# Recognizing Patterns

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 What is the common difference between successive terms in the sequence? 9, 2.5, -4, -10.5, -17, … -6.5 What is the common ratio between successive terms in the sequence? 1.5, 1.2, 0.96, 0.768, … 0.8 Which best describes the relationship between the successive terms in the sequence shown? 2.4, -4.8, 9.6, -19.2 The common ratio is -2.0. Which sequences are geometric? Check all that apply. -2.7, -9, -30, -100, … -1, 2.5, -6.25, 15.625, … 8, 0.8, 0.08, 0.008, … A sequence is defined recursively by the formula f(n + 1) = f(n) + 3 . The first term of the sequence is -4. What is the next term in the sequence? -1 A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)? 60 A sequence is defined recursively using the formula f(n + 1) = -0.5 f(n) . If the first term of the sequence is 120, what is f(5)? 7.5 A sequence is defined by the formula f(n + 1) = f(n) – 3. If f(4) = 22, what is f(1)? 31 A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula? -12, -18, -27, … Shaunta is developing a recursive formula to represent an arithmetic sequence in which 5 is added to each term to determine each successive term. Which formula could represent her sequence? f(n + 1) = f(n) + 5 Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1? f(n +1) = f(n) – 6 Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1? f(n + 1) = -0.5f(n) An electrician earns \$110 after his first hour of working for a client. His total pay based on the number of hours worked can be represented using the sequence shown. 110, 130, 150, 170, … Which recursive formula can be used to determine the total amount of money earned for each successive hour worked based on the amount of money currently earned? f(n + 1) = f(n) + 20 Martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. She earns interest on her initial deposit. The total amount of money in her savings account at the end of each year is represented by the sequence shown. 100, 105, 110.25, … Which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year? f(n + 1) = 1.05f(n) Zina spends 1.5 hours setting up her sewing machine and making one hat. The total amount of time spent making hats can be represented by the sequence below. 1.5, 2.25, 3.0, 3.75, … Which recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously? f(n + 1) = f(n) + 0.75 What is the common difference between successive terms in the sequence? 2, 8, 14, 20, 26, … 6 What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, -0.04, -0.14, … -0.1 What is the common ratio between successive terms in the sequence? 27, 9, 3, 1, 1/3,1/9 1/27, , … 1/3 What is the common ratio between successive terms in the sequence? 2, -4, 8, -16, 32, -64, … -2 A sequence is defined by the recursive function f(n + 1) = -10f(n). If f(1) = 1, what is f(3)? 100

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