Question 1

Find the first five terms of the geometric sequence.   $a _ { 1 } = 4 , r = e$

Accepted Answer

A)  $4 , e , 2 e , 3 e , 4 e$ 
B)  $4 , e ^ { 2 } , e ^ { 3 } , e ^ { 4 } , e ^ { 5 }$ 
C)  $e , e , e , e , e$ 
D)  $4 , e , 2 e ^ { 2 } , 3 e ^ { 3 } , 4 e ^ { 4 }$ 
E)  $4,4 e , 4 e ^ { 2 } , 4 e ^ { 3 } , 4 e ^ { 4 }$ 
A)  $4 , e , 2 e , 3 e , 4 e$ 
B)  $4 , e ^ { 2 } , e ^ { 3 } , e ^ { 4 } , e ^ { 5 }$ 
C)  $e , e , e , e , e$ 
D)  $4 , e , 2 e ^ { 2 } , 3 e ^ { 3 } , 4 e ^ { 4 }$ 
E)  $4,4 e , 4 e ^ { 2 } , 4 e ^ { 3 } , 4 e ^ { 4 }$

Question 2

Find the indicated term of the sequence. $a _ { n } = ( - 1 ) ^ { n } ( 4 n - 2 )$ $a _ { 27 } =$

Accepted Answer

A) 102 
B) -106 
C) -110 
D) 6 
E) -104 
A) 102 
B) -106 
C) -110 
D) 6 
E) -104

Question 3

Evaluate the expression.
  $C ( 4,3 )$

Accepted Answer

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

Question 4

Use the Binominal Theorem to expand the complex number.Simplify your result.   $( 3 - 2 i ) ^ { 4 }$

Accepted Answer

A)   $- 135 + 344 i$ 
B)   $- 151 + 344 i$ 
C)   $- 135 - 88 i$ 
D)   $- 151 - 88 i$ 
E)   $313 - 88 i$ 
A)   $- 135 + 344 i$ 
B)   $- 151 + 344 i$ 
C)   $- 135 - 88 i$ 
D)   $- 151 - 88 i$ 
E)   $313 - 88 i$

Question 5

Evaluate using a graphing utility: ${ } _ { 15 } P _ { 5 }$

Accepted Answer

A) 3,003 
B) 32,760 
C) 360,360 
D) 75 
E) undefined 
A) 3,003 
B) 32,760 
C) 360,360 
D) 75 
E) undefined

Question 6

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.   ${ } _ { 5 } C _ { 2 }$

Accepted Answer

A) 20 
B) 28 
C) 10 
D) 21 
E) 15 
A) 20 
B) 28 
C) 10 
D) 21 
E) 15

Question 7

Use summation notation to write the sum.   $12 + 36 + 108 + \ldots + 8,748$

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n - 1 }$ 
B)  $\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n + 1 }$ 
C)  $\sum _ { n = 1 } ^ { 6 } 12 ( 3 ) ^ { n - 1 }$ 
D)  $\sum _ { n = 1 } ^ { 7 } 3 ^ { n - 1 }$ 
E)  $\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n }$ 
A)  $\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n - 1 }$ 
B)  $\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n + 1 }$ 
C)  $\sum _ { n = 1 } ^ { 6 } 12 ( 3 ) ^ { n - 1 }$ 
D)  $\sum _ { n = 1 } ^ { 7 } 3 ^ { n - 1 }$ 
E)  $\sum _ { n = 1 } ^ { 7 } 12 ( 3 ) ^ { n }$

Question 8

Expand the binomial by using Pascal's Triangle to determine the coefficients.   $( x + 2 y ) ^ { 5 }$

Accepted Answer

A)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } - 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
B)  $x ^ { 5 } - 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
C)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } - 80 x y ^ { 4 } - 32 y ^ { 5 }$ 
D)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
E)  $x ^ { 5 } + 10 x ^ { 4 } y - 40 x ^ { 3 } y ^ { 2 } - 80 x ^ { 2 } y ^ { 3 } - 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
A)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } - 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
B)  $x ^ { 5 } - 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
C)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } - 80 x y ^ { 4 } - 32 y ^ { 5 }$ 
D)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
E)  $x ^ { 5 } + 10 x ^ { 4 } y - 40 x ^ { 3 } y ^ { 2 } - 80 x ^ { 2 } y ^ { 3 } - 80 x y ^ { 4 } + 32 y ^ { 5 }$

Question 9

There were approximately 6.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.Estimate the number of unemployed workers in the 16-19 age group.(Round your answer to two decimal places.) ​   ​

Accepted Answer

A) 2.97 million 
B) 4.97 million 
C) 1.97 million 
D) 0.97 million 
E) 3.97 million 
A) 2.97 million 
B) 4.97 million 
C) 1.97 million 
D) 0.97 million 
E) 3.97 million

Question 10

A ball is dropped from a height of 15 feet.Each time it drops h feet, it rebounds 0.85h feet. Find the total vertical distance traveled by the ball.(Round your answer to two decimal places.)
​

Accepted Answer

A) 187.00 ft 
B) 185.00 ft 
C) 188.00 ft 
D) 186.00 ft 
E) 184.00 ft 
A) 187.00 ft 
B) 185.00 ft 
C) 188.00 ft 
D) 186.00 ft 
E) 184.00 ft

Question 11

Find the sum of the indicated terms of the geometric sequence.
  $\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }$

Accepted Answer

The answer of Find the sum of the indicated terms...

Question 12

Find the first five terms of the geometric sequence.   $a _ { 1 } = 4 , r = \pi$

Accepted Answer

A)  $4,4 \pi , 4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 }$ 
B)  $4,4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 } , 4 \pi ^ { 5 }$ 
C)  $4 , \pi ^ { 2 } , \pi ^ { 3 } , \pi ^ { 4 } , \pi ^ { 5 }$ 
D)  $4 , \pi , \pi ^ { 2 } , \pi ^ { 3 } , \pi ^ { 4 }$ 
E)  $4 , \pi , 4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 }$ 
A)  $4,4 \pi , 4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 }$ 
B)  $4,4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 } , 4 \pi ^ { 5 }$ 
C)  $4 , \pi ^ { 2 } , \pi ^ { 3 } , \pi ^ { 4 } , \pi ^ { 5 }$ 
D)  $4 , \pi , \pi ^ { 2 } , \pi ^ { 3 } , \pi ^ { 4 }$ 
E)  $4 , \pi , 4 \pi ^ { 2 } , 4 \pi ^ { 3 } , 4 \pi ^ { 4 }$

Question 13

Find a formula for the sum of the first n terms of the sequence.   $17,21,25,29,33 , \ldots$

Accepted Answer

A)  $S _ { n } = n ( 2 n + 15 )$ 
B)  $S _ { n } = n ( 5 n + 1 )$ 
C)  $S _ { n } = \frac { ( n + 1 ) } { n }$ 
D)  $S _ { n } = n ( 2 n + 1 )$ 
E)  $S _ { n } = n ( 17 n - 1 )$ 
A)  $S _ { n } = n ( 2 n + 15 )$ 
B)  $S _ { n } = n ( 5 n + 1 )$ 
C)  $S _ { n } = \frac { ( n + 1 ) } { n }$ 
D)  $S _ { n } = n ( 2 n + 1 )$ 
E)  $S _ { n } = n ( 17 n - 1 )$

Question 14

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.)   $a _ { 1 } = 900 , r = 1.02 , n = 40$

Accepted Answer

A)  $a _ { n } = 900 ( 1.02 ) ^ { n + 1 }$ , About 1948.270 
B)  $a _ { n } = ( 1.02 ) ^ { n - 1 }$ , About 1948.270 
C)  $a _ { n } = 900 ( 1.02 ) ^ { n - 1 }$ , About 1948.270 
D)  $a _ { n } = 900 ( 1.02 ) ^ { n - 1 }$ , About 1987.236 
E)  $a _ { n } = ( 1.02 ) ^ { n + 1 }$ , About 1948.270 
A)  $a _ { n } = 900 ( 1.02 ) ^ { n + 1 }$ , About 1948.270 
B)  $a _ { n } = ( 1.02 ) ^ { n - 1 }$ , About 1948.270 
C)  $a _ { n } = 900 ( 1.02 ) ^ { n - 1 }$ , About 1948.270 
D)  $a _ { n } = 900 ( 1.02 ) ^ { n - 1 }$ , About 1987.236 
E)  $a _ { n } = ( 1.02 ) ^ { n + 1 }$ , About 1948.270

Question 15

Determine whether the sequence is arithmetic.If so, find the common difference. ​
​2, 4, 8, 16, 32, ...
​

Accepted Answer

A) Arithmetic sequence, d = 6 
B) Arithmetic sequence, d = 2 
C) Arithmetic sequence, d = -2 
D) Arithmetic sequence, d = -30 
E) Not an arithmetic sequence 
A) Arithmetic sequence, d = 6 
B) Arithmetic sequence, d = 2 
C) Arithmetic sequence, d = -2 
D) Arithmetic sequence, d = -30 
E) Not an arithmetic sequence

Question 16

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 = (2n)n
​

Accepted Answer

A) 2, 8, 24, 64, 160Arithmetic sequenced = -2 
B) 160, 64, 24, 8, 2Arithmetic sequenced = 2 
C) 160, 64, 24, 8, 2Not an Arithmetic sequence 
D) 2, 8, 24, 64, 160Arithmetic sequenced = 2 
E) 2, 8, 24, 64, 160Not an Arithmetic sequence 
A) 2, 8, 24, 64, 160Arithmetic sequenced = -2 
B) 160, 64, 24, 8, 2Arithmetic sequenced = 2 
C) 160, 64, 24, 8, 2Not an Arithmetic sequence 
D) 2, 8, 24, 64, 160Arithmetic sequenced = 2 
E) 2, 8, 24, 64, 160Not an Arithmetic sequence

Question 17

Find the probability for the experiment of tossing a six-sided die twice.  
The sum is less than 4.

Accepted Answer

A) 36 
B)  $\frac { 36 } { 13 }$ 
C)  $\frac { 1 } { 12 }$ 
D)  $\frac { 13 } { 36 }$ 
E)  $\frac { 13 } { 36 }$. 
A) 36 
B)  $\frac { 36 } { 13 }$ 
C)  $\frac { 1 } { 12 }$ 
D)  $\frac { 13 } { 36 }$ 
E)  $\frac { 13 } { 36 }$.

Question 18

Find a formula for an for the arithmetic sequence.  
A1 = 7, d = -8

Accepted Answer

A)  $a _ { n } = 7 \left( - \frac { 1 } { 8 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = - 8 + 7 ( n - 1 )$ 
C)  $a _ { n } = 7 - 9 n$ 
D)   $a _ { n } = 15 - 8 n$ 
E)  $a _ { n } = 7 - 8 ^ { n - 1 }$ 
A)  $a _ { n } = 7 \left( - \frac { 1 } { 8 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = - 8 + 7 ( n - 1 )$ 
C)  $a _ { n } = 7 - 9 n$ 
D)   $a _ { n } = 15 - 8 n$ 
E)  $a _ { n } = 7 - 8 ^ { n - 1 }$

Question 19

Write an expression for the nth term of the geometric sequence.Then find the indicated term.   $a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10$

Accepted Answer

A)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
B)  $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
C)  $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$ 
D)  $a _ { n } = 6 \left( \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$ 
E)  $a _ { n } = \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
A)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
B)  $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$ 
C)  $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$ 
D)  $a _ { n } = 6 \left( \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$ 
E)  $a _ { n } = \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$

Question 20

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 6 } n ^ { 2 }$

Accepted Answer

A) 21 
B) 42 
C) 546 
D) 441 
E) 91 
A) 21 
B) 42 
C) 546 
D) 441 
E) 91

Find the first five terms of the geometric sequence. $a _ { 1 } = 4 , r = e$

Find the indicated term of the sequence. $a _ { n } = ( - 1 ) ^ { n } ( 4 n - 2 )$ $a _ { 27 } =$

Evaluate the expression. $C ( 4,3 )$

Use the Binominal Theorem to expand the complex number.Simplify your result. $( 3 - 2 i ) ^ { 4 }$

Evaluate using a graphing utility: ${ } _ { 15 } P _ { 5 }$

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 5 } C _ { 2 }$

Use summation notation to write the sum. $12 + 36 + 108 + \ldots + 8,748$

Expand the binomial by using Pascal's Triangle to determine the coefficients. $( x + 2 y ) ^ { 5 }$

There were approximately 6.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.Estimate the number of unemployed workers in the 16-19 age group.(Round your answer to two decimal places.)

A ball is dropped from a height of 15 feet.Each time it drops h feet, it rebounds 0.85h feet. Find the total vertical distance traveled by the ball.(Round your answer to two decimal places.)

Find the sum of the indicated terms of the geometric sequence. $\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }$

Find the first five terms of the geometric sequence. $a _ { 1 } = 4 , r = \pi$

Find a formula for the sum of the first n terms of the sequence. $17,21,25,29,33 , \ldots$

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.) $a _ { 1 } = 900 , r = 1.02 , n = 40$

Determine whether the sequence is arithmetic.If so, find the common difference. 2, 4, 8, 16, 32, ...

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 = (2n)n

Find the probability for the experiment of tossing a six-sided die twice. The sum is less than 4.

Find a formula for a_n for the arithmetic sequence. A₁ = 7, d = -8

Write an expression for the nth term of the geometric sequence.Then find the indicated term. $a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 6 } n ^ { 2 }$

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 first five terms of the geometric sequence. a1=4,r=ea _ { 1 } = 4 , r = ea1​=4,r=e

Find the indicated term of the sequence. an=(−1)n(4n−2)a _ { n } = ( - 1 ) ^ { n } ( 4 n - 2 )an​=(−1)n(4n−2) a27=a _ { 27 } =a27​=

Evaluate the expression. C(4,3)C ( 4,3 )C(4,3)

Use the Binominal Theorem to expand the complex number.Simplify your result. (3−2i)4( 3 - 2 i ) ^ { 4 }(3−2i)4

Evaluate using a graphing utility: 15P5{ } _ { 15 } P _ { 5 }15​P5​

Evaluate nCr{ } _ { n } C _ { r }n​Cr​ using the formula from this section. 5C2{ } _ { 5 } C _ { 2 }5​C2​

Use summation notation to write the sum. 12+36+108+…+8,74812 + 36 + 108 + \ldots + 8,74812+36+108+…+8,748

Expand the binomial by using Pascal's Triangle to determine the coefficients. (x+2y)5( x + 2 y ) ^ { 5 }(x+2y)5

There were approximately 6.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.Estimate the number of unemployed workers in the 16-19 age group.(Round your answer to two decimal places.) ​ ​

A ball is dropped from a height of 15 feet.Each time it drops h feet, it rebounds 0.85h feet. Find the total vertical distance traveled by the ball.(Round your answer to two decimal places.) ​

Find the sum of the indicated terms of the geometric sequence. ∑n=1n=56(2)n−1\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }∑n=1n=5​6(2)n−1

Find the first five terms of the geometric sequence. a1=4,r=πa _ { 1 } = 4 , r = \pia1​=4,r=π

Find a formula for the sum of the first n terms of the sequence. 17,21,25,29,33,…17,21,25,29,33 , \ldots17,21,25,29,33,…

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.) a1=900,r=1.02,n=40a _ { 1 } = 900 , r = 1.02 , n = 40a1​=900,r=1.02,n=40

Determine whether the sequence is arithmetic.If so, find the common difference. ​ ​2, 4, 8, 16, 32, ... ​

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 = (2n)n ​

Find the probability for the experiment of tossing a six-sided die twice. The sum is less than 4.

Find a formula for an for the arithmetic sequence. A1 = 7, d = -8

Write an expression for the nth term of the geometric sequence.Then find the indicated term. a1=4,r=16,n=10a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10a1​=4,r=61​,n=10

Find the sum using the formulas for the sums of powers of integers. ∑n=16n2\sum _ { n = 1 } ^ { 6 } n ^ { 2 }∑n=16​n2

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 first five terms of the geometric sequence. $a _ { 1 } = 4 , r = e$

Find the indicated term of the sequence. $a _ { n } = ( - 1 ) ^ { n } ( 4 n - 2 )$ $a _ { 27 } =$

Evaluate the expression. $C ( 4,3 )$

Use the Binominal Theorem to expand the complex number.Simplify your result. $( 3 - 2 i ) ^ { 4 }$

Evaluate using a graphing utility: ${ } _ { 15 } P _ { 5 }$

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 5 } C _ { 2 }$

Use summation notation to write the sum. $12 + 36 + 108 + \ldots + 8,748$

Expand the binomial by using Pascal's Triangle to determine the coefficients. $( x + 2 y ) ^ { 5 }$

There were approximately 6.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.Estimate the number of unemployed workers in the 16-19 age group.(Round your answer to two decimal places.)

A ball is dropped from a height of 15 feet.Each time it drops h feet, it rebounds 0.85h feet. Find the total vertical distance traveled by the ball.(Round your answer to two decimal places.)

Find the sum of the indicated terms of the geometric sequence. $\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }$

Find the first five terms of the geometric sequence. $a _ { 1 } = 4 , r = \pi$

Find a formula for the sum of the first n terms of the sequence. $17,21,25,29,33 , \ldots$

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.) $a _ { 1 } = 900 , r = 1.02 , n = 40$

Determine whether the sequence is arithmetic.If so, find the common difference. 2, 4, 8, 16, 32, ...

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 = (2n)n

Find a formula for a_n for the arithmetic sequence. A₁ = 7, d = -8

Write an expression for the nth term of the geometric sequence.Then find the indicated term. $a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 6 } n ^ { 2 }$