1059 11.2 Arithmetic Sequences and Series Evaluate each sum as described. See Example 7(b). 55. the sum of the first 80 positive integers 56. the sum of the first 120 positive integers 57. the sum of the first 50 positive odd integers 58. the sum of the first 90 positive odd integers 59. the sum of the first 60 positive even integers 60. the sum of the first 70 positive even integers Determine a1 for each arithmetic sequence. See Example 5. 33. a5 = 27, a15 = 87 34. a12 = 60, a20 = 84 35. a8 = -15, a18 = -85 36. a6 = -72, a13 = 26 37. a7 = 23.5, a20 = 69 38. a10 = -49.5, a14 = -73.5 Write a formula for the nth term of the finite arithmetic sequence an shown in each graph. Then state the domain and range of the sequence. See Example 6. 39. 4 6 –2 2 0 n an 40. 2 4 6 –2 2 0 n an 41. 0 1 2 3 4 5 6 7 1 2 3 n an 42. 1 3 5 –5 5 0 15 10 n an 43. 1 3 5 –70 –50 –30 –10 10 n an 44. 1 3 5 –1 1 3 5 n an Evaluate S10, the sum of the first ten terms, for each arithmetic sequence. See Example 7(a). 45. 8, 11, 14, c 46. -9, -5, -1, c 47. 5, 9, 13, c 48. 8, 6, 4, c 49. a2 = 9, a4 = 13 50. a3 = 5, a4 = 8 51. a1 = 10, a10 = 5.5 52. a1 = -8, a10 = -1.25 53. a1 = p, a10 = 10p 54. Concept Check Is this statement accurate? To find the sum of the first n positive integers, find half the product of n and n + 1. Find a1 and d for each arithmetic series. See Example 8. 61. S20 = 1090, a20 = 102 62. S31 = 5580, a31 = 360 63. S16 = -160, a16 = -25 64. S25 = 650, a25 = 62 65. S12 = -108, a12 = -19 66. S31 = 620, a31 = 30
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