Algebra 2  Arithmetic Sequence Practice Date: Period:


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1 Algebra 2  Arithmetic Sequence Practice Name: Date: Period: A sequence is an ordered list of numbers. In an arithmetic sequence, each term is equal to the previous term, plus (or minus) a constant. The constant is called the common difference (d). EXAMPLE: Given the sequence: 10, 14, 18, What type is it? What is the equation of this sequence? Find each of the following: The 20 th term How do you know? In this equation, 10 corresponds to what value of n? t(19) t(20) What is the value of the generator? t(21) Which are the same? And under what condition? PRACTICE: 1. How many integers (terms) are there from 20 to 100? What is the sequence generator? 2. List the first 8 terms of the sequence t(n) = 4 5n. What is the sequence generator?
2 3. How many terms in the sequence 7, 15, 23,, 191? What is the sequence generator? 4. How many terms in the sequence 15, 9, 3,, 363? What is the sequence generator? 5. Find the 21 st term in the sequence 12, 11.5, 11, What is the equation? 6. Find the 18 th term in the sequence 5, 7.5, 10, What is the equation? 7. If the third term of an arithmetic sequence is 13 and the seventeenth term is 29, what is the eighth term? 8. Write an equation that represents the sequence 1, 6, 11, 9. If the fifth term of an arithmetic sequence is 6 and the ninth term is 18, what is the twelfth term? 10. Write an equation that represents the sequence 24, 22.5, 21, 11. Given the sequence: 6, 2, 2,. a) Write the next 3 terms: b) Identify the generator and the initial value: c) Write the equation that represents the sequence: d) Find the 18 th term of the sequence: e) Determine if 334 is a term of the sequence. 12. Given t(2) = 14 and t(4) = 20 a) Calculate the generator: b) Determine the initial value: c) Write the equation that represents the sequence: d) Find the 20 th term of the sequence: e) Determine if 520 is a term of the sequence.
3 Algebra 2  Geometric Sequence Practice Name: Date: Period: A geometric sequence is a sequence in which each term after the first term (a) is obtained by multiplying the previous term by a constant, called the common ratio (r). EXAMPLE: Given the sequence: 16, 19.2, 23.04, What type is it? What is the equation of this sequence? Find each of the following: The 8 th term t(7) How do you know? In this equation, 16 corresponds to what value of n? t(8) t(9) What is the value of the generator? Which are the same? And under what condition? PRACTICE: 1. Given the sequence: 8, 12, 18. a) Write the next 3 terms: b) Identify the generator and the initial value: c) Write the equation that represents the sequence: d) What percentage increase or decrease does this represent? e) Find the 10 th term of the sequence: f) Determine if is a term of the sequence.
4 2. Given t(1) = and t(3) = a) Calculate the generator: b) What percentage increase or decrease does this represent? c) Determine the initial value: d) Write the equation that represents the sequence: e) Find the 6 th term of the sequence: f) Determine if is a term of the sequence. 3. ARITHMETIC SEQUENCE Initial Value: n = 0 10, 11.5, 13, ARITHMETIC SEQUENCE Initial Value: n = 1 10, 11.5, 13, FUNCTION (0, 10), (1,11.5), (2, 13) b) Find the 6 th term: b) Find the 6 th term: b) Find the f(6): c) Determine if 27 is a term. c) Determine if 27 is a term. c) Determine if 27 is an output of the function. d) What kind of function is this? 4. Given t(3) = 14 and t(6) = 112, write the equation of the sequence if it is: a) Arithmetic b) Geometric 5. Given t(2) = 4 and t(6) = , write the equation of the sequence if it is: a) Arithmetic b) Geometric
5 6. Given t(5) = 1.2 and t(9) = 750, write the equation of the sequence if it is: a) Arithmetic b) Geometric 7. GEOMETRIC SEQUENCE Initial Value: n = 0 GEOMETRIC SEQUENCE Initial Value: n = 1 FUNCTION 1200, 960, 768, 1200, 960, 768, (0, 1200), (1,960), (2, 768) b) Find the 9 th term: b) Find the 9 th term: b) Find the f(9): c) Determine if 6.35 is a term. c) Determine if 6.35 is a term. c) Determine if 6.35 is an output of the function. d) What kind of function is this? e) What is the percentage increase or decrease? f) If this represented a bouncing ball situation, what would the detail of the bouncing ball be?
6 Write the equation for each sequence that is given for the condition specified: 8. 21, 16.2,11.4, 21, 16.2,11.4, ,,, , 61.3, 60.2, , 960, 1152, geometric 14. t(4) = t(12) = ,,, , 61.3, 60.2, , 960, 1152,.geometric t(4) = t(12) = 426.8
Since the ratios are constant, the sequence is geometric. The common ratio is.
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