Chapter 11 Answers 26. an = 32(-0.5)n-1; 32, -16, 8, -4, 2
Practice 11-1
27. an = 2187 a 31 b
1. an = an-1 + 6 where a1 = -14; 16 2. an = an-1 - 0.3 where a1 = 6; 4.5 3. an = -2an-1 where a1 = 1; -32 4. an = 3an-1 where a1 = 1; 81
3
3
7. an = an-1 + 3 where a1 = 36; 51 8. an = an-1 - 6 where a1 = 36; 6 9. a n 5 1 a n 2 1 where a1 = 9.6; 0.3 10. an = 7n; 140 2 11. an = 6n - 4; 116 12. an = n + 4; 24 13. an = n - 2; 18 14. an = 2n + 1; 41 15. an = 0.8n; 16 16. a n 5 n ; 5 17. a n 5 1 ; 1
4 2n 40 2 1 18. a n 5 n 2 ; 19 19. multiply by 2; 32, 64, 128 3 3 20. subtract 5; 19, 14, 9 21. add 0.1; 1.2, 1.3, 1.4 22. add 7; 39, 46, 53 23. multiply by 2; 40, 80, 160 24. subtract 3; -21, -24, -27 25. explicit; 1 , 2 , 1, 4 , 5 3 3 3 3 26. explicit; -5, -2, 3, 10, 19 27. recursive; 5, 8, 17, 44, 125 28. explicit; 0, 1 , 1, 1 1 , 2 29. recursive; 5, -2, 5, -2, 5 2 2 30. recursive; -4, -8, -16, -32, -64 31a. 1, 6, 36, 216 31b. a n 5 6a n 2 1 where a1 = 1 32a. 60° 32b. a n 5 360 n 32c. No polygon has one or two angles.
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Practice 11-2 1. 96 2. -406.9 3. 36.3 4. -99 5. 464 6. -231 7. 5.5 8. -10.5 9. 171 10. no 11. yes; -3 12. yes; -0.4 13. yes; 5 14. yes; -29 15. yes; 0.3 16. yes; 6 17. yes; 0.2 18. yes; 13 19. 36 20. 21 21. 31 22. 14.5 23. -42 24. -3.5 25. 0 26. -2 27. 21.5 28. -28.5 29. 227 30. 189.5 31. 4.5 32. 14.5 33. 9 34. 3 35. -1 36. -6.5 5
37a. a n 5 a n 2 1 1 5 where a1 = 32 37b. 32, 37, 42, 47, 52 37c. a n 5 32 1 5(n 2 1) 37d. 127 people
Practice 11-3 1. 8 2. 12 3. 4 4. 6 5. 10 6. 4.8 7. yes; 3; 243, 729 8. yes; 2; 64, 128 9. no 10. yes; -2; 64, -128 11. yes; 0.5; 0.0625, 0.03125 12. yes; 0.3; 0.81, 0.243 13. no 14. yes; -0.5; 4, -2 15. no 16. geometric; 1 , 1 17. neither; -9, -14 9 27
18. geometric; 2, -2 19. arithmetic; 17, 22 20. arithmetic; -11, -14 21. neither; 5, -6 22. an = 3(-2)n-1; 3, -6, 12, -24, 48 23. an = 5(3)n-1; 5, 15, 45, 135, 405 24. an = -1(4)n-1; -1, -4, -16, -64, -256 25. an = -2(-3)n-1; -2, 6, -18, 54, -162 Algebra 2 Chapter 11
; 2187, 729, 243, 81, 27
28. an = 9(2)n-1; 9, 18, 36, 72, 144 29. an = -4(4)n-1; -4, -16, -64, -256, -1024 30. an = 0.1(-2)n-1; 0.1, -0.2, 0.4, -0.8, 1.6 31a. about 19.2 in. 31b. 9 mm 32a. an = 2537(1.025)n-1 32b. about 2732 33a. an = 1(1.5)n-1 33b. 1.5 in. 33c. 2.25 in. 33d. about 86.5 in.
5. a n 5 1 a n 2 1 where a1 = 1; 1 32 2 1 6. a n 5 a n 2 1 1 where a1 = 2 ; 2 1 3
n21
Practice 11-4 1. 4; 0; 3; 6 2. 5; 3; 11; 35 3. 6; 28; 33; 183 4. 4; 13; 28; 82 5. 4; 2.5; 8.5; 22 6. 6; 2; -3; -3 7. 6; 5; 10; 45 8. 4; -4; -7; -22 9. 4; 11; 20; 62 10. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15; 64 11. 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26; 124 12. 4 + 9 + 14 + 19 + 24 + 29 + 34 + 39 + 44; 216 13. 10 + 25 + 40 + 55 + 70 + 85; 285 14. 17 + 25 + 33 + 41 + 49 + 57 + 65; 287 15. 125 + 126 + 127 + 128 + 129 + 130 + 131; 896 7
5
16. a (2n 2 1) 17. a (0.3n 1 2) n51 4
n51 6
18. a 4n 19. a (23n 1 13) n51 8
n51 7
20. a (4n 2 1) 21. a (10n 1 5) n51
n51
22. sequence; finite 23. series; infinite 24. sequence; infinite 25. series; finite 26. sequence; infinite 27. series; finite 28. -9 29. 39 30. -72 31. -51 32. 4.5 33. 60 34. 1025 stitches 35. 19 musicians; 84 musicians
Practice 11-5 1. converges; yes 2. converges; yes 3. converges; yes 4. diverges; no 5. converges; yes 6. diverges; no 7. 15 8. no sum 9. 23 10. no sum 11. 16 12. 1.5 13. 600 255 14. 4000 15. arithmetic; 126 16. geometric; 1024 17. geometric; 1023 18. arithmetic; 240 19. 79.921875 20. 28,697,812 21. about 74.99 22. 40.5 23. 0.22222222 24. 6300 25. $8553.71 26. $40,928.80 27. 5000 cm 28. about 177.78 mm 29. $2,319,367.05; $4,950,000
Practice 11-6 For Exercises 1–19, answers are in units2. 1a. 0.5(3.75) + 0.5(3) + 0.5(1.75) + 0.5(0); 4.25 1b. 0.5(4) + 0.5(3.75) + 0.5(3) + 0.5(1.75); 6.25 2a. 0.5(15.5) + 0.5(14) + 0.5(11.5) + 0.5(8); 24.5 2b. 0.5(16) + 0.5(15.5) + 0.5(14) + 0.5(11.5); 28.5 3a. 0.5(1.875) + 0.5(1.5) + 0.5(0.875) + 0.5(0); 2.125 3b. 0.5(2) + 0.5(1.875) + 0.5(1.5) + 0.5(0.875); 3.125 4a. 0.5(4) + 0.5(4.25) + 0.5(5) + 0.5(6.25); 9.75 4b. 0.5(4.25) + 0.5(5) + 0.5(6.25) + 0.5(8); 11.75
Answers
33
Chapter 11 Answers
(continued)
5a. 0.5(6) + 0.5(6.5) + 0.5(8) + 0.5(10.5); 15.5 5b. 0.5(6.5) + 0.5(8) + 0.5(10.5) + 0.5(14); 19.5 6a. 0.5(2) + 0.5(2.125) + 0.5(2.5) + 0.5(3.125); 4.875 6b. 0.5(2.125) + 0.5(2.5) + 0.5(3.125) + 0.5(4); 5.875 7a. 0.5(14.25) + 0.5(12) + 0.5(8.25) + 0.5(3); 18.75 7b. 0.5(15) + 0.5(14.25) + 0.5(12) + 0.5(8.25); 24.75 8a. 0.5(2) + 0.5(2.75) + 0.5(5) + 0.5(8.75); 9.25 8b. 0.5(2.75) + 0.5(5) + 0.5(8.75) + 0.5(14); 15.25 9a. 0.5(9.75) + 0.5(9) + 0.5(7.75) + 0.5(6); 16.25 9b. 0.5(10) + 0.5(9.75) + 0.5(9) + 0.5(7.75); 18.25 10a. y
1 2. 10,935 3. 2 2 64 1. 128 59,049 4. 729 5. 25,600 6. 512 128
7. an = 1 a 21 b
n21
; 1, 1 , 1 , 1 , 1 2 4 8 16
8. an = 2(3)n-1; 2, 6, 18, 54, 162 9. an = 12(3)n-1; 12, 36, 108, 324, 972 10. an = 1a 41 b
n21
; 1, 1 , 1 , 1 , 1 4 16 64 256
n21
12
1b 11. an = 5a 10
8
12. an = 1a 31 b
n21
18. an = 2 a 12 b
n21
19. an = 1 a 51 b
n21
21. an = 5 a 41 b
n21
4 x 4
Reteaching 11-3
O
4
10b. 5.5 10c. 9.5 10d. 7.5; the mean 11. 6.75 12. 16.5 13. 9 14. 12 15. 2.25 16. 18 17. 9 18. 6 19. 4.6 20. total feet 21. total number of computers 22. total miles 23. total gallons 24. total molecules 25. total price 26. ; 3.25 units2 y 4
; 5, 1 , 1 , 1 , 1 2 20 200 2000
; 1, 1 , 1 , 1 , 1 3 9 27 81 13. an = 5(2)n-1; 5, 10, 20, 40, 80 14. an = 1(3)n-1; 1, 3, 9, 27, 81 15. an = 3(6)n-1; 3, 18, 108, 648, 3888 16. an = 3(3)n-1; 3, 9, 27, 81, 243 17. an = 2(2)n-1; 2, 4, 8, 16, 32 ; 2, 1, 1 , 1 , 1 2 4 8
; 1, 1 , 1 , 1 , 1 5 25 125 625 n-1 20. an = 3(4) ; 3, 12, 48, 192, 768 ; 5, 5 , 5 , 5 , 5 4 16 64 256
2 2
27. 12
4
; 4.25 units2
y
8
Reteaching 11-5
4
1. 4095 2. 341 3. 2 635 4. 3415 5. 20 6. 2 11 7. 2 32 512 32 13 x
4
25 3. 93 4. 22 5. -56 1. -6 2. 36 6. 120 7. 108 8. -35 9. 74 10. an = 87 + 2n; 5985 seats
O
5 9. 2 1 10. 100 11. 18 12. 1 13. 5 8. 14 9 6 6
4
Reteaching 11-1 1. subtract 5; 18, 13, 8 2. multiply by 2; 112, 224, 448 3. subtract 2; -13, -15, -17 4. multiply by 3; 162, 486, 1458 5. add 0.5; 6.5, 7, 7.5 6. each time the addend increases by 2; 37, 47, 59 7. B 8. E 9. A 10. F 11. C 12. D
Reteaching 11-6 Answers are in units2. 1. 3.5 2. 4.25 3. 9 4. 1.5 5. 3.75 6. 8.25
Enrichment 11-1 6; 12; 16; 14; 11; 2; 4; 15; 5; 3; 13; 7; 10; 1; 17; 9 SIMILAR TRIANGLES
Reteaching 11-2 1. -28 2. 0.0129 3. -92 4. 12.2 5. 18.8 6. 118 7. $110 8. $143 9. 31 rows
34
Answers
Algebra 2 Chapter 11
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Reteaching 11-4
x O
