Find a 1 eh sub 1  for each arithmetic series.

53. S 8 = 440 s sub 8 , equals 440  and d = 6 d equals 6
54. S 30 = 240 s sub 30 , equals 240  and d = − 2 d equals negative 2
55. Evaluate S 10 s sub 10  for the series x + ( x + y ) + ( x + 2 y ) + … x plus open x plus y close plus open x plus 2 y close plus dot dot dot
56. Evaluate S 15 s sub 15  for the series 3 x + ( 3 x − 2 y ) + ( 3 x − 4 y ) + … 3 x plus open 3 x minus 2 y close plus open 3 x minus 4 y close plus dot dot dot

Standardized Test Prep

SAT/ACT

57. Which expression represents the series 14 + 20 + 26 + 32 + 38 + 44 + 50 ? 14 plus 20 , plus , 26 plus 32 , plus . 38 plus 44 plus 50 question mark
    1. ∑ n = 2 8 ( 7 n − 1 ) sum , from , n equals 2 , to , 8 , of . open , 7 n minus 1 , close
    2. ∑ n = 3 9 ( 6 n − 4 ) sum , from , n equals 3 , to , 9 , of . open , 6 n minus 4 , close
    3. ∑ n = 3 8 ( 6 n − 4 ) sum , from , n equals 3 , to , 8 , of . open , 6 n minus 4 , close
    4. ∑ n = 8 14 ( n + 6 ) sum , from , n equals 8 , to , 14 , of . open , n plus 6 , close
58. What is the common ratio in the geometric sequence 9 2 , 3 , 2 , 4 3 , … ? 9 halves , comma . 3 comma 2 comma , 4 thirds . comma dot dot dot question mark
    6. 3 2 3 halves
    7. 9 2 9 halves
    8. 2 3 2 thirds
    9. 27 2 27 over 2
59. Which expression is NOT equivalent to 4 n 2 4 ? the fourth , root of 4 , n squared end root , . question mark
    1. ( 4 n 2 ) 1 4 open , 4 , n squared , close super 1 fourth end super
    2. 2 n 1 2 2 , n super 1 half end super
    3. ( 2 | n | ) 1 2 open , 2 vertical line n vertical line , close super 1 half end super
    4. 2 | n | square root of 2 vertical line n vertical line end root

60. The graph shows the inverse of which function?

    

    6. y = 3 x y equals 3 , x
    7. y = − 3 2 x y equals negative , 3 super 2 x end super
    8. y = 3 x y equals , 3 to the x
    9. y = 2 3 x y equals , 2 super 3 x end super

Short Response

61. Solve the equation x 2 + 10 x + 40 = 5 x squared , plus 10 . x plus 40 equals 5  by completing the square.

Mixed Review

See Lesson 9-3.

Write an explicit formula for each geometric sequence. Then find the first three terms.

62. a 1 = 1 , r = 2 eh sub 1 , equals 1 . comma , r equals 2
63. a 1 = − 1 , r = − 1 eh sub 1 , equals , minus 1 comma r equals negative 1
64. a 1 = 3 , r = 3 2 eh sub 1 , equals 3 comma r equals , 3 halves

See Lesson 8-4.

Simplify each rational expression. State any restrictions on the variable.

65. x 2 + 4 x + 3 x 2 − 3 x − 4 fraction x squared , plus 4 x plus 3 , over x squared , minus 3 x minus 4 end fraction
66. c 2 − 8 c + 12 c 2 − 11 c + 30 fraction c squared , minus 8 c plus 12 , over c squared , minus 11 c plus 30 end fraction
67. 3 z 4 + 36 z 3 + 60 z 2 3 z 3 − 3 z 2 fraction 3 , z to the fourth , plus 36 , z cubed , plus 60 , z squared , over 3 , z cubed , minus 3 , z squared end fraction

Get Ready! To prepare for Lesson 9-5, do Exercises 68–70.

See Lesson 9-3.

Find the common ratio for each geometric sequence.

68. 90 , − 30 , 10 , … 90 comma negative 30 comma . 10 comma dot dot dot
69. 64, 48, 36, …
70. − 9 , 4.5 , − 2.25 , … negative 9 comma 4.5 comma negative , 2.25 , comma dot dot dot

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