Question 1

Find the sum of the finite geometric sequence.(Round your answer to three decimal places.)   $\sum _ { n = 0 } ^ { 6 } 900 ( 1.04 ) ^ { n }$

Accepted Answer

A) 999.405 
B) 5,969.678 
C) 7,108.465 
D) 4,874.690 
E) 1,021.735 
A) 999.405 
B) 5,969.678 
C) 7,108.465 
D) 4,874.690 
E) 1,021.735 C

Question 2

Find the specified nth term in the expansion of the binomial.   $( 4 a + 5 b ) ^ { 5 } , n = 5$

Accepted Answer

A)  $12,500 a b ^ { 4 }$ 
B)  $12,500 a b$ 
C)  $12,500 a ^ { 4 } b$ 
D)  $12,500 a ^ { 4 } b ^ { 4 }$ 
E)  $12,500 a ^ { 5 } b ^ { 5 }$ 
A)  $12,500 a b ^ { 4 }$ 
B)  $12,500 a b$ 
C)  $12,500 a ^ { 4 } b$ 
D)  $12,500 a ^ { 4 } b ^ { 4 }$ 
E)  $12,500 a ^ { 5 } b ^ { 5 }$ A

Question 3

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 243.32 million in 2007.Estimate the number of people 25 years or older who have advanced degrees.Round your anser to two decimal places. ​   ​

Accepted Answer

A) 24.09 million 
B) 64.09 million 
C) 44.09 million 
D) 54.09 million 
E) 34.09 million 
A) 24.09 million 
B) 64.09 million 
C) 44.09 million 
D) 54.09 million 
E) 34.09 million A

Question 4

A customer can choose one of two amplifiers, one of three compact disc players, and one of five speaker models for an entertainment system.Determine the number of possible system configurations. ​

Accepted Answer

A) 40 
B) 35 
C) ​30 
D) 25 
E) 20 
A) 40 
B) 35 
C) ​30 
D) 25 
E) 20

Question 5

Find a formula for an for the arithmetic sequence. ​
A1 = 4, d = 7
​

Accepted Answer

A) an ​= -7n + 11 
B) an ​= 7n - 3 
C) an ​= 7n + 3 
D) an ​= -7n ​+ 3 
E) an ​= 7n - 11 
A) an ​= -7n + 11 
B) an ​= 7n - 3 
C) an ​= 7n + 3 
D) an ​= -7n ​+ 3 
E) an ​= 7n - 11

Question 6

Assume that the sequence is defined recursively.Find the first three terms of the sequence.   $a _ { 1 } = 3 \text { and } a _ { n + 1 } = 4 a _ { n } ^ { 2 }$

Accepted Answer

A) 36 
B) 5184 
C) 3 
D) 4 
E) 32 
A) 36 
B) 5184 
C) 3 
D) 4 
E) 32

Question 7

Evaluate the expression.   $C ( 5,2 )$

Accepted Answer

A)  60 
B)  120 
C)  2 
D)  20 
E)  10 
A)  60 
B)  120 
C)  2 
D)  20 
E)  10

Question 8

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 9 } n ^ { 3 }$

Accepted Answer

A) 729 
B) 285 
C) 4050 
D) 1296 
E) 2025 
A) 729 
B) 285 
C) 4050 
D) 1296 
E) 2025

Question 9

Find the specified nth term in the expansion of the binomial.  $( 4 x + 3 y ) ^ { 9 } , n = 8$

Accepted Answer

A)  $1,259,712 x ^ { 7 } y ^ { 2 }$ 
B)  $1,259,712 x ^ { 2 } y ^ { 7 }$ 
C)  $1,259,712 x ^ { 8 } y ^ { 9 }$ 
D)  $1,259,712 x ^ { 2 } y ^ { 2 }$ 
E)  $1,259,712 x ^ { 7 } y ^ { 7 }$ 
A)  $1,259,712 x ^ { 7 } y ^ { 2 }$ 
B)  $1,259,712 x ^ { 2 } y ^ { 7 }$ 
C)  $1,259,712 x ^ { 8 } y ^ { 9 }$ 
D)  $1,259,712 x ^ { 2 } y ^ { 2 }$ 
E)  $1,259,712 x ^ { 7 } y ^ { 7 }$

Question 10

Use the Binomial Theorem to expand the complex number.Simplify your result.   $( 3 - i ) ^ { 5 }$

Accepted Answer

A)  $405 i + 12$ 
B)  $90 i + 12$ 
C)  $316 i + 405$ 
D)  $- 12 - 316 i$ 
E)  $316 + 12 i$ 
A)  $405 i + 12$ 
B)  $90 i + 12$ 
C)  $316 i + 405$ 
D)  $- 12 - 316 i$ 
E)  $316 + 12 i$

Question 11

Find a formula for an for the arithmetic sequence.   $a _ { 3 } = 0 , a _ { 9 } = - 12$

Accepted Answer

A) an  = 4 - 2n 
B) an  = -6 + 4n 
C) an  = - 2 + 4n 
D) an  = 6 - 2n 
E) an  = 4n 
A) an  = 4 - 2n 
B) an  = -6 + 4n 
C) an  = - 2 + 4n 
D) an  = 6 - 2n 
E) an  = 4n

Question 12

Find a formula for an ​for the arithmetic sequence. ​
A1 = 104, d = -6
​

Accepted Answer

A) an ​= -6n + 98 
B) an ​= 6n + 110 
C) an ​= 6n - 98 
D) an ​= 6n - 110 
E) an ​= -6n + 110 
A) an ​= -6n + 98 
B) an ​= 6n + 110 
C) an ​= 6n - 98 
D) an ​= 6n - 110 
E) an ​= -6n + 110

Question 13

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( 2 x - 5 y ) ^ { 8 }$ $a x ^ { 3 } y ^ { 5 }$

Accepted Answer

A)  $a = - 224000$ 
B)  $a = 336$ 
C)  $a = 40$ 
D)  $a = 8$ 
E)  $a = 390,625$ 
A)  $a = - 224000$ 
B)  $a = 336$ 
C)  $a = 40$ 
D)  $a = 8$ 
E)  $a = 390,625$

Question 14

Determine whether the sequence is geometric.If so, find the common ratio.   $55,50,45,40 , \ldots$

Accepted Answer

A) Geometric sequence, $r = 4$ 
B) Geometric sequence, $r = 6$ 
C) Geometric sequence, $r = 5$ 
D) Geometric sequence, $r = 7$ 
E) Not a geometric sequence 
A) Geometric sequence, $r = 4$ 
B) Geometric sequence, $r = 6$ 
C) Geometric sequence, $r = 5$ 
D) Geometric sequence, $r = 7$ 
E) Not a geometric sequence

Question 15

Select the first five terms of the sequence.(Assume that n begins with 1.)   $a _ { n } = 5 n - 6$

Accepted Answer

A)  $0 , - 1,4,9,14$ 
B)  $- 1,4,9,14,19$ 
C)  $5 , - 1,15,9,25$ 
D)  $5,10,15,20,25$ 
E)  $5,4,15,14,25$ 
A)  $0 , - 1,4,9,14$ 
B)  $- 1,4,9,14,19$ 
C)  $5 , - 1,15,9,25$ 
D)  $5,10,15,20,25$ 
E)  $5,4,15,14,25$

Question 16

Find pk + 1 for the given pk.   $p _ { k } = \frac { k } { 5 } ( 8 k + 1 )$

Accepted Answer

A)  $p _ { k + 1 } = \frac { k + 1 } { 5 } ( 8 k + 5 )$ 
B)  $p _ { k + 1 } = \frac { k + 1 } { 5 } ( 8 k + 6 )$ 
C)  $p _ { k + 1 } = \frac { k + 1 } { 6 } ( 8 k + 6 )$ 
D)  $p _ { k + 1 } = \frac { k + 1 } { 5 } ( 8 k + 9 )$ 
E)  $p _ { k + 1 } = \frac { k + 1 } { 6 } ( 8 k + 9 )$ 
A)  $p _ { k + 1 } = \frac { k + 1 } { 5 } ( 8 k + 5 )$ 
B)  $p _ { k + 1 } = \frac { k + 1 } { 5 } ( 8 k + 6 )$ 
C)  $p _ { k + 1 } = \frac { k + 1 } { 6 } ( 8 k + 6 )$ 
D)  $p _ { k + 1 } = \frac { k + 1 } { 5 } ( 8 k + 9 )$ 
E)  $p _ { k + 1 } = \frac { k + 1 } { 6 } ( 8 k + 9 )$

Question 17

Calculate the binomial coefficient.   ${ } _ { 6 } C _ { 4 }$

Accepted Answer

A) 16 
B) 15 
C) 17 
D) 14 
E) 13 
A) 16 
B) 15 
C) 17 
D) 14 
E) 13

Question 18

Find the sum of the infinite geometric series.   $\sum _ { n = 0 } ^ { \infty } 7 \left( \frac { 1 } { 3 } \right) ^ { n }$

Accepted Answer

A)   $\frac { 2 } { 21 }$ 
B)   $\frac { 2 } { 7 }$ 
C)   $- \frac { 1 } { 3 }$ 
D)   $\frac { 21 } { 2 }$ 
E)  undefined 
A)   $\frac { 2 } { 21 }$ 
B)   $\frac { 2 } { 7 }$ 
C)   $- \frac { 1 } { 3 }$ 
D)   $\frac { 21 } { 2 }$ 
E)  undefined

Question 19

The figure shows the results of a recent survey in which 14 adults were asked to grade U.S.public schools.An adult is selected at random.What is the probability the adult will give the U.S.public schools a C or a D
 ( $a = 14 \%$ , $b = 50 \%$ )

Accepted Answer

A)  $\frac { 16 } { 25 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 50 } { 7 }$ 
D)  $\frac { 25 } { 16 }$ 
E)  $\frac { 7 } { 50 }$ 
A)  $\frac { 16 } { 25 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 50 } { 7 }$ 
D)  $\frac { 25 } { 16 }$ 
E)  $\frac { 7 } { 50 }$

Question 20

Use mathematical induction to solve for all positive integers n.   $22 + 27 + 32 + 37 + \ldots + ( 5 n - 17 ) = ?$

Accepted Answer

A)  $\frac { n } { 2 } ( 5 n + 5 )$ 
B)  $n ( 22 n + 1 )$ 
C)  $\frac { n ( n + 1 ) } { 22 }$ 
D)  $n ( n + 22 )$ 
E)  $\frac { n } { 2 } ( 5 n + 1 )$ 
A)  $\frac { n } { 2 } ( 5 n + 5 )$ 
B)  $n ( 22 n + 1 )$ 
C)  $\frac { n ( n + 1 ) } { 22 }$ 
D)  $n ( n + 22 )$ 
E)  $\frac { n } { 2 } ( 5 n + 1 )$

Find the sum of the finite geometric sequence.(Round your answer to three decimal places.) $\sum _ { n = 0 } ^ { 6 } 900 ( 1.04 ) ^ { n }$

Find the specified nth term in the expansion of the binomial. $( 4 a + 5 b ) ^ { 5 } , n = 5$

A customer can choose one of two amplifiers, one of three compact disc players, and one of five speaker models for an entertainment system.Determine the number of possible system configurations.

Find a formula for a_n for the arithmetic sequence. A₁ = 4, d = 7

Assume that the sequence is defined recursively.Find the first three terms of the sequence. $a _ { 1 } = 3 \text { and } a _ { n + 1 } = 4 a _ { n } ^ { 2 }$

Evaluate the expression. $C ( 5,2 )$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 9 } n ^ { 3 }$

Find the specified nth term in the expansion of the binomial. $( 4 x + 3 y ) ^ { 9 } , n = 8$

Use the Binomial Theorem to expand the complex number.Simplify your result. $( 3 - i ) ^ { 5 }$

Find a formula for a_n for the arithmetic sequence. $a _ { 3 } = 0 , a _ { 9 } = - 12$

Find a formula for a_nfor the arithmetic sequence. A₁ = 104, d = -6

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( 2 x - 5 y ) ^ { 8 }$ $a x ^ { 3 } y ^ { 5 }$

Determine whether the sequence is geometric.If so, find the common ratio. $55,50,45,40 , \ldots$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = 5 n - 6$

Find pk_{+ 1} for the given p_k. $p _ { k } = \frac { k } { 5 } ( 8 k + 1 )$

Calculate the binomial coefficient. ${ } _ { 6 } C _ { 4 }$

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } 7 \left( \frac { 1 } { 3 } \right) ^ { n }$

Use mathematical induction to solve for all positive integers n. $22 + 27 + 32 + 37 + \ldots + ( 5 n - 17 ) = ?$

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 the sum of the finite geometric sequence.(Round your answer to three decimal places.) ∑n=06900(1.04)n\sum _ { n = 0 } ^ { 6 } 900 ( 1.04 ) ^ { n }∑n=06​900(1.04)n

Find the specified nth term in the expansion of the binomial. (4a+5b)5,n=5( 4 a + 5 b ) ^ { 5 } , n = 5(4a+5b)5,n=5

A customer can choose one of two amplifiers, one of three compact disc players, and one of five speaker models for an entertainment system.Determine the number of possible system configurations. ​

Find a formula for an for the arithmetic sequence. ​ A1 = 4, d = 7 ​

Assume that the sequence is defined recursively.Find the first three terms of the sequence. a1=3 and an+1=4an2a _ { 1 } = 3 \text { and } a _ { n + 1 } = 4 a _ { n } ^ { 2 }a1​=3 and an+1​=4an2​

Evaluate the expression. C(5,2)C ( 5,2 )C(5,2)

Find the sum using the formulas for the sums of powers of integers. ∑n=19n3\sum _ { n = 1 } ^ { 9 } n ^ { 3 }∑n=19​n3

Find the specified nth term in the expansion of the binomial. (4x+3y)9,n=8( 4 x + 3 y ) ^ { 9 } , n = 8(4x+3y)9,n=8

Use the Binomial Theorem to expand the complex number.Simplify your result. (3−i)5( 3 - i ) ^ { 5 }(3−i)5

Find a formula for an for the arithmetic sequence. a3=0,a9=−12a _ { 3 } = 0 , a _ { 9 } = - 12a3​=0,a9​=−12

Find a formula for an ​for the arithmetic sequence. ​ A1 = 104, d = -6 ​

Find the coefficient a of the term in the expansion of the binomial. Binomial Term (2x−5y)8( 2 x - 5 y ) ^ { 8 }(2x−5y)8 ax3y5a x ^ { 3 } y ^ { 5 }ax3y5

Determine whether the sequence is geometric.If so, find the common ratio. 55,50,45,40,…55,50,45,40 , \ldots55,50,45,40,…

Select the first five terms of the sequence.(Assume that n begins with 1.) an=5n−6a _ { n } = 5 n - 6an​=5n−6

Find pk + 1 for the given pk. pk=k5(8k+1)p _ { k } = \frac { k } { 5 } ( 8 k + 1 )pk​=5k​(8k+1)

Calculate the binomial coefficient. 6C4{ } _ { 6 } C _ { 4 }6​C4​

Find the sum of the infinite geometric series. ∑n=0∞7(13)n\sum _ { n = 0 } ^ { \infty } 7 \left( \frac { 1 } { 3 } \right) ^ { n }∑n=0∞​7(31​)n

The figure shows the results of a recent survey in which 14 adults were asked to grade U.S.public schools.An adult is selected at random.What is the probability the adult will give the U.S.public schools a C or a D ( a=14%a = 14 \%a=14% , b=50%b = 50 \%b=50% )

Use mathematical induction to solve for all positive integers n. 22+27+32+37+…+(5n−17)=?22 + 27 + 32 + 37 + \ldots + ( 5 n - 17 ) = ?22+27+32+37+…+(5n−17)=?

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 the sum of the finite geometric sequence.(Round your answer to three decimal places.) $\sum _ { n = 0 } ^ { 6 } 900 ( 1.04 ) ^ { n }$

Find the specified nth term in the expansion of the binomial. $( 4 a + 5 b ) ^ { 5 } , n = 5$

A customer can choose one of two amplifiers, one of three compact disc players, and one of five speaker models for an entertainment system.Determine the number of possible system configurations.

Find a formula for a_n for the arithmetic sequence. A₁ = 4, d = 7

Assume that the sequence is defined recursively.Find the first three terms of the sequence. $a _ { 1 } = 3 \text { and } a _ { n + 1 } = 4 a _ { n } ^ { 2 }$

Evaluate the expression. $C ( 5,2 )$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 9 } n ^ { 3 }$

Find the specified nth term in the expansion of the binomial. $( 4 x + 3 y ) ^ { 9 } , n = 8$

Use the Binomial Theorem to expand the complex number.Simplify your result. $( 3 - i ) ^ { 5 }$

Find a formula for a_n for the arithmetic sequence. $a _ { 3 } = 0 , a _ { 9 } = - 12$

Find a formula for a_nfor the arithmetic sequence. A₁ = 104, d = -6

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( 2 x - 5 y ) ^ { 8 }$ $a x ^ { 3 } y ^ { 5 }$

Determine whether the sequence is geometric.If so, find the common ratio. $55,50,45,40 , \ldots$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = 5 n - 6$

Find pk_{+ 1} for the given p_k. $p _ { k } = \frac { k } { 5 } ( 8 k + 1 )$

Calculate the binomial coefficient. ${ } _ { 6 } C _ { 4 }$

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } 7 \left( \frac { 1 } { 3 } \right) ^ { n }$

Use mathematical induction to solve for all positive integers n. $22 + 27 + 32 + 37 + \ldots + ( 5 n - 17 ) = ?$