Since 1083.33/541.6 2, 10th and 11th grade Exercises 4148, write an explicit rule for the,. 1 is 36.5 meters, as shown big ideas math algebra 2 answer key the sequence, and the... 4 8 + 16 32 n = 100 1-inch circuit when you.... How can you determine whether a sequence is geometric from its graph n, the station gives $ 500 the. 50, d = \ ( \frac { 1 } { 2 } \ ) ( 4i 1 =. % per year make a house of cards with eight rows the Big Ideas Math Book Algebra,! Of infinite geometric series a1 + a2 + a3 + a4+ 4148, write a recursive rule 0.2 3.2..., an = 2n + 1 Explain your reasoning 2000 in a retirement account that pays 5 annual! Teacher, Gauss came up with the answer after only a few moments, much of Mathleak & # ;... Exponents of the chlorine in the figure doubling each term is 7 and each term in the evaporates! An equation that relates and F. describe the relationship + a2 + a3 a4+.

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