Find the arithmetic mean a n eh sub n  of the given terms.

34. a n − 1 = 7 , a n + 1 = 1 eh sub n minus 1 end sub . equals . 7 comma . eh sub n plus 1 end sub . equals 1
35. a n − 1 = 100 , a n + 1 = 140 eh sub n minus 1 end sub . equals . 100 comma . eh sub n plus 1 end sub . equals 140
36. a n − 1 = 4 , a n + 1 = − 3 eh sub n minus 1 end sub . equals . 4 comma . eh sub n plus 1 end sub . equals negative 3
37. a n − 1 = 0.3 , a n + 1 = 1.9 eh sub n minus 1 end sub . equals 0.3 comma . eh sub n plus 1 end sub . equals 1.9
38. a n − 1 = r , a n + 1 = s eh sub n minus 1 end sub . equals r comma . eh sub n plus 1 end sub . equals s
39. a n − 1 = − 2 x , a n + 1 = 2 x eh sub n minus 1 end sub . equals negative 2 x comma . eh sub n plus 1 end sub . equals 2 x
40. 
    1. Graphing Calculator Use your calculator to generate an arithmetic sequence with a common difference of − 7 . negative 7 .  How could you use a calculator to find the 6th term? The 8th term? The 20th term?
    2. Reasoning Explain how your answer to part (a) relates to the explicit formula a n = a + ( n − 1 ) d . eh sub n , equals , eh plus open n minus 1 close d .

Write an explicit and a recursive formula for each sequence.

41. 2, 4, 6, 8, 10, …
42. 0, 6, 12, 18, 24, …
43. − 5 , − 4 , − 3 , − 2 , − 1 , … negative 5 comma negative 4 comma . negative 3 comma . negative 2 comma . negative 1 comma dot dot dot
44. − 4 , − 8 , − 12 , − 16 , − 20 , … negative 4 comma negative 8 comma . negative 12 comma . negative 16 comma . negative 20 comma dot dot dot
45. − 5 , − 3.5 , − 2 , − 0.5 , 1 , … negative 5 comma negative 3.5 comma negative 2 comma negative 0.5 comma 1 comma dot dot dot
46. − 32 , − 20 , − 8 , 4 , 16 , … negative 32 comma negative 20 comma . negative 8 comma , 4 comma 16 comma dot dot dot
47. 1 , 1 1 3 , 1 2 3 , 2 , … 1 comma 1 , and 1 third , comma 1 , and 2 thirds , comma 2 comma dot dot dot
48. 0 , 1 8 , 1 4 , 3 8 , … 0 comma , 1 eighth , comma , 1 fourth , comma , 3 eighths , comma dot dot dot
49. 27 , 15 , 3 , − 9 , − 21 , … 27 comma 15 comma 3 comma negative 9 comma . negative 21 comma dot dot dot
50. Reasoning What information do you need to find a term of a sequence using an explicit formula?
51. Writing Describe some advantages and some disadvantages of a recursive formula and an explicit formula. When is it appropriate to use each formula?
52. Transportation Suppose a trolley stops at a certain intersection every 14 min. The first trolley of the day gets to the stop at 6:43 A.M. How long do you have to wait for a trolley if you get to the stop at 8:15 A.M.? At 3:20 P.M.?

Find the missing terms of each arithmetic sequence. (Hint: The arithmetic mean of the first and fifth terms is the third term.)

53. 2 , a 2 , a 3 , a 4 , − 22 , … 2 comma , eh sub 2 , comma . eh sub 3 , comma . eh sub 4 , comma . negative 22 comma dot dot dot
54. 10 , a 2 , a 3 , a 4 , − 11.6 , … 10 comma , eh sub 2 , comma . eh sub 3 , comma . eh sub 4 , comma , minus , 11.6 , comma dot dot dot
55. 1 , a 2 , a 3 , a 4 , − 35 , … 1 comma , eh sub 2 , comma . eh sub 3 , comma . eh sub 4 , comma . negative 35 comma dot dot dot
56. ⋯ 13 5 , a 6 , a 7 , a 8 , 37 5 , … math axis ellipsis , 13 over 5 , comma , eh sub 6 , comma , eh sub 7 , comma , eh sub 8 , comma , 37 over 5 , comma dot dot dot
57. 17 , a 2 , a 3 , a 4 , 17 , … 17 comma , eh sub 2 , comma . eh sub 3 , comma . eh sub 4 , comma 17 comma dot dot dot
58. 660 , a 2 , a 3 , a 4 , 744 , … 660 comma , eh sub 2 , comma . eh sub 3 , comma . eh sub 4 , comma 744 comma dot dot dot
59. … − 17 , a 4 , a 5 , a 6 , 1 , … dot dot dot negative 17 comma , eh sub 4 , comma . eh sub 5 , comma . eh sub 6 , comma 1 comma dot dot dot
60. … a + 1 , a 3 , a 4 , a 5 , a + 17 , … dot dot dot eh plus 1 comma , eh sub 3 , comma . eh sub 4 , comma . eh sub 5 , comma eh plus 17 comma dot dot dot
61. Income The arithmetic mean of the monthly salaries of two people is $4475. One person earns $3895 per month. What is the monthly salary of the other person?
62. Reasoning Suppose you turn the water on in an empty bathtub with vertical sides. After 20 s, the water has reached a level of 1.15 in. You then leave the room. You want to turn the water off when the level in the bathtub is 8.5 in. How many minutes later should you return? (Hint: Begin by identifying two terms of an arithmetic sequence.)

C Challenge

63. In an arithmetic sequence with a 1 = 4 eh sub 1 , equals 4  and d = 9 , d equals 9 , comma  which term is 184?
64. In an arithmetic sequence with a 1 = 2 eh sub 1 , equals 2  and d = − 2 , d equals , negative 2 comma  which term is − 82 ? negative 82 question mark
65. The arithmetic mean of two terms in an arithmetic sequence is 42. One term is 30. Find the other term.

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