10-1 Sequences as Functions. Determine whether each sequence is arithmetic. Write yes or no , 3, 0, 3, 9
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1 Determine whether each sequence is arithmetic. Write yes or no , 3, 0, 3, 9 Find the next four terms of each arithmetic sequence. Then graph the sequence , 2, 6, 14, There is no common difference. Therefore, the sequence is not arithmetic. The common difference is 8. Therefore, this sequence is arithmetic. To find the next term, add 8 to the last term ( 8) = ( 8) = ( 8) = ( 8) = 46 The common difference is. Therefore, the sequence is arithmetic. esolutions Manual - Powered by Cognero Page 1
2 28. 19, 2, 15, 30. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term = = = = 83 The common difference is 1. Therefore, the sequence is arithmetic. To find the next term, add 1 to the last term. esolutions Manual - Powered by Cognero Page 2
3 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? b. On what day will Mario first row an hour or more? c. Is it reasonable for this pattern to continue indefinitely? Explain. a. Given a 1 = 5, d = 1.5 and n = 18. Find a 18. Determine whether each sequence is Write yes or no , 186, 248, Since the ratios are not the same, the sequence is not , 108, 72, Therefore he will row for 30 minutes and 30 seconds on the 38th day. b. Given a 1 = 5, d = 1.5 and a n = 60. Find n. Since the ratios are same, the sequence is 38. 4, 2, 0, 2, Mario will first row an hour or more on the 38th day. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be dedicated to rowing. Since the ratios are not same, the sequence is not esolutions Manual - Powered by Cognero Page 3
4 Find the next three terms of the sequence. Then graph the sequence , 12, 8, , 108, 144, Since the ratios are same, the sequence is geometric Since the ratios are same, the sequence is To find the next term, multiply the previous term by To find the next term, multiply the previous term by.. esolutions Manual - Powered by Cognero Page 4
5 44. 1, 0.1, 0.01, 0.001, Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning , 2, 5, 8, Since the ratios are same, the sequence is To find the next term, multiply the previous term by 0.1. Subtract each term from the term directly after it. The common difference is 3. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not esolutions Manual - Powered by Cognero Page 5
6 48. Subtract each term from the term directly after it. 52. DEPRECIATION Tammy s car is expected to depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? Substitute 0.15, 6 and for r, t and P in then evaluate. There is no common difference. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. The worth of the car will be about $9052 after 6 years. The common ratio is. Since the ratios are the same, the sequence is 50. 6, 9, 14, 21, 53. CCSS REGULARITY When a piece of paper is folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, how thick would it be? Given a 0 = 0.1, n = 37 and r = 2. Find a 37. Subtract each term from the term directly after it. The thickness would be about 13,744 km. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. Sample answer: The consecutive terms do not share a common difference. For instance, = 5, while = 4. Since the ratios are not same, the sequence is not esolutions Manual - Powered by Cognero Page 6
7 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8, is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is 42. Find the terms. Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. Sample answer: Neither; the sequence is both arithmetic and Sample answer: Let d = 5. Therefore, the terms are 3, 2, OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,. Sample answer: geometric: 3, 9, 27, 81, 243, arithmetic: 3, 9, 15, 21, 27, neither geometric nor arithmetic: 3, 9, 21, 45, 93,... esolutions Manual - Powered by Cognero Page 7
8 59. REASONING If a geometric sequence has a ratio r such that, what happens to the terms as n increases? What would happen to the terms if? 62. The pattern of filled circles and white circles below can be described by a relationship between two variables. Sample answer: If a geometric sequence has a ratio r such that, as n increases, the absolute value of the terms will decrease and approach zero because they are continuously being multiplied by a fraction. When, the absolute value of the terms will increase and approach infinity because they are continuously being multiplied by a value greater than WRITING IN MATH Describe what happens to the terms of a geometric sequence when the common ratio is doubled. What happens when it is halved? Explain your reasoning. Which rule relates w, the number of white circles, to f, the number of dark circles? A B C D Sample answer: When the value of r is doubled, a 2 doubles, a 3 quadruples, a 4 is multiplied by 8, a 5 is multiplied by 2 4 or 16, and so on. So, the new terms are. When the value of r is halved, the The relation between w and f is. Option C is the correct answer. new terms are. esolutions Manual - Powered by Cognero Page 8
9 64. Find the next term in the geometric sequence A B C D Find the common ratio. The common ratio is. The next term in the geometric sequence is. Therefore, option D is the correct answer. esolutions Manual - Powered by Cognero Page 9
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4-5 Graphing Other Trigonometric Functions
Locate the vertical asymptotes, and sketch the graph of each function. 1. y = 2 tan x 4. y = 3 tan 2. 5. 3. 6. y = tan 3x esolutions Manual - Powered by Cognero Page 1 7. y = 2 tan (6x π) 10. 8. 11. y
Interactive Study Guide Solving Two-Step Equations
11-1 To solve equations with more than one operation, or a two-step equation, follow the order of operations in reverse. First add or subtract then, multiply or divide. Solving Two-Step Equations Using
2-5 Dividing Integers
Find each quotient. 1. 40 ( 10) 2. 4 3 3. 26 ( 3) 4. 9 5. 48 3 6. 16 4 7. 36 ( 4) 8. 9 8 Evaluate each expression if s = 2 and t = 7. 9. 14s t 4 10. 35 11. 4t (2s) 7 12. Financial Literacy The following
Study Guide and Review - Chapter 12
Choose the correct term to complete each sentence. 1. The slope of a nonlinear graph at a specific point is the and can be represented by the slope of the tangent line to the graph at that point. The slope
0-8 Area. Find the area of each figure. 1. SOLUTION: The area of the rectangle is 6 square centimeters. 2. SOLUTION:
Find the area of each figure. 1. The area of the rectangle is 6 square centimeters. 2. The area of the square is 36 square inches. 3. The area of the parallelogram is 120 square meters. esolutions Manual
7-8 Using Exponential and Logarithmic Functions
1. PALEONTOLOGY The half-life of Potassium-40 is about 1.25 billion years. a. Determine the value of k and the equation of decay for Potassium-40. b. A specimen currently contains 36 milligrams of Potassium-40.
AQR Unit 4: Using Recursion in Models and Decision Making Sequence Notes. Name: Date: Sequences
Name: Date: Sequences A number sequence is a set of numbers, usually separated by commas, arranged in an order. The first term is referred to as t 1, the second term as t 2, the third term as t 3 and so
8-4 Special Products. Find each product. 1. (x + 5) 2 SOLUTION: 2. (11 a) 2 SOLUTION: 3. (2x + 7y) 2 SOLUTION: 4. (3m 4)(3m 4) SOLUTION:
Find each product. 1. (x + 5) 2 2. (11 a) 2 3. (2x + 7y) 2 4. (3m 4)(3m 4) 5. (g 4h)(g 4h) 6. (3c + 6d) 2 esolutions Manual - Powered by Cognero Page 1 7. GENETICS The color of a Labrador retriever s fur
6-3 Solving Linear Systems using Inverses and Cramer's Rule
1. Use an inverse matrix to solve each system of equations, if possible. (3, 2) 2. 3. ( 5, 4) 4. ( 1, 6) ( 4, 3) 5. ( 6, 7, 8) 6. (4, 9, 1) 7. no unique solution esolutions Manual - Powered by Cognero
Name Class Date. Geometric Sequences and Series Going Deeper. Writing Rules for a Geometric Sequence
Name Class Date 5-3 Geometric Sequences and Series Going Deeper Essential question: How can you write a rule for a geometric sequence and find the sum of a finite geometric series? In a geometric sequence,
13-2 Verifying Trigonometric Identities. CCSS PRECISION Verify that each equation is an identity. ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER:
CCSS PRECISION Verify that each equation is an identity. 4.. 5. 2. 3. 6. 7. MULTIPLE CHOICE Which expression can be used to form an identity with? A. B. C. D. D esolutions Manual - Powered by Cognero Page
SOLUTION: The domain of a square root function only includes values for which the radicand is nonnegative.
19. Graph each function. State the domain and range. 21. The domain of a square root function only includes values for which the radicand is nonnegative. esolutions Manual - Powered by Cognero Page 1 23.
SAMPLE. MODULE 1 Arithmetic and geometric sequences
C H A P T E R 9 MODULE 1 Arithmetic and geometric sequences What is an arithmetic sequence? What is a geometric sequence? How do we find the nth term of an arithmetic or geometric sequence? How do we find
Geometric Sequences and Series
12-2 OBJECTIVES Find the nth term and geometric means of a geometric sequence. Find the sum of n terms of a geometric series. Geometric Sequences and Series ACCOUNTING Bertha Blackwell is an accountant
Study Guide and Review - Chapter 7
Choose a word or term from the list above that best completes each statement or phrase. 1. A function of the form f (x) = b x where b > 1 is a(n) function. exponential growth 2. In x = b y, the variable
7-2 Division Properties of Exponents. Simplify each expression. Assume that no denominator equals zero. ANSWER: a 3 b 2 c 9.
2. Simplify each expression. Assume that no denominator equals zero. a 3 b 2 c 9 4. c 3 f 3 6. r 4 8. 10. nq 2 w 5 12. 1 14. 2rt 2 esolutions Manual - Powered by Cognero Page 1 16. 18. FINANCIAL LITERACY
ax + b < c ax + b c Graphing Inequalities:
An inequality is a statement that contains one or more of the following symbols. < is less than is less than or equal to > is greater than is greater than or equal to is not equal to An inequality can
Practice Test - Chapter 4
Find the value of x. Round to the nearest tenth, if necessary. 1. An acute angle measure and the length of the hypotenuse are given, so the sine function can be used to find the length of the side opposite.
8-5 Variation Functions. 1. If y varies directly as x and y = 12 when x = 8, find y when x = 14. ANSWER: 21
1. If y varies directly as x and y = 12 when x = 8, find y when x = 14. 21 2. Suppose y varies jointly as x and z. Find y when x = 9 and z = 3, if y = 50 when z is 5 and x is 10. 27 3. If y varies inversely
Intermediate Mathematics League of Eastern Massachusetts
Intermediate Mathematics League of Eastern Massachusetts Meet #4 February, 2002 Category 1 Mystery You may use a calculator today! 1. Margie had a 3-by-3-by-3 cube, a 4-by-4-by-4 cube, and a 5-by-5-by-5
Write an equation of the line that passes through the given point and has the given slope. 10. (3, 1), slope 2 ANSWER: y = 2x 5
Write an equation of the line that passes through the given point and has the given slope. 10. (3, 1), slope 2 y = 2x 5 11. ( 1, 4), slope 1 y = x + 3 12. (1, 0), slope 1 y = x 1 13. (7, 1), slope 8 y