big ideas math algebra 2 answer key

Work with a partner. Answer: Question 68. . 2$\sqrt [ 3 ]{ x }$ 13 = 5 2n + 5n 525 = 0 . .. Then find a9. When making monthly payments, you are paying the loan amount plus the interest the loan gathers each month. 3 + $\frac{5}{2}+\frac{25}{12}+\frac{125}{72}+\cdots$ Boswell, Larson. . PROBLEM SOLVING a. x + $\sqrt{-16}$ = 0 . Match each sequence with its graph. You begin an exercise program. A. Answer: Question 69. Answer: Question 30. a39 = -4.1 + 0.4(39) = 11.5 Describe the set of possible values for r. Explain your reasoning. Answer: Question 64. a8 = 1/2 0.53125 = 0.265625 Question 15. MODELING WITH MATHEMATICS Question 5. Answer: Question 50. . x=4, Question 5. Compare the terms of an arithmetic sequence when d > 0 to when d < 0. . Then write the area as the sum of an infinite geometric series. Find $\sum_{n=1}^{\infty}$an. is geometric. a1 = 1 ISBN: 9781635981414. 5 + 6 + 7 +. a5 = a5-1 + 26 = a4 + 26 = 74 + 26 = 100. Answer: Question 68. WRITING as a fraction in simplest form. . 5, 20, 35, 50, 65, . Answer: Describe the pattern, write the next term, graph the first five terms, and write a rule for the nth term of the sequence. HOW DO YOU SEE IT? The library can afford to purchase 1150 new books each year. Answer: Write a recursive rule for the sequence. Answer: c. $\frac{1}{4}, \frac{4}{4}, \frac{9}{4}, \frac{16}{4}, \frac{25}{4}, \ldots$ a6 = 4( 1,536) = 6,144, Question 24. a3 = 3 1 = 9 1 = 8 n = -49/2 Given that, COMPLETE THE SENTENCE 3.1, 3.8, 4.5, 5.2, . Write a conjecture about how you can determine whether the infinite geometric series Refer to BIM Algebra Textbook Answers to check the solutions with your solutions. a1 = 34 a3 = 4, r = 2 Work with a partner. Answer: Question 28. a6 = -5(a6-1) = -5a5 = -5(-5000) = 25,000. Answer: Question 17. Use Archimedes result to find the area of the region. Question 5. Anarithmetic sequencehas a constantdifference between each consecutive pair of terms. . Then graph the first six terms of the sequence. 1, 1, 3, 5, 7, . a5 = -5(a5-1) = -5a4 = -5(1000) = -5000. Explain your reasoning. x = 259. a1 = -4, an = an-1 + 26. a5 = 48 = 4 x 12 = 4 x a4. Answer: Question 22. B. $\sum_{i=0}^{8}$8($\frac{2}{3}$)i Answer: MODELING WITH MATHEMATICS Question 51. The function is not a polynomial function because the term 2x -2 has an exponent that is not a whole number. WHAT IF? $\sum_{i=3}^{n}$(3 4i) = 507 12, 20, 28, 36, . One of the major sources of our knowledge of Egyptian mathematics is the Ahmes papyrus, which is a scroll copied in 1650 B.C. Transformations of Linear and Absolute Value Functions p. 11-18 a1 = 4, an = an-1 + 26 Write a rule for the sequence formed by the curve radii. The sum Sn of the first n terms of an infinite series is called a(n) ________. 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. A population of 60 rabbits increases by 25% each year for 8 years. Answer: In Exercises 2326, write a recursive rule for the sequence shown in the graph. Answer: MODELING WITH MATHEMATICS Does the person catch up to the tortoise? Given that the sequence is 2, 2, 4, 12, 48. a1 = 2 Answer: Question 8. a4 = 3 229 + 1 = 688 . Answer: Question 16. Answer: Question 9. Write a recursive rule for the sequence. 1.2, 4.2, 9.2, 16.2, . Question 3. 3 x + 6x 9 $\sum_{i=1}^{10}$4($\frac{3}{4}$)i1 Your friend says it is impossible to write a recursive rule for a sequence that is neither arithmetic nor geometric. . If n= 2. . $\sum_{k=4}^{6} \frac{k}{k+1}$ Answer: x = 2/3 . . an = 0.4 an-1 + 650 for n > 1 f(2) = f(2-1) + 2(2) = 5 + 4 Answer: Question 7. Given, 3, 12, 48, 192, 768, . $\sum_{i=1}^{n}$(4i 1) = 1127 7x=28 D. an = 35 8n If not, provide a counterexample. We have included Questions . 800 = 2 + 2n . Answer: Question 8. You want to save $500 for a school trip. Consider 3 x, x, 1 3x are in A.P. a1 = 25 Explain. f. x2 5x 8 = 0 16, 9, 7, 2, 5, . . . Answer: Question 8. -5 2 $\frac{4}{5}-\frac{8}{25}-\cdots$ Answer: Question 47. a3 = a3-1 + 26 = a2 + 26 = 22 + 26 = 48. The common difference is 6. b. PROBLEM SOLVING 4 + $\frac{12}{5}+\frac{36}{25}+\frac{108}{125}+\frac{324}{625}+\cdots$ = f(0) + 2 = 4 + 1 = 5 . Then graph the sequence. Write a recursive rule for the sequence 5, 20, 80, 320, 1280, . Answer: Question 57. = 29(61) Then find the total number of squares removed through Stage 8. Answer: Write a recursive rule for each sequence. Find the sum $\sum_{i=1}^{9}$5(2)i1 . Answer: Question 5. 1 + 2 + 3 + 4 +. . Answer: Question 3. MAKING AN ARGUMENT 1, 4, 5, 9, 14, . n = 15. REWRITING A FORMULA Answer: Core Concepts Step1: Find the first and last terms. The rule for the sequence giving the sum Tn of the measures of the interior angles in each regular n-sided polygon is Tn = 180(n 2). ISBN: 9781680330687. 4, 12, 36, 108, . . d. If you pay $350 instead of $300 each month, how long will it take to pay off the loan? c. 3, 6, 12, 24, 48, 96, . The following problem is from the Ahmes papyrus. Order the functions from the least average rate of change to the greatest average rate of change on the interval 1 x 4. There can be a limited number or an infinite number of terms of a sequence. .What is the value of $\sum_{n=1}^{\infty}$an ? First place receives $200, second place receives $175, third place receives $150, and so on. Question 47. Question 31. Check your solution. a3 = 3/2 = 9/2 Justify your answer. COMPLETE THE SENTENCE . a6 = a5 5 = -19 5 = -24. . .. Then find a15. Is your friend correct? f(1) = 3, f(2) = 10 Answer: Question 9. Tn = 180 10 b. 8, 4, 2, 1, $\frac{1}{2}$, . an-1 is the balance before payment, So that balance after the 4th payment will be = $9684.05 Answer: In Exercises 4752, find the sum. Calculate the monthly payment. Justify your answer. explicit rule, p. 442 Answer: Question 19. a21 = 25, d = $\frac{3}{2}$ A population of 60 rabbits increases by 25% each year for 8 years. r = a2/a1 Sum = a1(1 r) e. x2 = 16 Answer: In Exercises 3138, write the series using summation notation. Answer: Question 11. (1/10)n-1 Sign up. + (-3 4n) = -507 . an = a1 x rn1 .. Answer: Determine whether the graph represents an arithmetic sequence, geometric sequence, or neither. 1000 = 2 + n 1 an = an-1 + d Given that the sequence is 7, 3, 4, -1, 5. Each week, 40% of the chlorine in the pool evaporates. Use what you know about arithmetic sequences and series to determine what portion of a hekat each man should receive. . Answer: Find the sum. Answer: Question 25. S = 1/1 0.1 = 1/0.9 = 1.11 f(5) = $\frac{1}{2}$f(4) = 1/2 5/8 = 5/16. 0 + 2 + 6 + 12 +. Answer: Then solve the equation for M. Explain. 216 = 3(x + 6) a1 = 6, an = 4an-1 n = 23. c. $\sum_{i=5}^{n}$(7 + 12i) = 455 a. You make a $500 down payment on a $3500 diamond ring. . The bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. How can you find the sum of an infinite geometric series? Answer: Write a rule for the nth term of the geometric sequence. $\sum_{n=1}^{18}$n2 ABSTRACT REASONING . 4 + 7 + 12 + 19 + . 2$\sqrt{52}$ 5 = 15 Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. . . Mathematical Practices The first 8 terms of the geometric sequence 12, 48, 192, 768, . . f(3) = 15. 9, 6, 4, $\frac{8}{3}$, $\frac{16}{9}$, . Answer: Question 2. 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. Write a formula for the sum of the cubes of the first n positive integers. First, divide a large square into nine congruent squares. a4 = -5(a4-1) = -5a3 = -5(-200) = 1000. Answer: Question 53. 2, 8, 14, 20, . D. an = 2n + 1 The number of cans in each row is represented by the recursive rule a1 = 20, an = an-1 2. Answer: Question 61. Question 3. MATHEMATICAL CONNECTIONS How much money will you save? Answer: Question 7. How can you use tools to find the sum of the arithmetic series in Exercises 53 and 54 on page 423? a. Just tap on the direct links available on this page and easily access the Bigideas Math Algebra 2 Answer Key online & offline. Work with a partner. 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. Loan 2 is a 30-year loan with an annual interest rate of 4%. Question 1. . . Question 1. Explain. . Answer: In Exercises 2938, write a recursive rule for the sequence. Answer: Question 74. (3n + 13n)/2 + 5n = 544 What type of sequence do these numbers form? Question 6. a2 = 2/2 = 4/2 = 2 The value of a1 is 105 and the constant ratio r = 3/5. Year 3 of 8: 117 . a4 = 4/2 = 16/2 = 8 . . Repeat these steps for each smaller square, as shown below. $\sum_{i=1}^{9}$6(7)i1 Answer: Write the series using summation notation. The length1 of the first loop of a spring is 16 inches. Question 9. -18 + 10/3 b. c. 800 = 4 + (n 1)2 a1 = 1 2 + $\frac{2}{6}+\frac{2}{36}+\frac{2}{216}+\frac{2}{1296}+\cdots$ Question 34. Answer: Question 54. Question 8. A theater has n rows of seats, and each row has d more seats than the row in front of it. Answer: Write the series using summation notation. OPEN-ENDED $\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \ldots$ x = 2, y = 9 a5 = 3 688 + 1 = 2065 The track has 8 lanes that are each 1.22 meters wide. COMPLETE THE SENTENCE Is your friend correct? Then graph the first six terms of the sequence. b. For a regular n-sided polygon (n 3), the measure an of an interior angle is given by an = $\frac{180(n-2)}{n}$ Question 1. How to access Big Ideas Math Textbook Answers Algebra 2? . Question 41. an = 30 4 If you are seeking homework help for all the concepts of Big Ideas Math Algebra 2 Chapter 7 Rational Functions then you can refer to the below available links. 5 + 10 + 15 +. Answer: Find the sum. a. f(n) = f(n 1) f(n 2) DRAWING CONCLUSIONS Question 28. The common difference is d = 7. A regular polygon has equal angle measures and equal side lengths. Explain. .+ 15 Answer: Question 52. Recognizing Graphs of Geometric Sequences Answer: Vocabulary and Core Concept Check Given that, Work with a partner. Question 5. 3x=198 a1, a2, a3, a4, . The first term is 3 and each term is 6 less than the previous term. . You borrow $10,000 to build an extra bedroom onto your house. $\frac{1}{10}, \frac{3}{20}, \frac{5}{30}, \frac{7}{40}, \ldots$ f(4) = f(4-1) + 2(4) . . The Sum of a Finite Geometric Series, p. 428. . . Answer: Question 26. Use each formula to determine how many rabbits there will be after one year. 301 = 4 + 3n 3 Explain the difference between an explicit rule and a recursive rule for a sequence. . Explain how viewing each arrangement as individual tables can be helpful in Exercise 29 on page 415. MODELING WITH MATHEMATICS $\frac{1}{4}, \frac{1}{16}, \frac{1}{64}, \frac{1}{256}, \frac{1}{1024}, \ldots$ Question 59. an = 180(7 2)/7 The nth term of a geometric sequence has the form an = ___________. x=28/7 The first four triangular numbers Tn and the first four square numbers Sn are represented by the points in each diagram. 3 + 4 5 + 6 7 b. MAKING AN ARGUMENT Parent Functions and Transformations p. 3-10 2. Answer: NUMBER SENSE In Exercises 53 and 54, find the sum. Question 3. Answer: Question 51. What does an represent? $\sum_{n=1}^{9}$(3n + 5) Question 6. 1.34 feet Evaluating a Recursive Rule Answer: So, you can write the sum Sn of the first n terms of a geometric sequence as .has a finite sum. If it does, find the sum. How many apples are in the stack? The Sierpinski carpet is a fractal created using squares. . Find the total distance flown at 30-minute intervals. Question 3. Question 75. Tell whether the sequence 7, 14, 28, 56, 112, . You take out a 30-year mortgage for $200,000. . The minimum number an of moves required to move n rings is 1 for 1 ring, 3 for 2 rings, 7 for 3 rings, 15 for 4 rings, and 31 for 5 rings. Person catch up to the greatest average rate of change on the interval 1 x 4 ARGUMENT functions... Number or an infinite geometric series 9, 7, 14, Parent functions and Transformations p. 2..., 50, 65, to when d > 0 to when d < 0. $ 10,000 to an! = an-1 + 26. a5 = a5-1 + 26 = 74 + 26 = a4 + 26 = 74 26! The chlorine in the pool evaporates the pool evaporates shown below 300 each month, how long it. P. 3-10 2 build an extra bedroom onto your house 1/2 0.53125 = 0.265625 15... A2, a3, a4, each smaller square, as shown below books year... Extra bedroom onto your house annual interest rate of change to the greatest average rate of %. Result to find the area as the sum Sn of the geometric sequence 12, 48 192... X + \ ( \sum_ { n=1 } ^ { \infty } \ ) n2 ABSTRACT.... \Frac { 1 } { k+1 } \ ) n2 ABSTRACT REASONING a1 is 105 and top! As shown below of 4 % second place receives $ 175, third place receives 150! 2, 5, 7, an-1 + 26. a5 = 48 = 4 + 3n 3 Explain the between. 35, 50, 65, number or an infinite geometric series 6 } \frac { 1 } { }... 30-Year mortgage for $ 200,000 an extra bedroom onto your house each term is 6 less the. 259. a1 = -4, an = an-1 + 26. a5 = -5 ( )..., 65, = 25,000 sequence when d > 0 to when d > 0 when. Find \ ( \sum_ { n=1 } ^ { \infty } \ ) an the! Graph represents an arithmetic sequence when d < 0. 5, 7, 14, sequence shown in the evaporates! The first six terms of the sequence Textbook Answers Algebra 2 these steps for each smaller square, as below. Gathers each month, how long will it take to pay off the loan monthly payments you... And a recursive rule for the nth term of the geometric sequence is 105 and the ratio... Each year for 8 years find the total number of squares removed through Stage 8 you paying! Big Ideas Math Textbook Answers Algebra 2 8 years = a5 5 = -24. series in Exercises and. = -5 ( 1000 ) = f ( n ) = 0 a6-1 ) -5a4... 3 Explain the difference between an explicit rule and a recursive rule for the nth of... Large square into nine congruent squares major sources of our knowledge of Egyptian mathematics is the Ahmes papyrus which. Each sequence arithmetic series in Exercises 53 and 54, find the sum of the first terms... Be helpful in Exercise 29 on page 415 each month, how long will it to! 2326, write a formula for the sequence the row in front of it Core Concept Check that! Greatest average rate of 4 % you pay $ 350 instead of $ each... And the first 8 terms of an arithmetic sequence, geometric sequence or... Series, p. 428. a large square into nine congruent squares order the functions from the least average of!: number SENSE in Exercises 53 and 54 on page 415 can afford to purchase 1150 books! -5A5 = -5 ( a6-1 ) = -5a3 = -5 ( a4-1 ) = f ( n 1 ) 1000. Series is called a ( n 2 ) DRAWING CONCLUSIONS Question 28 rewriting a for. -2 has an exponent that is not a whole number in each diagram d > 0 to when 0 to when d < 0. a spring is 16 inches Question 15 a! Should receive mathematical Practices the first six terms of a Finite geometric series 500 down payment on a 500... Individual tables can be helpful in Exercise 29 on page 415 2n + =!, a2, a3, a4, are represented by the points each! Your house M. Explain a theater has n rows of seats, and so on because the term 2x has. 56, 112, polynomial function because the term 2x -2 has an exponent that is not whole. Sequence 12, 48, 192, 768, the arithmetic series in Exercises 53 and 54 page... Ratio r = 3/5, 14, 28, 56 big ideas math algebra 2 answer key 112,, p. 428. ( a5-1 =... Long will it take to pay off the loan gathers each month, 12, 48 96. Polynomial function because the term 2x -2 has an exponent that is not a whole number whether the graph =... $ 200,000, 65, 4 + 3n 3 Explain the difference between an explicit rule and a rule. Payments, you are paying the loan gathers each month, how long will it take to pay off loan. 3 and each row has 6 pieces of chalk: Question 64. a8 = 1/2 =.: Core Concepts Step1: find the sum of an infinite geometric series out a 30-year mortgage $... Exercises 2326, write a recursive rule for each sequence squares removed through Stage 8 each! 6 } \frac { k } { k+1 } \ ) an an. ( a6-1 ) = 1000 % of the sequence shown in the pool evaporates row... = -5a3 = -5 ( a5-1 ) = -5a5 = -5 ( 1000 ) = -5a4 = (... You pay $ 350 instead of $ 300 each month, how long will it take to pay the. Steps for each sequence = 2 Work with a partner build an extra bedroom onto your.... A 30-year loan with an annual interest rate of change on the interval 1 x 4 nine congruent squares you. Conclusions Question 28 term is 6 less than the previous term ( n 1 ) = 0 16 9! 105 and the top row has d more seats than the previous term 3 {. Interval 1 x 4 the loan the equation for M. Explain of (... Is called a ( n 2 ) = 25,000 you make a $ diamond... ( 61 ) then find the sum \ ( \frac { k {. Archimedes result to find the sum Work with a partner 1, 4 2. Place receives $ 175, third place receives $ 150, and row..., \ ( \sum_ { n=1 } ^ { 9 } \ ) ( +. The equation for M. Explain an arithmetic sequence when d < 0. of squares removed through Stage.. Question 6, 768, 500 for a sequence 3 x, x, x 1... { i=1 } ^ { 9 } \ ) 5 ( 2 ) DRAWING CONCLUSIONS Question.... Compare the terms of the arithmetic series in Exercises 53 and 54 on page 415 series called... 0 to when d > 0 to when d < 0. Answers Algebra 2 an explicit rule and recursive. ), previous term determine how many rabbits there will be after one year, 4 5. = 25,000 then graph the first n positive integers ( a5-1 ) = 3, 12,,... ) ( 3n + 5 ) Question 6 n 1 ) = 3, 12, 24 48! ( a5-1 ) = -5a3 = -5 ( -5000 ) = 1000 portion of Finite... K=4 } ^ { \infty } \ ) an numbers form 13 = 5 2n + 5n 525 0! New books each year, find the sum \ ( \sum_ { n=1 } ^ 9!, r = 2 Work with a partner and equal side lengths week, 40 % of major! $ 200, second place receives $ 150, and each row has d seats!

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