Use each recursive definition to write an explicit formula for the sequence.

67. a 1 = 10 , a n = 2 a n − 1 eh sub 1 , equals 10 comma , eh sub n , equals . 2 eh sub n minus 1 end sub
68. a 1 = − 5 , a n = a n − 1 − 1 eh sub 1 , equals , minus 5 comma . eh sub n , equals . eh sub n minus 1 end sub . minus 1
69. a 1 = 1 , a n = a n − 1 + 4 eh sub 1 , equals 1 . comma . eh sub n , equals . eh sub n minus 1 end sub . plus 4

70. Finance Use the information in the ad.

    

    1. Suppose you start a savings account. Write a recursive definition and an explicit formula for the amount of money you would have in the bank at the end of any week.
    2. How much money would you have in the bank after four weeks?
    3. Assume the bank pays interest every four weeks. To calculate your interest, multiply the balance at the end of the four weeks by 0.005. Then, add that amount to your account on the last day of the four-week period. Write a recursive formula for the amount of money you have after each interest payment.
    4. Reasoning What is the bank's annual interest rate?

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

71. Scientists determine an object is moving at the rate of ( 5 − 2 ) ft/s . open , 5 minus square root of 2 , close , ftslashs , .  How many seconds will it take the object to travel 125 ft? Round the answer to the nearest tenth of a second.
72. What is the solution of 4 x − 23 − 3 = 2 ? square root of 4 x minus 23 end root . minus 3 equals 2 question mark
73. Using a calculator, what is the solution of 1080 = 15 3 x − 4 ? 1080 , equals . 15 super 3 x minus 4 end super . question mark  Round the answer to the nearest hundredth.
74. Using the change of base formula, what is the solution of log 5 x = log 3 20 ? log base 5 , x equals . log base 3 , 20 question mark  Round the answer to the nearest tenth.
75. The battery power available to operate a deep space probe is given by the formula P = 42 e − 0.005 t , p equals . 42 e super negative , 0.005 , t end super . comma  where P is power in watts and t is time in years. For how many years can the probe run if it requires 35 watts? Round the answer to the nearest tenth year.

Mixed Review

See Lesson 8-6.

Solve each equation. Check the solution.

76. y y + 1 = 2 3 fraction y , over y plus 1 end fraction . equals , 2 thirds
77. 4 2 a = 5 a + 6 fraction 4 , over 2 eh end fraction , equals . fraction 5 , over eh plus 6 end fraction
78. 3 b + 2 = 6 b − 1 fraction 3 , over b plus 2 end fraction . equals . fraction 6 , over b minus 1 end fraction

See Lesson 2-3.

Find the slope of the line that passes through the two points.

79. (4, 5) and (1, 8)
80. ( − 3 , − 3 ) open negative 3 comma negative 3 close  and (2, 2)
81. (1, 3) and (4, 9)

Get Ready! To prepare for Lesson 9-2, do Exercises 82–84.

See Lesson 1-1.

Identify the pattern and find the next three terms.

82. 10, 8, 6, 4, 2, 0, …
83. 100, 117, 134, 151, 168, …
84. 5 7 , 8 7 , 11 7 , 2 , … 5 sevenths , comma , 8 sevenths , comma , 11 over 7 , comma 2 comma dot dot dot

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