Question 1

Write the first six terms of the arithmetic sequence with the given properties. ​
A​1 = 3, d = 4
​

Accepted Answer

A) 4, 8, 12, 16, 20, 24 
B) 3, 7, 11, 15, 19, 23 
C) 3, 6, 9, 12, 15, 18 
D) 4, 7, 10, 13, 16, 19 
E) 3, 8, 12, 16, 20, 24 
A) 4, 8, 12, 16, 20, 24 
B) 3, 7, 11, 15, 19, 23 
C) 3, 6, 9, 12, 15, 18 
D) 4, 7, 10, 13, 16, 19 
E) 3, 8, 12, 16, 20, 24

Question 2

A tool and die company buys a machine for $175,000 and it depreciates at a rate of 50% per year.(In other words, at the end of each year the depreciated value is 50% of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years. ​

Accepted Answer

A) $5470.75 
B) $5467.75 
C) $5468.75 
D) $5471.75 
E) $5469.75 
A) $5470.75 
B) $5467.75 
C) $5468.75 
D) $5471.75 
E) $5469.75

Question 3

Use a graphing utility to graph the first 10 terms of the sequence.   $a _ { n } = 3 ( - 0.7 ) ^ { n - 1 }$

Accepted Answer

A)    
B)    
C)    
D)     
E)    
A)    
B)    
C)    
D)     
E)

Question 4

The figure shows the results of a survey in which auto racing fans listed their favorite type of racing.What is the probability that an auto racing fan selected at random lists NASCAR racing as his or her favorite type of racing
 ( $a = 58 \%$ , $b = 14 \%$ )

Accepted Answer

A)  $\frac { 18 } { 25 }$ 
B)  $\frac { 5 } { 29 }$ 
C)  $\frac { 29 } { 5 }$ 
D)  $\frac { 50 } { 29 }$ 
E)  $\frac { 29 } { 50 }$ 
A)  $\frac { 18 } { 25 }$ 
B)  $\frac { 5 } { 29 }$ 
C)  $\frac { 29 } { 5 }$ 
D)  $\frac { 50 } { 29 }$ 
E)  $\frac { 29 } { 50 }$

Question 5

Write the first five terms of the arithmetic sequence defined recursively. ​
A1 = 206, an + 1 = an - 14
​
​

Accepted Answer

A) -206, -192, -178, -164, -136 
B) 206, 192, 178, 164, 122 
C) 206, 192, 178, 164, 150 
D) -206, -192, -178, -164, -150 
E) 206, 192, 178, 164, 136 
A) -206, -192, -178, -164, -136 
B) 206, 192, 178, 164, 122 
C) 206, 192, 178, 164, 150 
D) -206, -192, -178, -164, -150 
E) 206, 192, 178, 164, 136

Question 6

Evaluate using Pascal's triangle.   $\left( \begin{array} { l } 
6 \
5
\end{array} \right)$

Accepted Answer

A)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 720$ 
B)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 21$ 
C)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 56$ 
D)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 1$ 
E)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 6$ 
A)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 720$ 
B)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 21$ 
C)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 56$ 
D)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 1$ 
E)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 6$

Question 7

Find the partial sum.   $\sum _ { n = 1 } ^ { 240 } - 3 n - 1$

Accepted Answer

A) -87,724 
B) -86,520 
C) -86,279 
D) -87,000 
E) -87,001 
A) -87,724 
B) -86,520 
C) -86,279 
D) -87,000 
E) -87,001

Question 8

Evaluate the expression. 
  $P ( 9,9 )$

Accepted Answer

The answer of Evaluate the expression. 
  \(P (...

Question 9

Write the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = - n - 2$

Accepted Answer

A) -3, -2, -3, -4, -5 
B) -2, -3, -4, -5, -6 
C) -3, -4, -5, -6, -7 
D) -3, -5, -7, -9, -11 
E) 1, 0, -2, -2, -3 
A) -3, -2, -3, -4, -5 
B) -2, -3, -4, -5, -6 
C) -3, -4, -5, -6, -7 
D) -3, -5, -7, -9, -11 
E) 1, 0, -2, -2, -3

Question 10

Find the indicated term of the sequence.  $\begin{array} { l } 
a _ { n } = ( - 1 ) ^ { n } ( 6 n - 5 ) \
a _ { 15 } =
\end{array}$

Accepted Answer

A) 85 
B) -92 
C) -85 
D) -84 
E) 95 
A) 85 
B) -92 
C) -85 
D) -84 
E) 95

Question 11

Find the rational number representation of the repeating decimal.   $0.\overline {859}$

Accepted Answer

A)   $\frac { 859 } { 999 }$ 
B)   $\frac { 859 } { 9 }$ 
C)   $\frac { 859 } { 9999 }$ 
D)   $\frac { 85.9 } { 999 }$ 
E)   $\frac { 859 } { 99 }$ 
A)   $\frac { 859 } { 999 }$ 
B)   $\frac { 859 } { 9 }$ 
C)   $\frac { 859 } { 9999 }$ 
D)   $\frac { 85.9 } { 999 }$ 
E)   $\frac { 859 } { 99 }$

Question 12

Find the eighth term of the geometric sequence whose second and fourth terms are 6 and 54. ​

Accepted Answer

A) a8 = 39,366 
B) a8 = 4,374 
C) a8 = 13,122 
D) a8 = 1,458 
E) a8 = 486 
A) a8 = 39,366 
B) a8 = 4,374 
C) a8 = 13,122 
D) a8 = 1,458 
E) a8 = 486

Question 13

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 5 } \left( n ^ { 2 } - n \right)$

Accepted Answer

A) 40 
B) 330 
C) 225 
D) 15 
E) 55 
A) 40 
B) 330 
C) 225 
D) 15 
E) 55

Question 14

Find the sum of the infinite geometric series.(Round your answer to the nearest whole number.)   $\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 8 } \right) ^ { n }$

Accepted Answer

A)  $\frac { 8 } { 9 }$ 
B)  $\frac { 7 } { 8 }$ 
C)  $\frac { 9 } { 7 }$ 
D)  $\frac { 9 } { 8 }$ 
E)  $\frac { 8 } { 7 }$ 
A)  $\frac { 8 } { 9 }$ 
B)  $\frac { 7 } { 8 }$ 
C)  $\frac { 9 } { 7 }$ 
D)  $\frac { 9 } { 8 }$ 
E)  $\frac { 8 } { 7 }$

Question 15

There were approximately 28 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is in the 45-64 age group.( $a = 28 \%$ and $b = 38 \%$ )

Accepted Answer

A)  $\frac { 1 } { 38 }$ 
B)  $\frac { 19 } { 50 }$ 
C)  $\frac { 50 } { 19 }$ 
D) 38 
E)  $\frac { 1 } { 100 }$ 
A)  $\frac { 1 } { 38 }$ 
B)  $\frac { 19 } { 50 }$ 
C)  $\frac { 50 } { 19 }$ 
D) 38 
E)  $\frac { 1 } { 100 }$

Question 16

Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards such that the card is a 10 or higher (aces are low).

Accepted Answer

A)  $\frac { 3 } { 13 }$ 
B)   $\frac { 5 } { 13 }$ 
C)  $\frac { 1 } { 2 }$ 
D) 1 
E)  $\frac { 4 } { 13 }$ 
A)  $\frac { 3 } { 13 }$ 
B)   $\frac { 5 } { 13 }$ 
C)  $\frac { 1 } { 2 }$ 
D) 1 
E)  $\frac { 4 } { 13 }$

Question 17

Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​
An ​= 8 + 6n
​

Accepted Answer

A) -6 
B) -8 
C) 6 
D) 8 
E) not arithmetic 
A) -6 
B) -8 
C) 6 
D) 8 
E) not arithmetic

Question 18

Evaluate ${ } _ { n } P _ { r }$ .  ${ } _ { 2 } P _ { 2 }$

Accepted Answer

A) 2 
B) 20 
C) 30 
D) 6 
E) 12 
A) 2 
B) 20 
C) 30 
D) 6 
E) 12

Question 19

The educational attainment of a country population age 25 years or older in 2007 is shown in the circle graph.Use the fact that the population of people 25 years or older was approximately 293.32 million in 2007.Estimate the number of people 25 years or older who have high school diplomas.Round your anser to two decimal places. ​   ​

Accepted Answer

A) 261.38 million 
B) 251.38 million 
C) 291.38 million 
D) 271.38 million 
E) 281.38 million 
A) 261.38 million 
B) 251.38 million 
C) 291.38 million 
D) 271.38 million 
E) 281.38 million

Question 20

Select the first five terms of the sequence.(Assume that n begins with 1.)  $a _ { n } = n \left( n ^ { 2 } - 8 \right)$

Accepted Answer

A)  $32,85 , - 7 , - 8,3$ 
B)  $- 7 , - 8,3,32,85$ 
C)  $3,32,85 , - 7 , - 8$ 
D)  $- 8,3,32,85 , - 7$ 
E)  $85 , - 7 , - 8,3,32$ 
A)  $32,85 , - 7 , - 8,3$ 
B)  $- 7 , - 8,3,32,85$ 
C)  $3,32,85 , - 7 , - 8$ 
D)  $- 8,3,32,85 , - 7$ 
E)  $85 , - 7 , - 8,3,32$

Write the first six terms of the arithmetic sequence with the given properties. A₁ = 3, d = 4

A tool and die company buys a machine for $175,000 and it depreciates at a rate of 50% per year.(In other words, at the end of each year the depreciated value is 50% of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years.

Use a graphing utility to graph the first 10 terms of the sequence. $a _ { n } = 3 ( - 0.7 ) ^ { n - 1 }$

Write the first five terms of the arithmetic sequence defined recursively. A₁ = 206, an_{+ 1} = a_n - 14

Evaluate using Pascal's triangle. $\left( \begin{array} { l } 6 \\5\end{array} \right)$

Find the partial sum. $\sum _ { n = 1 } ^ { 240 } - 3 n - 1$

Evaluate the expression. $P ( 9,9 )$

Write the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = - n - 2$

Find the indicated term of the sequence. =(-1(6n-5) =

Find the rational number representation of the repeating decimal. $0.\overline {859}$

Find the eighth term of the geometric sequence whose second and fourth terms are 6 and 54.

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 5 } \left( n ^ { 2 } - n \right)$

Find the sum of the infinite geometric series.(Round your answer to the nearest whole number.) $\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 8 } \right) ^ { n }$

Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards such that the card is a 10 or higher (aces are low).

Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n= 8 + 6n

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 2 } P _ { 2 }$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = n \left( n ^ { 2 } - 8 \right)$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 9: Sequences Series and Probability

Write the first six terms of the arithmetic sequence with the given properties. ​ A​1 = 3, d = 4 ​

A tool and die company buys a machine for $175,000 and it depreciates at a rate of 50% per year.(In other words, at the end of each year the depreciated value is 50% of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years. ​

Use a graphing utility to graph the first 10 terms of the sequence. an=3(−0.7)n−1a _ { n } = 3 ( - 0.7 ) ^ { n - 1 }an​=3(−0.7)n−1

The figure shows the results of a survey in which auto racing fans listed their favorite type of racing.What is the probability that an auto racing fan selected at random lists NASCAR racing as his or her favorite type of racing ( a=58%a = 58 \%a=58% , b=14%b = 14 \%b=14% )

Write the first five terms of the arithmetic sequence defined recursively. ​ A1 = 206, an + 1 = an - 14 ​ ​

Evaluate using Pascal's triangle. (65)\left( \begin{array} { l } 6 \\5\end{array} \right)(65​)

Find the partial sum. ∑n=1240−3n−1\sum _ { n = 1 } ^ { 240 } - 3 n - 1∑n=1240​−3n−1

Evaluate the expression. P(9,9)P ( 9,9 )P(9,9)

Write the first five terms of the sequence.(Assume that n begins with 1.) an=−n−2a _ { n } = - n - 2an​=−n−2

Find the indicated term of the sequence. =(-1(6n-5) =

Find the rational number representation of the repeating decimal. 0.859‾0.\overline {859}0.859

Find the eighth term of the geometric sequence whose second and fourth terms are 6 and 54. ​

Find the sum using the formulas for the sums of powers of integers. ∑n=15(n2−n)\sum _ { n = 1 } ^ { 5 } \left( n ^ { 2 } - n \right)∑n=15​(n2−n)

Find the sum of the infinite geometric series.(Round your answer to the nearest whole number.) ∑n=0∞(18)n\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 8 } \right) ^ { n }∑n=0∞​(81​)n

Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards such that the card is a 10 or higher (aces are low).

Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​ An ​= 8 + 6n ​

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ . 2P2{ } _ { 2 } P _ { 2 }2​P2​

Select the first five terms of the sequence.(Assume that n begins with 1.) an=n(n2−8)a _ { n } = n \left( n ^ { 2 } - 8 \right)an​=n(n2−8)

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Write the first six terms of the arithmetic sequence with the given properties. A₁ = 3, d = 4

A tool and die company buys a machine for $175,000 and it depreciates at a rate of 50% per year.(In other words, at the end of each year the depreciated value is 50% of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years.

Use a graphing utility to graph the first 10 terms of the sequence. $a _ { n } = 3 ( - 0.7 ) ^ { n - 1 }$

Write the first five terms of the arithmetic sequence defined recursively. A₁ = 206, an_{+ 1} = a_n - 14

Evaluate using Pascal's triangle. $\left( \begin{array} { l } 6 \\5\end{array} \right)$

Find the partial sum. $\sum _ { n = 1 } ^ { 240 } - 3 n - 1$

Evaluate the expression. $P ( 9,9 )$

Write the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = - n - 2$

Find the rational number representation of the repeating decimal. $0.\overline {859}$

Find the eighth term of the geometric sequence whose second and fourth terms are 6 and 54.

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 5 } \left( n ^ { 2 } - n \right)$

Find the sum of the infinite geometric series.(Round your answer to the nearest whole number.) $\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 8 } \right) ^ { n }$

Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n= 8 + 6n

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 2 } P _ { 2 }$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = n \left( n ^ { 2 } - 8 \right)$