College Algebra & Trigonometry, 2018a

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6.1. SEQUENCES 289 Finding a general or recursive definition for a sequence can be trickier than just writing out the terms. Common things to look for - Is this an alternating sequence? That is, do the terms bounce back and forth between positive and negative values. If so, then you will need to include (−1) n or (−1) n+1 in your general term. Example: {−1, 2, −3, 4, ...} a n =(−1) n (n) or a 1 = −1 a n =(−1)(a n−1 )+(−1) n Is there a common difference between the terms? If so, then the sequence behaves much like a linear function and will have a form similar to y = mx + b, where m is the common difference. Example: {5, 8, 11, 14, ...} a n =3n +2 or a 1 =5 a n = a n−1 +3
290 CHAPTER 6. SEQUENCES AND SERIES Is there a common multiplier? If so, then this should be a power function where a particular base is being raised to the power of n. Example: {3, 15, 75, 375, ...} a n =3∗ 5 n−1 or a 1 =3 a n =5∗ a n−1 Other patterns to look for are perfect squares and perfect cubes.
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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10 CHAPTER 1. ALGEBRA REVIEW Exampl
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88 CHAPTER 2. POLYNOMIAL AND RATION
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100 CHAPTER 2. POLYNOMIAL AND RATIO
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190 CHAPTER 4. FUNCTIONS by substit
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192 CHAPTER 4. FUNCTIONS 4.2 Domain
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194 CHAPTER 4. FUNCTIONS Exercises
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196 CHAPTER 4. FUNCTIONS 8) 12 10 8
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198 CHAPTER 4. FUNCTIONS We can use
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200 CHAPTER 4. FUNCTIONS 3) 20 16 1
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202 CHAPTER 4. FUNCTIONS Vertical S
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208 CHAPTER 4. FUNCTIONS Stretching
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214 CHAPTER 4. FUNCTIONS 3) Match e
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College Algebra & Trigonometry, 2018a

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