Review 9 Alg thru 11-3 sequences
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1 Name: Class: Date: Review 9 Alg thru 11-3 sequences Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the pattern in the sequence. Find the next three terms , 15, 17, 19,... a. Add 2; 23, 25, 27. b. Multiply by 2; 38, 76, 152. c. Add 2; 17, 15, 13. d. Add 2; 21, 23, , 8, 16, 32,... a. Multiply by 2; 64, 128, 256. b. Multiply by 2; 64, 128, 256. c. Multiply by 2; 128, 256, 512. d. Add 2; 34, 36, , 2, 6, 16, 44,... a. Add the two previous terms and then multiply by 2; 120, 328, 896 b. Multiply by 2 and then add 4; 92, 188, 380 c. Alternate multiplying by 2 and by 3; 88, 264, 528 d. Add all the previous terms; 69, 138, , 250, 100, 40,... a. Divide by 3; 15, 5, 1. c. Add 7.5; 25, 32.5, b. Divide by 2.5; 16, 6.4, d. Subtract 15; 10, 5, Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth. a. 9.2 feet b feet c. 7.8 feet d. 1.9 feet 6. Orlando is making a design for a logo. He begins with a square measuring 24 inches on a side. The second square has a side length of 19.2 inches, and the third square has a side length of inches. Which square will be the first square with a side length of less than 12 inches? a. fourth square c. sixth square b. fifth square d. seventh square 7. Write a recursive formula for the sequence 8, 10, 12, 14, 16,... Then find the next term. + 2, where a 1 = 8; , where a 1 = 18; 8 c. 2, where a 1 = 8; 18 d. 2, where a 1 = 2; 2 1
2 Name: 8. Write a recursive formula for the sequence 15, 26, 48, 92, 180,... Then find the next term. = 2 1 4, where a 1 = 2 4, where a 1 c. = n 1, where a 1 d. = , where a 1 9. Write an explicit formula for the sequence 7, 2, 3, 8, 13,... Then find a 14. = 5n + 12; 53 c. = 5n + 12; 58 = 5n + 7; 58 d. = 5n + 7; The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit formula for the sequence of the number of bacteria. Hours (n) Number of Bacteria = 19n + 19 c. = 1 19 n = n + 19 d. = 19n 11. Is the formula = 4n(n 1) is explicit or recursive? Find the first five terms of the sequence. a. recursive; 1, 4, 16, 64, 256 c. explicit; 1, 4, 16, 64, 256 b. recursive; 0, 16, 24, 48, 80 d. explicit; 0, 8, 24, 48, 80 Is the sequence arithmetic? If so, identify the common difference , 20, 27, 34,... a. yes, 7 b. yes, 7 c. yes, 13 d. no , 21, 42, 77,... a. yes, 7 b. yes, 7 c. yes, 14 d. no , 9.8, 22, 34.2,... a. yes, 12 b. yes, 12.2 c. yes, 12.3 d. no 15. Viola makes gift baskets for Valentine s Day. She has 13 baskets left over from last year, and she plans to make 12 more each day. If there are 15 work days until the day she begins to sell the baskets, how many baskets will she have to sell? a. 193 baskets c. 205 baskets b. 156 baskets d. 181 baskets 16. Find the 50th term of the sequence 5, 2, 9, 16,... a. 352 b. 343 c. 338 d Find the missing term of the arithmetic sequence 22,, 34,... a. 46 b. 16 c. 28 d. 40 2
3 Name: 18. Find the arithmetic mean of 1 = 3.9, + 1 = 7.1. a. 11 b. 5.5 c. 3.7 d Find the arithmetic mean of 1 = 5 7, + 1 = 9 4. a b. 5 4 c d. 7 4 Is the sequence geometric? If so, identify the common ratio , 12, 24, 48,... a. yes, 2 b. yes, 2 c. yes, 4 d. no 21. 2, 4, 16, 36,... a. yes, 2 b. yes, 2 c. yes, 3 d. no , 2 9, 4 27, 8 81, ,... a. yes, 2 3 b. yes, 1 9 c. yes, 1 6 d. not geometric Write the explicit formula for the sequence. Then find the fifth term in the sequence. 23. a 1 = 3, r = 3 = 3 ( 3) n 1 ; 243 c. = 3 (3) n ; 243 = 3 (3) n 1 ; 243 d. = 3 ( 3) n ; a 1 = 120, r = 0.3 = 120 (0.3) n ; c. = 120 (0.3) n ; ; d. = 120 (0.3) n 1 ; Find the missing term of the geometric sequence ,, 1620,... a b. 51 c. 6 d ,, 50,... a b. 650 c. 250 d
4 Name: 27. Kaylee is painting a design on the floor of a recreation room using equilateral triangles. She begins by painting the outline of Triangle 1 measuring 50 inches on a side. Next, she paints the outline of Triangle 2 inside the first triangle. The side length of Triangle 2 is 80% of the length of Triangle 1. She continues painting triangles inside triangles using the 80% reduction factor. Which triangle will first have a side length of less than 29 inches? a. Triangle 4 c. Triangle 5 b. Triangle 3 d. Triangle A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 18 feet long and the third arc is 8 feet long, what is the length of the second arc? a. 12 feet b. 10 feet c. 5 feet d. 72 feet Essay 29. The table shows how the number of sit-ups Marla does each day has changed over time. At this rate, how many sit-ups will she do on Day 12? Explain your steps in solving this problem. Day1 Day 2 Day 3 Day 4 Day Other 30. Consider the sequence 7, 5.6, 4.2, 2.8, 1.4,... a. Write an explicit formula for the sequence. Explain your steps. b. Write a recursive formula for the sequence. Explain your steps. c. Suppose you need to find the 50th term of the sequence. Explain which formula you would use. d. Which term is the number 103.6? Explain your method for solving this problem. 4
5 Review 9 Alg thru 11-3 sequences Answer Section MULTIPLE CHOICE 1. D 2. A 3. A 4. B 5. A 6. B 7. A 8. A 9. C 10. D 11. D 12. A 13. D 14. B 15. A 16. C 17. C 18. B 19. A 20. A 21. D 22. A 23. A 24. D 25. D 26. C 27. A 28. A 1
6 ESSAY 29. [4] To find the number of sit-ups on Day 12, first write an explicit formula for the sequence using the explicit formula = a 1 + (n 1)d. You can see that the first term, a 1, is 28 and the common difference is 5. Substitute these values into the formula: = 28 + (n 1)5. Next, substitute 12 into the formula for n and solve for. = 28 + (12 1)5. Simplify to find that = 83. She will do 83 sit-ups on Day 12. [3] correct procedure with one minor mathematical error [2] correct procedure with two minor mathematical errors [1] incomplete procedure or correct answer with no explanation or work shown OTHER 30. a. To write the explicit formula, use the general explicit formula = a 1 + (n 1)d. You can see that the first term, a 1, is 7 and the common difference, d, is 1.4. Substitute these values into the formula: = 7 + (n 1)1.4. Simplify the formula to = n. b. To write the recursive formula, use the general recursive formula a 1 = a given value, + d. You can see that the first term is 7 and the common difference d is 1.4. Substitute these values into the formula: + 1.4, where a 1 = 7. c. Answers may vary. Sample: It would be easier to use the explicit formula since it does not depend upon knowing the previous term. You can just substitute 50 for n in the explicit formula to find the 50th term. d. Substitute for in the formula = n and solve for n = n; 112 = 1.4n; n = 80. The term is the 80th term of the sequence. 2
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