Question 1

Find a formula for an  for the arithmetic sequence.  a3 = 94, a6 = 87

Accepted Answer

A) an  = $\frac { 7 } { 3 }$ n - 101 
B) an  = $- \frac { 7 } { 3 }$ n + 101 
C) an  = 101 - 303n 
D) an  = $\frac { 7 } { 3 }$ n + 303 
E) an  = 101 + 303n 
A) an  = $\frac { 7 } { 3 }$ n - 101 
B) an  = $- \frac { 7 } { 3 }$ n + 101 
C) an  = 101 - 303n 
D) an  = $\frac { 7 } { 3 }$ n + 303 
E) an  = 101 + 303n

Question 2

Use mathematical induction to solve for all positive integers n.   $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = ?$

Accepted Answer

A)  $\frac { n ( 2 n + 13 ) } { 6 }$ 
B)  $\frac { n ( n + 1 ) ( 2 n + 13 ) } { 4 }$ 
C)  $\frac { n ( n + 1 ) ( n + 13 ) } { 6 }$ 
D)  $\frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$ 
E)  $\frac { n ( n + 1 ) ( 2 n + 13 ) } { 2 }$ 
A)  $\frac { n ( 2 n + 13 ) } { 6 }$ 
B)  $\frac { n ( n + 1 ) ( 2 n + 13 ) } { 4 }$ 
C)  $\frac { n ( n + 1 ) ( n + 13 ) } { 6 }$ 
D)  $\frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$ 
E)  $\frac { n ( n + 1 ) ( 2 n + 13 ) } { 2 }$

Question 3

Find the probability for the experiment of tossing a six-sided die twice.  
The sum is at least 8.

Accepted Answer

A)  $\frac { 7 } { 12 }$ 
B)  $\frac { 11 } { 12 }$ 
C)  $\frac { 13 } { 19 }$ 
D)  $\frac { 19 } { 12 }$ 
E)  $\frac { 5 } { 12 }$ 
A)  $\frac { 7 } { 12 }$ 
B)  $\frac { 11 } { 12 }$ 
C)  $\frac { 13 } { 19 }$ 
D)  $\frac { 19 } { 12 }$ 
E)  $\frac { 5 } { 12 }$

Question 4

Find the probability for the experiment of tossing a coin three times.Use the sample space  
 S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
 
The probability of getting exactly one tail.

Accepted Answer

A)   $\frac { 3 } { 8 }$ 
B)   $\frac { 1 } { 4 }$ 
C)   $\frac { 1 } { 2 }$ 
D)   $\frac { 8 } { 3 }$ 
E)  2 
A)   $\frac { 3 } { 8 }$ 
B)   $\frac { 1 } { 4 }$ 
C)   $\frac { 1 } { 2 }$ 
D)   $\frac { 8 } { 3 }$ 
E)  2

Question 5

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.)   $a _ { 1 } = 7 , r = \sqrt { 3 } , n = 8$

Accepted Answer

A)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n - 1 }$ , About 15.456 
B)  $a _ { n } = ( \sqrt { 3 } ) ^ { n - 1 }$ , About 982.073 
C)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n + 1 }$ , About 327.358 
D)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n - 1 }$ , About 327.358 
E)  $a _ { n } = ( \sqrt { 3 } ) ^ { n + 1 }$ , About 15.456 
A)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n - 1 }$ , About 15.456 
B)  $a _ { n } = ( \sqrt { 3 } ) ^ { n - 1 }$ , About 982.073 
C)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n + 1 }$ , About 327.358 
D)  $a _ { n } = 7 ( \sqrt { 3 } ) ^ { n - 1 }$ , About 327.358 
E)  $a _ { n } = ( \sqrt { 3 } ) ^ { n + 1 }$ , About 15.456

Question 6

Find the number of distinguishable permutations of the group of letters. G,A,U,S,S

Accepted Answer

A) ​15 
B) ​5 
C) ​120 
D) ​60 
E) ​30 
A) ​15 
B) ​5 
C) ​120 
D) ​60 
E) ​30

Question 7

Use sigma notation to write the sum. $\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
B)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { n ( n + 1 ) }$ 
C)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 2 ) ! }$ 
D)  $\sum _ { n = 1 } ^ { 4 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
E)  $\sum _ { n = 0 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
A)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
B)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { n ( n + 1 ) }$ 
C)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 2 ) ! }$ 
D)  $\sum _ { n = 1 } ^ { 4 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
E)  $\sum _ { n = 0 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$

Question 8

Find the sum of the finite geometric sequence.   $\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }$

Accepted Answer

A) 43 
B) 22 
C) 127 
D) 63 
E) 31 
A) 43 
B) 22 
C) 127 
D) 63 
E) 31

Question 9

Find the probability for the experiment of tossing a six-sided die twice.  
The sum is 7.

Accepted Answer

A)  $\frac { 36 } { 7 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 36 }$ 
D)  $\frac { 7 } { 36 }$ 
E) 6 
A)  $\frac { 36 } { 7 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 36 }$ 
D)  $\frac { 7 } { 36 }$ 
E) 6

Question 10

Use the Binomial Theorem to expand and simplify the expression.   $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$

Accepted Answer

A)  $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$ 
B)  $2 x ^ { 4 } + 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$ 
C)  $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x + 1375$ 
D)  $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x - 1375$ 
E)  $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x - 1375$ 
A)  $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$ 
B)  $2 x ^ { 4 } + 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$ 
C)  $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x + 1375$ 
D)  $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x - 1375$ 
E)  $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x - 1375$

Question 11

The probability that a basketball player will make a given free throw is $\frac { 7 } { 10 }$ .To find the probability that the player makes exactly 7 out of her next 10 free throws, evaluate the term ${ } _ { 10 } C _ { 7 } \left( \frac { 7 } { 10 } \right) ^ { 7 } \left( \frac { 3 } { 10 } \right) ^ { 3 }$ in the expansion of $\left( \frac { 7 } { 10 } + \frac { 3 } { 10 } \right) ^ { 10 }$ .Round to four decimal places.

Accepted Answer

A) 0.0090 
B) 3.3897 
C) 0.0007 
D) 0.2668 
E) 9.8825 
A) 0.0090 
B) 3.3897 
C) 0.0007 
D) 0.2668 
E) 9.8825

Question 12

Use mathematical induction to solve for all positive integers n.   $5 + 9 + 13 + 17 + \ldots + ( 4 n + 1 ) = ?$

Accepted Answer

A)  $n ( 9 n + 3 )$ 
B)  $\frac { n ( 2 n + 3 ) } { 2 }$ 
C)  $n ( n + 3 )$ 
D)  $\frac { n ( n + 3 ) } { 9 }$ 
E)  $n ( 2 n + 3 )$ 
A)  $n ( 9 n + 3 )$ 
B)  $\frac { n ( 2 n + 3 ) } { 2 }$ 
C)  $n ( n + 3 )$ 
D)  $\frac { n ( n + 3 ) } { 9 }$ 
E)  $n ( 2 n + 3 )$

Question 13

Match the arithmetic sequence with its graph from the choices below. ​
​an = 35 - 3n
​

Accepted Answer

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

Question 14

Evaluate: ${ } _ { 9 } P _ { 5 }$

Accepted Answer

A) undefined 
B) 45 
C) 15,120 
D) 3,024 
E) 126 
A) undefined 
B) 45 
C) 15,120 
D) 3,024 
E) 126

Question 15

A college sent a survey to a sample of juniors.Of the 512 students surveyed, 279 live on campus, of whom 110 have a GPA of 2.5 or greater.The other 233 juniors live off-campus, of whom 85 have a GPA of 2.5 or greater.What is the probability that a survey participant chosen at random lives on campus and has a GPA of 2.5 or greater?

Accepted Answer

A)  $\frac { 279 } { 512 }$ 
B)  $\frac { 22 } { 39 }$ 
C)  $\frac { 110 } { 279 }$ 
D)  $\frac { 195 } { 512 }$ 
E)  $\frac { 55 } { 256 }$ 
A)  $\frac { 279 } { 512 }$ 
B)  $\frac { 22 } { 39 }$ 
C)  $\frac { 110 } { 279 }$ 
D)  $\frac { 195 } { 512 }$ 
E)  $\frac { 55 } { 256 }$

Question 16

Simplify the factorial expression. $\frac { 9 ! } { 6 ! }$

Accepted Answer

A)  5040 
B)  504 
C)  3024 
D)  72 
E)   $\frac { 3 } { 2 }$ 
A)  5040 
B)  504 
C)  3024 
D)  72 
E)   $\frac { 3 } { 2 }$

Question 17

The first two terms of the arithmetic sequence are given.Find the missing term.  
A1 = -0.6, a2 = -12.8, a8 =

Accepted Answer

A) -86 
B) 61.6 
C) 122.6 
D) -98.2 
E) -73.8 
A) -86 
B) 61.6 
C) 122.6 
D) -98.2 
E) -73.8

Question 18

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 8.1 million in 2007 and let $a = 8.1 \%$ , $b = 17.8 \%$ , $c = 9.8 \%$ and $d = 16 \%$ .Find the probability that a person 25 years or older selected at random has earned an Associate's degree or higher.

Accepted Answer

A) 0.357 
B) 0.457 
C) 0.757 
D) 0.657 
E) 0.557 
A) 0.357 
B) 0.457 
C) 0.757 
D) 0.657 
E) 0.557

Question 19

The first two terms of the arithmetic sequence are given.Find the missing term.  
A1 = 7, a2 = 11, a10 =

Accepted Answer

A) 39 
B) 31 
C) 43 
D) 47 
E) 35 
A) 39 
B) 31 
C) 43 
D) 47 
E) 35

Question 20

Determine whether the sequence is arithmetic.If so, find the common difference. ​
​16, 14, 12, 10, 8, ...
​

Accepted Answer

A) Arithmetic sequence, d = -8 
B) Arithmetic sequence, d = 2 
C) Arithmetic sequence, d = ​4 
D) Arithmetic sequence, d = -2 
E) Not an arithmetic sequence 
A) Arithmetic sequence, d = -8 
B) Arithmetic sequence, d = 2 
C) Arithmetic sequence, d = ​4 
D) Arithmetic sequence, d = -2 
E) Not an arithmetic sequence

Find a formula for a_n for the arithmetic sequence. a₃ = 94, a₆ = 87

Use mathematical induction to solve for all positive integers n. $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = ?$

Find the probability for the experiment of tossing a six-sided die twice. The sum is at least 8.

Find the probability for the experiment of tossing a coin three times.Use the sample space S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} The probability of getting exactly one tail.

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.) $a _ { 1 } = 7 , r = \sqrt { 3 } , n = 8$

Find the number of distinguishable permutations of the group of letters. G,A,U,S,S

Use sigma notation to write the sum. $\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$

Find the sum of the finite geometric sequence. $\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }$

Find the probability for the experiment of tossing a six-sided die twice. The sum is 7.

Use the Binomial Theorem to expand and simplify the expression. $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$

Use mathematical induction to solve for all positive integers n. $5 + 9 + 13 + 17 + \ldots + ( 4 n + 1 ) = ?$

Match the arithmetic sequence with its graph from the choices below. a_n = 35 - 3n

Evaluate: ${ } _ { 9 } P _ { 5 }$

Simplify the factorial expression. $\frac { 9 ! } { 6 ! }$

The first two terms of the arithmetic sequence are given.Find the missing term. A₁ = -0.6, a₂ = -12.8, a₈ =

The first two terms of the arithmetic sequence are given.Find the missing term. A₁ = 7, a₂ = 11, a₁₀ =

Determine whether the sequence is arithmetic.If so, find the common difference. 16, 14, 12, 10, 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

Exam 9: Sequences Series and Probability

Find a formula for an for the arithmetic sequence. a3 = 94, a6 = 87

Use mathematical induction to solve for all positive integers n. ∑i=1ni(i+4)=?\sum _ { i = 1 } ^ { n } i ( i + 4 ) = ?∑i=1n​i(i+4)=?

Find the probability for the experiment of tossing a six-sided die twice. The sum is at least 8.

Find the probability for the experiment of tossing a coin three times.Use the sample space S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} The probability of getting exactly one tail.

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.) a1=7,r=3,n=8a _ { 1 } = 7 , r = \sqrt { 3 } , n = 8a1​=7,r=3​,n=8

Find the number of distinguishable permutations of the group of letters. G,A,U,S,S

Use sigma notation to write the sum. 13⋅2+14⋅3+…+18⋅7\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }3⋅21​+4⋅31​+…+8⋅71​

Find the sum of the finite geometric sequence. ∑n=172n−1\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }∑n=17​2n−1

Find the probability for the experiment of tossing a six-sided die twice. The sum is 7.

Use the Binomial Theorem to expand and simplify the expression. 2(x−5)4+5(x−5)22 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }2(x−5)4+5(x−5)2

Use mathematical induction to solve for all positive integers n. 5+9+13+17+…+(4n+1)=?5 + 9 + 13 + 17 + \ldots + ( 4 n + 1 ) = ?5+9+13+17+…+(4n+1)=?

Match the arithmetic sequence with its graph from the choices below. ​ ​an = 35 - 3n ​

Evaluate: 9P5{ } _ { 9 } P _ { 5 }9​P5​

Simplify the factorial expression. 9!6!\frac { 9 ! } { 6 ! }6!9!​

The first two terms of the arithmetic sequence are given.Find the missing term. A1 = -0.6, a2 = -12.8, a8 =

The first two terms of the arithmetic sequence are given.Find the missing term. A1 = 7, a2 = 11, a10 =

Determine whether the sequence is arithmetic.If so, find the common difference. ​ ​16, 14, 12, 10, 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

Find a formula for a_n for the arithmetic sequence. a₃ = 94, a₆ = 87

Use mathematical induction to solve for all positive integers n. $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = ?$

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.) $a _ { 1 } = 7 , r = \sqrt { 3 } , n = 8$

Use sigma notation to write the sum. $\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$

Find the sum of the finite geometric sequence. $\sum _ { n = 1 } ^ { 7 } 2 ^ { n - 1 }$

Use the Binomial Theorem to expand and simplify the expression. $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$

Use mathematical induction to solve for all positive integers n. $5 + 9 + 13 + 17 + \ldots + ( 4 n + 1 ) = ?$

Match the arithmetic sequence with its graph from the choices below. a_n = 35 - 3n

Evaluate: ${ } _ { 9 } P _ { 5 }$

Simplify the factorial expression. $\frac { 9 ! } { 6 ! }$

The first two terms of the arithmetic sequence are given.Find the missing term. A₁ = -0.6, a₂ = -12.8, a₈ =

The first two terms of the arithmetic sequence are given.Find the missing term. A₁ = 7, a₂ = 11, a₁₀ =

Determine whether the sequence is arithmetic.If so, find the common difference. 16, 14, 12, 10, 8, ...