Question 1

Write the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = - 8 n + 8$

Accepted Answer

A) -16, -24, -40, -40, -48 
B) 8, 0, -8, -16, -24 
C) 0, -16, -24, -32, -40 
D) 0, -8, -16, -24, -32 
E) 0, 8, 16, 24, 32 
A) -16, -24, -40, -40, -48 
B) 8, 0, -8, -16, -24 
C) 0, -16, -24, -32, -40 
D) 0, -8, -16, -24, -32 
E) 0, 8, 16, 24, 32

Question 2

Select the first five terms of the sequence.(Assume that n begins with 1.)   $a _ { n } = 4 ^ { n }$

Accepted Answer

A)  $1,4,16,64,256$ 
B)  $4,8,64,16,1024$ 
C)  $4,16,64,256,1024$ 
D)  $4,8,12,16,20$ 
E)  $4,8,12,64,20$ 
A)  $1,4,16,64,256$ 
B)  $4,8,64,16,1024$ 
C)  $4,16,64,256,1024$ 
D)  $4,8,12,16,20$ 
E)  $4,8,12,64,20$

Question 3

Determine whether the sequence is arithmetic.If so, find the common difference. 5, 25, 125, 625, 3125

Accepted Answer

A) -5 
B) 5 
C) 5n - 5n - 1 
D) not arithmetic 
E) ​5n 
A) -5 
B) 5 
C) 5n - 5n - 1 
D) not arithmetic 
E) ​5n

Question 4

Determine whether the sequence is arithmetic.If so, find the common difference. ​
​ln4, ln5, ln6, ln7, ln8, ...
​

Accepted Answer

A) Arithmetic sequence, d = 0.41 
B) Arithmetic sequence, d = -0.22 
C) Arithmetic sequence, d = -0.56 
D) Arithmetic sequence, d = 0.22 
E) Not an arithmetic sequence 
A) Arithmetic sequence, d = 0.41 
B) Arithmetic sequence, d = -0.22 
C) Arithmetic sequence, d = -0.56 
D) Arithmetic sequence, d = 0.22 
E) Not an arithmetic sequence

Question 5

Find the probability for the experiment of tossing a coin two times.Use the sample space  
 S = {HH,HT,TH,TT}
 
The probability of getting exactly two tails.

Accepted Answer

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

Question 6

Solve for n.   $56 ^ { n } n - 1 P _ { 6 } = { } _ { n + 1 } P _ { 7 }$

Accepted Answer

A) no solution 
B)  n = 7 
C)  n = 7, 48 
D)  n = 8, 47 
E)  n = 48 
A) no solution 
B)  n = 7 
C)  n = 7, 48 
D)  n = 8, 47 
E)  n = 48

Question 7

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​
An = 5 - 6(n - 4)
​

Accepted Answer

A) -13, -7, -1, 5, 11Arithmetic sequenced = -6 
B) -1, 5, 11, 17, 23Arithmetic sequenced = -6 
C) 23, 17, 11, 5, -1Arithmetic sequenced = 6 
D) 11, 5, -1, -7, -13Arithmetic sequenced = 6 
E) 23, 17, 11, 5, -1Arithmetic sequenced = -6 
A) -13, -7, -1, 5, 11Arithmetic sequenced = -6 
B) -1, 5, 11, 17, 23Arithmetic sequenced = -6 
C) 23, 17, 11, 5, -1Arithmetic sequenced = 6 
D) 11, 5, -1, -7, -13Arithmetic sequenced = 6 
E) 23, 17, 11, 5, -1Arithmetic sequenced = -6

Question 8

Write the first five terms of the arithmetic sequence defined recursively. ​
A1 = 17, an + 1 = an + 4
​
​

Accepted Answer

A) 17, 21, 25, 29, 33 
B) -17, -21, -25, -29, -33 
C) 17, 21, 25, 29, 41 
D) -17, -21, -25, -29, -37 
E) 17, 21, 25, 29, 37 
A) 17, 21, 25, 29, 33 
B) -17, -21, -25, -29, -33 
C) 17, 21, 25, 29, 41 
D) -17, -21, -25, -29, -37 
E) 17, 21, 25, 29, 37

Question 9

Evaluate ${ } _ { n } P _ { r }$ .   $40 P _ { 5 }$

Accepted Answer

A) 2,193,360 
B) 658,008 
C) 59,280 
D) 78,960,960 
E) 2,763,633,600 
A) 2,193,360 
B) 658,008 
C) 59,280 
D) 78,960,960 
E) 2,763,633,600

Question 10

Change the decimal to a common fraction.   $0 . \overline { 5 }$

Accepted Answer

A)  $\frac { 5 } { 90 }$ 
B)  $\frac { 5 } { 99 }$ 
C)  $\frac { 5 } { 9999 }$ 
D)  $\frac { 5 } { 9 }$ 
E)  $\frac { 5 } { 999 }$ 
A)  $\frac { 5 } { 90 }$ 
B)  $\frac { 5 } { 99 }$ 
C)  $\frac { 5 } { 9999 }$ 
D)  $\frac { 5 } { 9 }$ 
E)  $\frac { 5 } { 999 }$

Question 11

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 14 } n$

Accepted Answer

A) 11,025 
B) 210 
C) 6,090 
D) 105 
E) 1,015 
A) 11,025 
B) 210 
C) 6,090 
D) 105 
E) 1,015

Question 12

Determine the sample space for the experiment. ​
A six-sided die is tossed twice and the sum of the results is recorded.
​

Accepted Answer

A) ​{2,3,...,12} 
B) ​{3,4,...,6} 
C) ​{1,2,...,6} 
D) ​{1,2,...,6}. 
E) ​{3,4,...,18} 
A) ​{2,3,...,12} 
B) ​{3,4,...,6} 
C) ​{1,2,...,6} 
D) ​{1,2,...,6}. 
E) ​{3,4,...,18}

Question 13

Find the indicated nth term of the geometric sequence.  
7th term: $a _ { 4 } = - \frac { 4 } { 27 } , a _ { 10 } = - \frac { 4 } { 19,683 }$

Accepted Answer

A)   $\frac { 4 } { 6,561 }$ 
B)   $- \frac { 4 } { 243 }$ 
C)   $- \frac { 3 } { 4,096 }$ 
D)   $\frac { 4 } { 729 }$ 
E)   $- \frac { 4 } { 2,187 }$ 
A)   $\frac { 4 } { 6,561 }$ 
B)   $- \frac { 4 } { 243 }$ 
C)   $- \frac { 3 } { 4,096 }$ 
D)   $\frac { 4 } { 729 }$ 
E)   $- \frac { 4 } { 2,187 }$

Question 14

Find the sum of the finite geometric sequence.(Round your answer to three decimal places.)   $\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }$

Accepted Answer

A) 2,092.596 
B) 1,691.128 
C) 340.518 
D) 352.212 
E) 1,312.385 
A) 2,092.596 
B) 1,691.128 
C) 340.518 
D) 352.212 
E) 1,312.385

Question 15

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 5 \right) ^ { 4 }$

Accepted Answer

A)  $x ^ { 3 } + 625$ 
B)  $x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x + 500 x ^ { 3 / 4 } + 625$ 
C)  $x ^ { 3 } + 20 x ^ { 9 / 5 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625$ 
D)  $x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625$ 
E)  $- x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x + 625$ 
A)  $x ^ { 3 } + 625$ 
B)  $x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x + 500 x ^ { 3 / 4 } + 625$ 
C)  $x ^ { 3 } + 20 x ^ { 9 / 5 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625$ 
D)  $x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625$ 
E)  $- x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x + 625$

Question 16

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing two green, five yellow, and three red marbles such that the marbles are different colors.

Accepted Answer

A)   $\frac { 31 } { 90 }$ 
B)   $\frac { 31 } { 15 }$ 
C)   $\frac { 31 } { 45 }$ 
D)   $\frac { 1 } { 5 }$ 
E)   $\frac { 62 } { 9 }$ 
A)   $\frac { 31 } { 90 }$ 
B)   $\frac { 31 } { 15 }$ 
C)   $\frac { 31 } { 45 }$ 
D)   $\frac { 1 } { 5 }$ 
E)   $\frac { 62 } { 9 }$

Question 17

Determine whether the sequence is arithmetic.If so, find the common difference. ​
​128, 64, 32, 16, 8, ...
​

Accepted Answer

A) Arithmetic sequence, d = -120 
B) Arithmetic sequence, d = -8 
C) Arithmetic sequence, d = 8 
D) Arithmetic sequence, d = 24 
E) Not an arithmetic sequence 
A) Arithmetic sequence, d = -120 
B) Arithmetic sequence, d = -8 
C) Arithmetic sequence, d = 8 
D) Arithmetic sequence, d = 24 
E) Not an arithmetic sequence

Question 18

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = \frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$

Accepted Answer

1) When n = 1, @#IMG-DLM& or @#IMG-DLM& .
The form

Question 19

Determine the number of ways a computer can randomly generate an integer between 10 and 20 (inclusive) that is a composite number (a composite number is a number that is not a prime number).

Accepted Answer

A) ​8 
B) ​6 
C) 7 
D) 6 
E) 9 
A) ​8 
B) ​6 
C) 7 
D) 6 
E) 9

Question 20

Use the binomial theorem to expand the binomial.   $( c + y ) ^ { 4 }$

Accepted Answer

A)  $c ^ { 4 } + 4 c ^ { 3 } y + 6 c ^ { 2 } y ^ { 2 } + 4 c y ^ { 3 } + y ^ { 4 }$ 
B)  $c ^ { 4 } + y ^ { 4 }$ 
C)  $c ^ { 4 } + c ^ { 3 } y + c ^ { 2 } y ^ { 2 } + c y ^ { 3 } + y ^ { 4 }$ 
D)  $c ^ { 4 } + 6 c ^ { 3 } y + 6 c ^ { 2 } y ^ { 2 } + 4 c y ^ { 3 } + y ^ { 4 }$ 
E)  $c ^ { 4 } + 3 c ^ { 3 } y + 3 c y ^ { 3 } + y ^ { 4 }$ 
A)  $c ^ { 4 } + 4 c ^ { 3 } y + 6 c ^ { 2 } y ^ { 2 } + 4 c y ^ { 3 } + y ^ { 4 }$ 
B)  $c ^ { 4 } + y ^ { 4 }$ 
C)  $c ^ { 4 } + c ^ { 3 } y + c ^ { 2 } y ^ { 2 } + c y ^ { 3 } + y ^ { 4 }$ 
D)  $c ^ { 4 } + 6 c ^ { 3 } y + 6 c ^ { 2 } y ^ { 2 } + 4 c y ^ { 3 } + y ^ { 4 }$ 
E)  $c ^ { 4 } + 3 c ^ { 3 } y + 3 c y ^ { 3 } + y ^ { 4 }$

Write the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = - 8 n + 8$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = 4 ^ { n }$

Determine whether the sequence is arithmetic.If so, find the common difference. 5, 25, 125, 625, 3125

Determine whether the sequence is arithmetic.If so, find the common difference. ln4, ln5, ln6, ln7, ln8, ...

Find the probability for the experiment of tossing a coin two times.Use the sample space S = {HH,HT,TH,TT} The probability of getting exactly two tails.

Solve for n. $56 ^ { n } n - 1 P _ { 6 } = { } _ { n + 1 } P _ { 7 }$

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = 5 - 6(n - 4)

Write the first five terms of the arithmetic sequence defined recursively. A₁ = 17, an_{+ 1} = a_n + 4

Evaluate ${ } _ { n } P _ { r }$ . $40 P _ { 5 }$

Change the decimal to a common fraction. $0 . \overline { 5 }$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 14 } n$

Determine the sample space for the experiment. A six-sided die is tossed twice and the sum of the results is recorded.

Find the indicated nth term of the geometric sequence. 7th term: $a _ { 4 } = - \frac { 4 } { 27 } , a _ { 10 } = - \frac { 4 } { 19,683 }$

Find the sum of the finite geometric sequence.(Round your answer to three decimal places.) $\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }$

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 5 \right) ^ { 4 }$

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing two green, five yellow, and three red marbles such that the marbles are different colors.

Determine whether the sequence is arithmetic.If so, find the common difference. 128, 64, 32, 16, 8, ...

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = \frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$

Determine the number of ways a computer can randomly generate an integer between 10 and 20 (inclusive) that is a composite number (a composite number is a number that is not a prime number).

Use the binomial theorem to expand the binomial. $( c + y ) ^ { 4 }$

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 five terms of the sequence.(Assume that n begins with 1.) an=−8n+8a _ { n } = - 8 n + 8an​=−8n+8

Select the first five terms of the sequence.(Assume that n begins with 1.) an=4na _ { n } = 4 ^ { n }an​=4n

Determine whether the sequence is arithmetic.If so, find the common difference. 5, 25, 125, 625, 3125

Determine whether the sequence is arithmetic.If so, find the common difference. ​ ​ln4, ln5, ln6, ln7, ln8, ... ​

Find the probability for the experiment of tossing a coin two times.Use the sample space S = {HH,HT,TH,TT} The probability of getting exactly two tails.

Solve for n. 56nn−1P6=n+1P756 ^ { n } n - 1 P _ { 6 } = { } _ { n + 1 } P _ { 7 }56nn−1P6​=n+1​P7​

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​ An = 5 - 6(n - 4) ​

Write the first five terms of the arithmetic sequence defined recursively. ​ A1 = 17, an + 1 = an + 4 ​ ​

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ . 40P540 P _ { 5 }40P5​

Change the decimal to a common fraction. 0.5‾0 . \overline { 5 }0.5

Find the sum using the formulas for the sums of powers of integers. ∑n=114n\sum _ { n = 1 } ^ { 14 } n∑n=114​n

Determine the sample space for the experiment. ​ A six-sided die is tossed twice and the sum of the results is recorded. ​

Find the indicated nth term of the geometric sequence. 7th term: a4=−427,a10=−419,683a _ { 4 } = - \frac { 4 } { 27 } , a _ { 10 } = - \frac { 4 } { 19,683 }a4​=−274​,a10​=−19,6834​

Find the sum of the finite geometric sequence.(Round your answer to three decimal places.) ∑n=05300(1.06)n\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }∑n=05​300(1.06)n

Use the Binomial Theorem to expand and simplify the expression. (x3/4+5)4\left( x ^ { 3 / 4 } + 5 \right) ^ { 4 }(x3/4+5)4

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing two green, five yellow, and three red marbles such that the marbles are different colors.

Determine whether the sequence is arithmetic.If so, find the common difference. ​ ​128, 64, 32, 16, 8, ... ​

Use mathematical induction to prove the formula for every positive integer n.Show all your work. ∑i=1ni(i+4)=n(n+1)(2n+13)6\sum _ { i = 1 } ^ { n } i ( i + 4 ) = \frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }∑i=1n​i(i+4)=6n(n+1)(2n+13)​

Determine the number of ways a computer can randomly generate an integer between 10 and 20 (inclusive) that is a composite number (a composite number is a number that is not a prime number).

Use the binomial theorem to expand the binomial. (c+y)4( c + y ) ^ { 4 }(c+y)4

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 five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = - 8 n + 8$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = 4 ^ { n }$

Determine whether the sequence is arithmetic.If so, find the common difference. ln4, ln5, ln6, ln7, ln8, ...

Solve for n. $56 ^ { n } n - 1 P _ { 6 } = { } _ { n + 1 } P _ { 7 }$

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = 5 - 6(n - 4)

Write the first five terms of the arithmetic sequence defined recursively. A₁ = 17, an_{+ 1} = a_n + 4

Evaluate ${ } _ { n } P _ { r }$ . $40 P _ { 5 }$

Change the decimal to a common fraction. $0 . \overline { 5 }$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 14 } n$

Determine the sample space for the experiment. A six-sided die is tossed twice and the sum of the results is recorded.

Find the indicated nth term of the geometric sequence. 7th term: $a _ { 4 } = - \frac { 4 } { 27 } , a _ { 10 } = - \frac { 4 } { 19,683 }$

Find the sum of the finite geometric sequence.(Round your answer to three decimal places.) $\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }$

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 5 \right) ^ { 4 }$

Determine whether the sequence is arithmetic.If so, find the common difference. 128, 64, 32, 16, 8, ...

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = \frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$

Use the binomial theorem to expand the binomial. $( c + y ) ^ { 4 }$