66. The arithmetic mean of two terms in an arithmetic sequence is − 6 . negative 6 .  One term is − 20 . negative 20 .  Find the other term.

Given two terms of each arithmetic sequence, find a 1 eh sub 1  and d.

67. a 3 = 5 eh sub 3 , equals 5  and a 5 = 11 eh sub 5 , equals 11
68. a 4 = 8 eh sub 4 , equals 8  and a 7 = 20 eh sub 7 , equals 20
69. a 3 = 32 eh sub 3 , equals 32  and a 7 = − 8 eh sub 7 , equals negative 8
70. a 10 = 17 eh sub 10 , equals 17  and a 14 = 34 eh sub 14 , equals 34
71. a 4 = − 34.5 eh sub 4 , equals , minus , 34.5  and a 5 = − 12.5 eh sub 5 , equals negative , 12.5
72. a 4 = − 2.4 eh sub 4 , equals , minus 2.4  and a 6 = 2 eh sub 6 , equals 2

Find the indicated term of each arithmetic sequence.

73. a 1 = k , d = k + 4 ; a 9 eh sub 1 , equals k comma d equals k plus 4 semicolon , eh sub 9
74. a 1 = k + 7 , d = 2 k − 5 ; a 11 eh sub 1 , equals , k plus 7 comma d equals 2 k minus 5 semicolon , eh sub 11

Standardized Test Prep

SAT/ACT

75. The equation X ( t ) = t 4 − 5 t 2 + 6 x open t close equals , t to the fourth , minus , 5 t squared . plus 6  gives the position of a comet relative to a fixed point, measured in millions of miles, at time t, measured in days. Solve the equation X ( t ) = 0 . x open t close equals 0 .  At what times is the position zero?
    1. 2, 3
    2. − 2 , − 3 negative 2 comma negative 3
    3. ± 2 , ± 3 plus minus 2 comma plus minus 3
    4. ± 2 , ± 3 plus minus square root of 2 , comma plus minus square root of 3
76. Simplify 3 − 1 x 1 2 x − 5 . fraction 3 minus , 1 over x , over fraction 1 , over 2 x end fraction , minus 5 end fraction . .
    6. 6 x − 2 1 − 10 x fraction 6 x minus 2 , over 1 minus 10 x end fraction
    7. 3 x − 1 1 − 10 x fraction 3 x minus 1 , over 1 minus 10 x end fraction
    8. 4 1 − 10 x fraction 4 , over 1 minus 10 x end fraction
    9. 3 x − 1 1 − 5 x fraction 3 x minus 1 , over 1 minus 5 x end fraction

Extended Response

77. What are all the solutions of 3 x 2 − 1 + 4 x x + 1 = 1.5 x − 1 ? fraction 3 , over x squared , minus 1 end fraction . plus . fraction 4 x , over x plus 1 end fraction . equals . fraction 1.5 , over x minus 1 end fraction . question mark  Show your work.

Mixed Review

See Lesson 9-1.

Determine whether each formula is explicit or recursive. Then find the first five terms of each sequence.

78. a 1 = − 2 , a n = a n − 1 − 5 eh sub 1 , equals , minus 2 comma , eh sub n , equals . eh sub n minus 1 end sub . minus 5
79. a n = 3 n ( n + 1 ) eh sub n , equals 3 n open n plus 1 close
80. a n = n 2 − 1 eh sub n , equals . n squared , minus 1
81. a 1 = − 121 , a n = a n − 1 + 13 eh sub 1 , equals , minus 121 comma , eh sub n , equals . eh sub n minus 1 end sub . plus 13

See Lesson 2-4.

Write an equation in point-slope form for each pair of points.

82. (0, 3) and (3, 11)
83. (4, 6) and (10, 30)
84. (1, 10) and (5, 42)

See Lesson 6-2.

85. Geometry The formula for volume V of a sphere with radius r is V = 4 3 π r 3 . v equals , 4 thirds , pi , r cubed , .  Find the radius of a sphere as a function of its volume. Rationalize the denominator.

Get Ready! To prepare for Lesson 9-3, do Exercises 86–88.

See Problem 9-1.

Find the next term in each sequence.

86. 2, 4, 8, 16, …
87. 1, 5, 25, 125, …
88. − 1 , − 3 , − 9 , − 27 , … negative 1 comma negative 3 comma . negative 9 comma . negative 27 comma dot dot dot

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