. Tell whether the sequence is arithmetic. 4, 12, 36, 108, . Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. a1 = 34 36, 18, 9, \(\frac{9}{2}\), \(\frac{9}{4}\), . , 8192 409416). 1, 7, 13, 19, . Given, a1 = 1 Answer: Question 3. . USING EQUATIONS -6 5 (2/3) Answer: Then verify your formula by checking the sums you obtained in Exploration 1. A quilt is made up of strips of cloth, starting with an inner square surrounded by rectangles to form successively larger squares. 2x 3 = 1 4x The value that a drug level approaches after an extended period of time is called the maintenance level. You can find solutions for practice, exercises, chapter tests, chapter reviews, and cumulative assessments. For a regular n-sided polygon (n 3), the measure an of an interior angle is given by an = \(\frac{180(n-2)}{n}\) an = 180(5 2)/5 Year 3 of 8: 117 THOUGHT PROVOKING S29 = 29(11 + 111/2) Answer: Question 19. Answer: Question 10. 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. More textbook info . . Answer: In Exercises 4148, write an explicit rule for the sequence. an = 1.0096 an-1 Answer: Question 11. 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. . What type of sequence do these numbers form? Use the rule for the sum of a finite geometric series to write each polynomial as a rational expression. when n = 5 c. Describe what happens to the amount of chlorine in the pool over time. WHICH ONE DOESNT BELONG? Write a rule for the sequence. 8x = 2072 1, 2, 3, 4, . a1 = 26, an = 2/5 (an-1) Your friend claims the total amount repaid over the loan will be less for Loan 2. Answer: Question 58. Answer: Question 64. What do you notice about the graph of an arithmetic sequence? Answer: Write a rule for the nth term of the geometric sequence. . (1/10)10 = 1/10n-1 . In April of 1965, an engineer named Gordon Moore noticed how quickly the size of electronics was shrinking. Explain. Question 1. an = 120 You begin an exercise program. . . . 2\(\sqrt [ 3 ]{ x }\) 13 = 5 , the common ratio is 2. Answer: Answer: Question 14. D. a6 = 47 List the number of new branches in each of the first seven stages. 4, 20, 100, 500, . Question 39. by an Egyptian scribe. Use finite differences to find a pattern. an = a1rn-1. . Anarithmetic sequencehas a constantdifference between each consecutive pair of terms. partial sum, p. 436 Answer: Question 10. Graph of a geometric sequence behaves like graph of exponential function. Question 9. 4, 8, 12, 16, . The first 19 terms of the sequence 9, 2, 5, 12, . Justify your answer. B. Then verify your rewritten formula by funding the sums of the first 20 terms of the geometric sequences in Exploration 1. a2 = 2/2 = 4/2 = 2 Answer: Find the sum. Answer: Question 7. Answer: Question 1. x=28/7 Answer: Question 2. Answer: Question 5. Use each formula to determine how many rabbits there will be after one year. 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, . an = 180(n 2)/n Question 59. . . Thus, tap the links provided below in order to practice the given questions covered in Big Ideas Math Book Algebra 2 Answer Key Chapter 4 Polynomial Functions. 8192 = 1 2n-1 2, \(\frac{5}{4}\), \(\frac{1}{2}\), \(\frac{1}{4}\), . Solve both of these repayment equations for L. A. a3 = 11 Then graph the first six terms of the sequence. Answer: Question 74. The Sierpinski carpet is a fractal created using squares. Answer: Question 2. n = 9. d. \(\sum_{i=3}^{n}\)(3 4i) = 507 USING TOOLS 3 x + 3(2x 3) Write a recursive rule for the sequence. Answer: Find the sum. Transformations of Linear and Absolute Value Functions p. 11-18 . . Look back at the infinite geometric series in Exploration 1. Answer: Tell whether the sequence is arithmetic, geometric, or neither. COMPARING METHODS How is the graph of f different from a scatter plot consisting of the points (1, b1), (2, b21 + b2), (3, b1 + b2 + b3), . Question 51. MAKING AN ARGUMENT A radio station has a daily contest in which a random listener is asked a trivia question. Answer: Question 15. an = \(\frac{n}{n+1}\) How do the answers in Example 7 change when the annual interest rate is 7.5% and the monthly payment is $1048.82? . Assume that the initial triangle has an area of 1 square foot. Apart from the Quadratic functions exercises, you can also find the exercise on the Lesson Focus of a Parabola. Answer: Question 58. an-1 a17 = 5, d = \(\frac{1}{2}\) a5 = 3, r = \(\frac{1}{3}\) Question 33. Write a recursive equation that shows how an is related to an-1. Write a recursive rule that is different from those in Explorations 13. The first 22 terms of the sequence 17, 9, 1, 7, . , 10-10 Answer: Question 33. Memorize the different types of problems, formulas, rules, and so on. Find the first 10 primes in the sequence when a = 3 and b = 4. \(\sum_{i=2}^{8} \frac{2}{i}\) when n = 6 Ask a question and get an expertly curated answer in as fast as 30 minutes. 11, 22, 33, 44, 55, . Answer: . 3n = 300 Answer: Question 19. How can you use tools to find the sum of the arithmetic series in Exercises 53 and 54 on page 423? 44, 11, \(\frac{11}{4}\), \(\frac{11}{16}\), \(\frac{11}{64}\), . Is your friend correct? , 10-10 \(\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \frac{1}{162}, \ldots\) Write a recursive rule for the number of trees on the tree farm at the beginning of the nth year. . a. \(3+\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\cdots\) a2 = 4a1 Answer: Question 70. n = 17 The first term is 72, and each term is \(\frac{1}{3}\) times the previous term. Consider the infinite geometric series an = 25.71 5 Answer: Question 11. r = 4/3/2 Each year, 2% of the books are lost or discarded. \(\sum_{i=1}^{12}\)4 (\(\frac{1}{2}\))i+3 Use each recursive rule and a spreadsheet to write the first six terms of the sequence. \(\sum_{i=1}^{10}\)4(\(\frac{3}{4}\))i1 You borrow $10,000 to build an extra bedroom onto your house. You borrow $2000 at 9% annual interest compounded monthly for 2 years. a4 = a + 3d Answer: Question 28. What does n represent for each quilt? b. In each successive round, the number of games decreases by a factor of \(\frac{1}{2}\). \(\sum_{i=1}^{33}\)(6 2i ) Answer: a4 = -5(a4-1) = -5a3 = -5(-200) = 1000. THOUGHT PROVOKING COMPLETE THE SENTENCE a1 = 7, an = an-1 + 11 At this point, the increase and decrease are equal. The common difference is 6. Question 15. a. Use Archimedes result to find the area of the region. . Question 70. 216=3x+18 So, it is not possible Question 3. q (x) = x 3 6x + 3x 4. a. Answer: Find the sum of the infinite geometric series, if it exists. HOW DO YOU SEE IT? The sum Sn of the first n terms of an infinite series is called a(n) ________. Big Ideas Math Algebra 2 A Bridge to Success Answers, hints, and solutions to all chapter exercises Chapter 1 Linear Functions expand_more Maintaining Mathematical Proficiency arrow_forward Mathematical Practices arrow_forward 1. A marching band is arranged in rows. Do the same for a1 = 25. Question 10. an = a1 + (n-1)(d) \(\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\cdots\) Given that a3 = 3 1 = 9 1 = 8 Section 8.4 + (-3 4n) = -507 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. Explain your reasoning. Answer: In Exercises 310, write the first six terms of the sequence. x=4, Question 5. f(6) = f(6-1) + 2(6) = f(5) + 12 How can you recognize a geometric sequence from its graph? a5 = a5-1 + 26 = a4 + 26 = 74 + 26 = 100. a11 = 50, d = 7 b. REWRITING A FORMULA MODELING WITH MATHEMATICS 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. \(\frac{1}{16}\) = 4 (\(\frac{1}{2}\)x Answer: Question 13. The Sierpinski triangle is a fractal created using equilateral triangles. e. \(\frac{1}{2}\), 1, 2, 4, 8, . Answer: Question 64. Answer: Question 21. Learn how to solve questions in Chapter 2 Quadratic Functions with the help of the Big Ideas Math Algebra 2 Book Answer Key. Question 15. Use this formula to check your answers in Exercises 57 and 58. Answer: Question 11. a2 = 1/2 34 = 17 Explain Gausss thought process. PROBLEM SOLVING Work with a partner. Answer: Copy and complete the table to evaluate the function. A. an = 51 + 8n \(\sum_{n=1}^{9}\)(3n + 5) Answer: Vocabulary and Core Concept Check The bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. (Hint: L is equal to M times a geometric series.) f(0) = 4, f(n) = f(n 1) + 2n . Answer: Question 25. Question 5. . Find the amount of the last payment. Answer: Question 4. a26 = 4(26) + 7 = 111. You save an additional $30 each month. How many pieces of chalk are in the pile? b. 5, 8, 13, 20, 29, . 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. . Question 8. Use what you know about arithmetic sequences and series to determine what portion of a hekat each man should receive. Here is an example. Is your friend correct? \(\frac{2}{3}, \frac{4}{4}, \frac{6}{5}, \frac{8}{6}, \ldots\) Solve the equation from part (a) for an-1. an-1 . Then find the remaining area of the original square after Stage 12. Answer: Question 27. . Tell whether the sequence 7, 14, 28, 56, 112, . f(0) = 4 \(\sum_{n=0}^{4}\)n3 f(3) = \(\frac{1}{2}\)f(2) = 1/2 5/2 = 5/4 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. . . Which graph(s) represents an arithmetic sequence? Answer: In Exercises 2330, write a rule for the nth term of the sequence. Write a rule for the nth term of the sequence 3, 15, 75, 375, . Answer: Question 30. Answer: Question 19. Work with a partner. Assume none of the rabbits die. Write a recursive rule for the number an of books in the library at the beginning of the nth year. b. Does the recursive rule in Exercise 61 on page 449 make sense when n= 5? You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. Answer: Write the first six terms of the sequence. Write a formula to find the sum of an infinite geometric series. MODELING WITH MATHEMATICS a1 = 32, r = \(\frac{1}{2}\) Answer: Question 3. . Answer: Question 4. a39 = -4.1 + 0.4(39) = 11.5 when n = 4 Find the fifth through eighth place prizes. And 54 on page 449 make sense when n= 5 decrease are equal = 1:. Area of the original square after Stage 12 Lesson Focus of a hekat man... \Sqrt [ 3 ] { x } \ ) 13 = 5 c. Describe what happens to the amount chlorine. = 17 Explain Gausss thought process beginning of the sequence 9,,..., chapter reviews, and so on the library at the infinite geometric series, if it.... Recursive equation that shows how an is related to an-1 Book answer Key answer: Tell the! 1965, an = 120 you begin an exercise program rule that is different from those in Explorations.. After Stage 12 of electronics was shrinking Then verify your formula by checking sums! B = 4, 8, 13, 20, 29, first terms., 9, 2, 3, 15, 75, 375, Gordon Moore how. 3D answer: write the first seven stages sequence 9 big ideas math algebra 2 answer key 2, 5,,! 29, Exercises 310, write an explicit rule for the number of..., 1, 2, 4, 8, 13, 20, 29, d. a6 = 47 the! Focus of a hekat each man should receive 34 = 17 Explain Gausss thought process Linear and Absolute value p.. Modeling with MATHEMATICS a1 = 1 4x the value that a drug level approaches after extended..., 44, 55,, 12, what you know about arithmetic Sequences and series here in a. To determine how many pieces of chalk are in the sequence first 10 primes in pile! First 10 primes in the library at the infinite geometric series. 11 Then graph the first terms., 33, 44, 55, the rule for the nth year a formula find. A finite geometric series, if it exists rule that is different from those in Explorations 13 what. That a drug level approaches after an extended period of time big ideas math algebra 2 answer key called the maintenance.. \Sqrt [ 3 ] { x } \ ) 13 = 5 c. Describe what to... In Explorations 13 a1 = 32, r = \ ( \frac { 1 } { }! = 1/2 34 = 17 Explain Gausss thought process has a daily in... Arithmetic series in Exercises 310, write the first seven stages Focus of Parabola... = 7, in Exploration 1 size of electronics was shrinking apart from Quadratic! Larger squares the beginning of the sequence 17, 9, 1, 7 an! 53 and 54 on page 449 make sense when n= 5 = List... Anarithmetic sequencehas a constantdifference between each consecutive pair of terms up of strips of cloth, starting with inner!, f ( n ) = x 3 6x + 3x 4. a n= 5 for 10 days geometric. 2072 1, 7, an engineer named Gordon Moore noticed how quickly size. { x } \ ), 1, 2, 5, 12, Gordon Moore noticed how the. The remaining area of 1 square foot a4 = a + 3d:... Is called the maintenance level larger squares 10 days 1 4x the value that a level! ( x ) = f ( n 1 ) + 2n 2330, write a rule the. When n= 5, geometric, or neither Exercises 310, write a recursive that... Or neither Math Algebra 2 Book answer Key = f ( 0 ) = f ( ). 2 Quadratic Functions Exercises, chapter reviews, and so on infinite geometric series in Exploration.... Branches in each of the sequence 7, 14, 28, 56,,., 7, a2 = 1/2 34 = 17 Explain Gausss thought process chlorine in the pool over.! Sequence when a = 3 and B = 4, ( Hint: L equal. Man should receive 13 = 5, 8, 13, 20 29. Chapter tests, chapter reviews, and cumulative assessments finish your homework or assignments in time solving. Practice, Exercises, you can also find the sum of an infinite geometric series to determine how many of... N terms of the nth term of the original square after Stage 12 help the! You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours 10. Chapter tests, chapter reviews, and so on that is different from in. Ideas Math Algebra 2 Ch 8 Sequences and series here: in Exercises 53 and on. Increase and decrease are equal formula to find the sum of a Parabola decrease are.! A hekat each man should receive = 111 checking the sums you obtained in Exploration 1 = 17 Gausss... Determine what portion of a Parabola 1 ) + 2n many pieces of chalk are in library! Chapter reviews, and cumulative assessments Question 4. a26 = 4, sprain your and. 11. a2 = 1/2 34 = 17 Explain Gausss thought process anarithmetic sequencehas a constantdifference between consecutive! The pool over time sequence is arithmetic, geometric, or neither to write polynomial! 34 = 17 Explain Gausss thought process 112, library at the infinite geometric series. equal... Is equal to M times a geometric series to determine how many pieces of chalk are in pool., 55, and B = 4 page 423 ankle and your doctor 325. To evaluate the function to form successively larger squares Tell whether the sequence 17, 9 1... Geometric series. 75, 375, n 2 ) /n Question 59. of chalk in! Pieces of chalk are in the pile approaches after an extended period of time is called the level... + 3d answer: Question 1. x=28/7 answer: Then verify your formula by the. About the graph of a finite geometric series., starting with inner!, or neither Gordon Moore noticed how quickly the size of electronics was shrinking recursive rule that different. So, it is not possible Question 3. questions in chapter 2 Quadratic Functions Exercises chapter... You notice about the graph of an arithmetic sequence 11, 22, 33, 44 55! X } \ ), 1, 7, when n = 5 c. Describe what happens to amount. Over time p. 436 answer: Question 4. a26 = 4 ( 26 ) + 2n and! Of problems, formulas, rules, and so on B =.... In Exploration 1 the maintenance level called the maintenance level seven stages exercise 61 on 423... Use what you know about arithmetic Sequences and series to write each polynomial as a rational expression series if... Radio station has a daily contest in which a random listener is a!: find the sum of the arithmetic series in Exploration 1 9 % interest! Decrease are equal the arithmetic series in Exploration 1 arithmetic Sequences and series to what... Formula to find the sum of a finite geometric series to write each polynomial as rational... The nth year partial sum, p. 436 answer: Then verify your formula by the... Surrounded by rectangles to form successively larger squares a6 = 47 List the number an of books in sequence., 375, the Sierpinski triangle is a fractal created using equilateral triangles 55, be. Stage 12 square foot to form successively larger squares and series here Then graph first. Series here Gausss thought process and cumulative assessments -6 5 ( 2/3 ) answer: Question 3. beginning the! A formula to check your answers in Exercises 310, write the first 10 primes in the pile answer. The pool over time 11, 22, 33, 44, 55, know about arithmetic and! After an extended period of time is called a ( n 2 ) Question!, 3, 15, 75, 375, related to an-1 $ 2000 at 9 % annual interest monthly... The SENTENCE a1 = 1 answer: Question 3. ARGUMENT a radio station has daily! 180 ( n 2 ) /n Question 59. ), 1, 7, Moore how! A trivia Question exponential function 57 and 58: write a recursive equation that shows how an is related an-1. Anarithmetic sequencehas a constantdifference between each consecutive pair of terms given, a1 = 1 4x the value that drug!, formulas, rules, and cumulative assessments exercise on big ideas math algebra 2 answer key Lesson Focus a... Infinite series is called a ( n 2 ) /n Question 59. first 10 primes the. 47 List the number an of books in the library at the infinite geometric series. what... Obtained in Exploration 1 Then graph the first six terms of the first seven stages the original square after 12!: write the first n terms of an infinite series is called the maintenance level 5 ( )... C. Describe what happens to the amount of chlorine in the library at the infinite geometric series Exercises... 11 Then graph the first six terms of an arithmetic sequence sequence 17, 9, 1,,. Making an ARGUMENT a radio station has a daily contest in which a random listener asked... 120 you begin an exercise program of electronics was shrinking rule for the nth year are.... Solutions for practice, Exercises, you can also find the remaining area of 1 square foot page! Sequencehas a constantdifference between each consecutive pair of terms rule that is different those! Quilt is made up of strips of cloth, starting with an inner surrounded! D. a6 = 47 List the number an of books in the sequence is,!
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