Question 1

Select the first five terms of the sequence.(Assume that n begins with 1.)    $a _ { n } = ( - 1 ) ^ { n } \left( \frac { n } { n + 11 } \right)$

Accepted Answer

A)  $\frac { 1 } { 12 } , \frac { 2 } { 13 } , \frac { 3 } { 14 } , \frac { 4 } { 15 } , \frac { 5 } { 16 }$ 
B)  $- \frac { 1 } { 12 } , - \frac { 2 } { 13 } , - \frac { 3 } { 14 } , - \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ 
C)  $- \frac { 1 } { 12 } , \frac { 2 } { 13 } , \frac { 3 } { 14 } , \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ 
D)  $- 12 , - \frac { 2 } { 13 } , - \frac { 3 } { 14 } , \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ 
E)  $- \frac { 1 } { 12 } , \frac { 2 } { 13 } , - \frac { 3 } { 14 } , \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ 
A)  $\frac { 1 } { 12 } , \frac { 2 } { 13 } , \frac { 3 } { 14 } , \frac { 4 } { 15 } , \frac { 5 } { 16 }$ 
B)  $- \frac { 1 } { 12 } , - \frac { 2 } { 13 } , - \frac { 3 } { 14 } , - \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ 
C)  $- \frac { 1 } { 12 } , \frac { 2 } { 13 } , \frac { 3 } { 14 } , \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ 
D)  $- 12 , - \frac { 2 } { 13 } , - \frac { 3 } { 14 } , \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ 
E)  $- \frac { 1 } { 12 } , \frac { 2 } { 13 } , - \frac { 3 } { 14 } , \frac { 4 } { 15 } , - \frac { 5 } { 16 }$

Question 2

Find pk + 1 for the given pk .   $p _ { k } = \frac { k ^ { 2 } ( k + 4 ) ^ { 2 } } { 8 }$

Accepted Answer

A)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } ( k + 5 ) ^ { 2 } } { 8 }$ 
B)  $p _ { k + 1 } = \frac { k ^ { 2 } ( k + 5 ) ^ { 2 } } { 8 }$ 
C)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } ( k + 5 ) ^ { 2 } } { 9 }$ 
D)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } ( k + 9 ) ^ { 2 } } { 8 }$ 
E)  $p _ { k + 1 } = \frac { k ^ { 2 } ( k + 9 ) ^ { 2 } } { 8 }$ 
A)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } ( k + 5 ) ^ { 2 } } { 8 }$ 
B)  $p _ { k + 1 } = \frac { k ^ { 2 } ( k + 5 ) ^ { 2 } } { 8 }$ 
C)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } ( k + 5 ) ^ { 2 } } { 9 }$ 
D)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } ( k + 9 ) ^ { 2 } } { 8 }$ 
E)  $p _ { k + 1 } = \frac { k ^ { 2 } ( k + 9 ) ^ { 2 } } { 8 }$

Question 3

Find the indicated nth term of the geometric sequence.  
7th term : $3,21,147 , \ldots$

Accepted Answer

A)  $a _ { 7 } = 50,421$ 
B)  $a _ { 7 } = 7,203$ 
C)  $a _ { 7 } = 17,294,403$ 
D)  $a _ { 7 } = 352,947$ 
E)  $a _ { 7 } = 2,470,629$ 
A)  $a _ { 7 } = 50,421$ 
B)  $a _ { 7 } = 7,203$ 
C)  $a _ { 7 } = 17,294,403$ 
D)  $a _ { 7 } = 352,947$ 
E)  $a _ { 7 } = 2,470,629$

Question 4

Determine whether the sequence is geometric.If so, find the common ratio.   $7,1.4,0.28,0.056 , \ldots$

Accepted Answer

A) Geometric sequence, $r = 0.5$ 
B) Geometric sequence, $r = 0.2$ 
C) Geometric sequence, $r = 0.4$ 
D) Not a geometric sequence 
E) Geometric sequence, $r = 0.3$ 
A) Geometric sequence, $r = 0.5$ 
B) Geometric sequence, $r = 0.2$ 
C) Geometric sequence, $r = 0.4$ 
D) Not a geometric sequence 
E) Geometric sequence, $r = 0.3$

Question 5

Determine whether the sequence is arithmetic.If so, find the common difference.  
3, $\frac { 11 } { 4 }$ , $\frac { 5 } { 2 }$ , $\frac { 9 } { 4 }$ , 2,...

Accepted Answer

A) Arithmetic sequence, $d = - \frac { 1 } { 4 }$ 
B) Arithmetic sequence, d = $\frac { 1 } { 4 }$ 
C) Arithmetic sequence, d = -1 
D) Arithmetic sequence, $d = \frac { 3 } { 4 }$ 
E) Not an arithmetic sequence 
A) Arithmetic sequence, $d = - \frac { 1 } { 4 }$ 
B) Arithmetic sequence, d = $\frac { 1 } { 4 }$ 
C) Arithmetic sequence, d = -1 
D) Arithmetic sequence, $d = \frac { 3 } { 4 }$ 
E) Not an arithmetic sequence

Question 6

Find the indicated nth partial sum of the arithmetic sequence. 1.5, 3.1, 4.7, 6.3, ...., n = 40

Accepted Answer

A) 1,234 
B) 1,308.1 
C) 1,308 
D) 1,307.9 
E) 1,372 
A) 1,234 
B) 1,308.1 
C) 1,308 
D) 1,307.9 
E) 1,372

Question 7

Calculate the binomial coefficient.   ${ } _ { 29 } C _ { 29 }$

Accepted Answer

A) 0 
B) 4 
C) 1 
D) 3 
E) 2 
A) 0 
B) 4 
C) 1 
D) 3 
E) 2

Question 8

A college sent a survey to a sample of juniors.Of the 620 students surveyed, 307 live on campus, of whom 139 have a GPA of 2.5 or greater.The other 313 juniors live off-campus, of whom 153 have a GPA of 2.5 or greater.What is the probability that a survey participant chosen at random has a GPA less than 2.5?

Accepted Answer

A)  $\frac { 307 } { 620 }$ 
B)  $\frac { 139 } { 620 }$ 
C)  $\frac { 82 } { 155 }$ 
D)  $\frac { 139 } { 292 }$ 
E)  $\frac { 139 } { 307 }$ 
A)  $\frac { 307 } { 620 }$ 
B)  $\frac { 139 } { 620 }$ 
C)  $\frac { 82 } { 155 }$ 
D)  $\frac { 139 } { 292 }$ 
E)  $\frac { 139 } { 307 }$

Question 9

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 7 } n ^ { 5 }$

Accepted Answer

A) 840 
B) 29,008 
C) 4,676 
D) 784 
E) 140 
A) 840 
B) 29,008 
C) 4,676 
D) 784 
E) 140

Question 10

Use sigma notation to write the sum.   $\frac { 1 } { 3 ( 1 ) } + \frac { 1 } { 3 ( 2 ) } + \frac { 1 } { 3 ( 3 ) } + \ldots + \frac { 1 } { 3 ( 9 ) }$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 9 } - \frac { 1 } { 3 i }$ 
B)  $\sum _ { i = 0 } ^ { 10 } \frac { 1 } { 3 i }$ 
C)  $\sum _ { i = 1 } ^ { 9 } 3 i$ 
D)  $\sum _ { i = 1 } ^ { 9 } \frac { 1 } { 3 i }$ 
E)  $\sum _ { i = 1 } ^ { - 9 } \frac { 1 } { 3 i }$ 
A)  $\sum _ { i = 1 } ^ { 9 } - \frac { 1 } { 3 i }$ 
B)  $\sum _ { i = 0 } ^ { 10 } \frac { 1 } { 3 i }$ 
C)  $\sum _ { i = 1 } ^ { 9 } 3 i$ 
D)  $\sum _ { i = 1 } ^ { 9 } \frac { 1 } { 3 i }$ 
E)  $\sum _ { i = 1 } ^ { - 9 } \frac { 1 } { 3 i }$

Question 11

Use the binomial theorem to expand the binomial.   $\left( \frac { z } { 2 } + b \right) ^ { 4 }$

Accepted Answer

A)  $z ^ { 4 } + z ^ { 3 } b + z ^ { 2 } b ^ { 2 } + z b ^ { 3 } + b ^ { 4 }$ 
B)  $\frac { 1 } { 8 } z ^ { 4 } + \frac { 1 } { 2 } z ^ { 3 } b + \frac { 3 } { 2 } z ^ { 2 } b ^ { 2 } + 2 z b ^ { 3 } + b ^ { 4 }$ 
C)  $\frac { 1 } { 2 } z ^ { 4 } + b ^ { 4 }$ 
D)  $\frac { 1 } { 16 } z ^ { 4 } + \frac { 1 } { 8 } z ^ { 3 } b + \frac { 1 } { 4 } z ^ { 2 } b ^ { 2 } + \frac { 1 } { 2 } z b ^ { 3 } + b ^ { 4 }$ 
E)  $\frac { 1 } { 16 } z ^ { 4 } + \frac { 1 } { 2 } z ^ { 3 } b + \frac { 3 } { 2 } z ^ { 2 } b ^ { 2 } + 2 z b ^ { 3 } + b ^ { 4 }$ 
A)  $z ^ { 4 } + z ^ { 3 } b + z ^ { 2 } b ^ { 2 } + z b ^ { 3 } + b ^ { 4 }$ 
B)  $\frac { 1 } { 8 } z ^ { 4 } + \frac { 1 } { 2 } z ^ { 3 } b + \frac { 3 } { 2 } z ^ { 2 } b ^ { 2 } + 2 z b ^ { 3 } + b ^ { 4 }$ 
C)  $\frac { 1 } { 2 } z ^ { 4 } + b ^ { 4 }$ 
D)  $\frac { 1 } { 16 } z ^ { 4 } + \frac { 1 } { 8 } z ^ { 3 } b + \frac { 1 } { 4 } z ^ { 2 } b ^ { 2 } + \frac { 1 } { 2 } z b ^ { 3 } + b ^ { 4 }$ 
E)  $\frac { 1 } { 16 } z ^ { 4 } + \frac { 1 } { 2 } z ^ { 3 } b + \frac { 3 } { 2 } z ^ { 2 } b ^ { 2 } + 2 z b ^ { 3 } + b ^ { 4 }$

Question 12

Evaluate ${ } _ { n } P _ { r }$ .  ${ } _ { 7 } P _ { 4 }$

Accepted Answer

A) 5,040 
B) 1,680 
C) 3,024 
D) 35 
E) 840 
A) 5,040 
B) 1,680 
C) 3,024 
D) 35 
E) 840

Question 13

Use mathematical induction to solve for all positive integers n.   $16 + 34 + 52 + 70 + \ldots + ( 18 n - 2 ) = ?$

Accepted Answer

A)  $\frac { n ( n + 16 ) ( 16 n + 1 ) } { 6 }$ 
B)  $\frac { n } { 2 } ( 3 n + 1 )$ 
C)  $\frac { n } { 2 } ( 3 n + 14 )$ 
D)  $n ( n + 16 )$ 
E)  $\frac { n ( n + 16 ) } { 2 }$ 
A)  $\frac { n ( n + 16 ) ( 16 n + 1 ) } { 6 }$ 
B)  $\frac { n } { 2 } ( 3 n + 1 )$ 
C)  $\frac { n } { 2 } ( 3 n + 14 )$ 
D)  $n ( n + 16 )$ 
E)  $\frac { n ( n + 16 ) } { 2 }$

Question 14

How many four-digit numbers can be formed under the following condition? ​
The leading digit cannot be zero and the number must be less than 7,000.
​

Accepted Answer

A) 5,800 
B) 6,000 
C) 5,700 
D) 5,600 
E) 5,900 
A) 5,800 
B) 6,000 
C) 5,700 
D) 5,600 
E) 5,900

Question 15

In how many ways can seven people sit in a seven-passenger car? ​

Accepted Answer

A) 6,040 
B) 5,090 
C) 5,040 
D) 5,140 
E) 5,540 
A) 6,040 
B) 5,090 
C) 5,040 
D) 5,140 
E) 5,540

Question 16

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither.  
A1 = 2
An = an - 1 + 2

Accepted Answer

A) 2, 4, 6, 8, 10, 12
First differences: 0, 0, 0, 0
Second differences: 2, 2, 2, 2, 2
Quadratic 
B) 0, 2, 4, 6, 8, 10
First differences: 0, 0, 0, 0
Second differences: 2, 2, 2, 2, 2
Linear 
C) 0, 2, 4, 6, 8, 10
First differences: 2, 2, 2, 2, 2
Second differences: 0, 0, 0, 0
Quadratic 
D) 2, 4, 6, 8, 10, 12
First differences: 2, 2, 2, 2, 2
Second differences: 0, 0, 0, 0
Linear 
E) 0, 2, 4, 6, 8, 10
First differences: 2, 2, 2, 2, 2
Second differences: -1, -1, -1, -1
Quadratic 
A) 2, 4, 6, 8, 10, 12
First differences: 0, 0, 0, 0
Second differences: 2, 2, 2, 2, 2
Quadratic 
B) 0, 2, 4, 6, 8, 10
First differences: 0, 0, 0, 0
Second differences: 2, 2, 2, 2, 2
Linear 
C) 0, 2, 4, 6, 8, 10
First differences: 2, 2, 2, 2, 2
Second differences: 0, 0, 0, 0
Quadratic 
D) 2, 4, 6, 8, 10, 12
First differences: 2, 2, 2, 2, 2
Second differences: 0, 0, 0, 0
Linear 
E) 0, 2, 4, 6, 8, 10
First differences: 2, 2, 2, 2, 2
Second differences: -1, -1, -1, -1
Quadratic

Question 17

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.   ${ } _ { 5 } C _ { 3 }$

Accepted Answer

A) 84 
B) 60 
C) 10 
D) 20 
E) 35 
A) 84 
B) 60 
C) 10 
D) 20 
E) 35

Question 18

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.)   $a _ { 1 } = 2500 , r = 1.005 , n = 60$

Accepted Answer

A)  $a _ { n } = ( 1.005 ) ^ { n - 1 }$ , About 3355.349 
B)  $a _ { n } = 2500 ( 1.005 ) ^ { n - 1 }$ , About 3355.349 
C)  $a _ { n } = 2500 ( 1.005 ) ^ { n - 1 }$ , About 5520.099 
D)  $a _ { n } = ( 1.005 ) ^ { n + 1 }$ , About 3355.349 
E)  $a _ { n } = 2500 ( 1.005 ) ^ { n + 1 }$ , About 3355.349 
A)  $a _ { n } = ( 1.005 ) ^ { n - 1 }$ , About 3355.349 
B)  $a _ { n } = 2500 ( 1.005 ) ^ { n - 1 }$ , About 3355.349 
C)  $a _ { n } = 2500 ( 1.005 ) ^ { n - 1 }$ , About 5520.099 
D)  $a _ { n } = ( 1.005 ) ^ { n + 1 }$ , About 3355.349 
E)  $a _ { n } = 2500 ( 1.005 ) ^ { n + 1 }$ , About 3355.349

Question 19

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither.  
A1 = 3
 an = an - 1 - n

Accepted Answer

A) 0, 3, 1, -2, -6, -11
First differences: 3, -2, -3, -4, -5
Second differences: -1, -1, -1, -1
Quadratic 
B) 0, 3, 1, -2, -6, -11, -17
First differences: -2, -3, -4, -5, -6
Second differences: 1, 1, 1, 1
Linear 
C) 3, 1, -2, -6, -11, -17
First differences: -2, -3, -4, -5, -6
Second differences: 1, 1, 1, 1
Quadratic 
D) 3, 1, -2, -6, -11, -17
First differences: -2, -3, -4, -5, -6
Second differences: -1, -1, -1, -1
Quadratic 
E) 0, 3, 1, -2, -6, -11
First differences: 3, -2, -3, -4, -5
Second differences: 1, 1, 1, 1
Quadratic 
A) 0, 3, 1, -2, -6, -11
First differences: 3, -2, -3, -4, -5
Second differences: -1, -1, -1, -1
Quadratic 
B) 0, 3, 1, -2, -6, -11, -17
First differences: -2, -3, -4, -5, -6
Second differences: 1, 1, 1, 1
Linear 
C) 3, 1, -2, -6, -11, -17
First differences: -2, -3, -4, -5, -6
Second differences: 1, 1, 1, 1
Quadratic 
D) 3, 1, -2, -6, -11, -17
First differences: -2, -3, -4, -5, -6
Second differences: -1, -1, -1, -1
Quadratic 
E) 0, 3, 1, -2, -6, -11
First differences: 3, -2, -3, -4, -5
Second differences: 1, 1, 1, 1
Quadratic

Question 20

Use the Binomial Theorem to expand the complex number.Simplify your result.   $( 5 + i ) ^ { 4 }$

Accepted Answer

A)  $480 i - 476$ 
B)  $- 480 i - 476$ 
C)  $- 480 i + 476$ 
D)  $480 i + 476$ 
E)  $480 i + 476 i$ 
A)  $480 i - 476$ 
B)  $- 480 i - 476$ 
C)  $- 480 i + 476$ 
D)  $480 i + 476$ 
E)  $480 i + 476 i$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = ( - 1 ) ^ { n } \left( \frac { n } { n + 11 } \right)$

Find pk_{+ 1} for the given pk. $p _ { k } = \frac { k ^ { 2 } ( k + 4 ) ^ { 2 } } { 8 }$

Find the indicated nth term of the geometric sequence. 7th term : $3,21,147 , \ldots$

Determine whether the sequence is geometric.If so, find the common ratio. $7,1.4,0.28,0.056 , \ldots$

Determine whether the sequence is arithmetic.If so, find the common difference. 3, $\frac { 11 } { 4 }$ , $\frac { 5 } { 2 }$ , $\frac { 9 } { 4 }$ , 2,...

Find the indicated nth partial sum of the arithmetic sequence. 1.5, 3.1, 4.7, 6.3, ...., n = 40

Calculate the binomial coefficient. ${ } _ { 29 } C _ { 29 }$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 7 } n ^ { 5 }$

Use sigma notation to write the sum. $\frac { 1 } { 3 ( 1 ) } + \frac { 1 } { 3 ( 2 ) } + \frac { 1 } { 3 ( 3 ) } + \ldots + \frac { 1 } { 3 ( 9 ) }$

Use the binomial theorem to expand the binomial. $\left( \frac { z } { 2 } + b \right) ^ { 4 }$

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 7 } P _ { 4 }$

Use mathematical induction to solve for all positive integers n. $16 + 34 + 52 + 70 + \ldots + ( 18 n - 2 ) = ?$

How many four-digit numbers can be formed under the following condition? The leading digit cannot be zero and the number must be less than 7,000.

In how many ways can seven people sit in a seven-passenger car?

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A₁ = 2 A_n = an_{- 1} + 2

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 5 } C _ { 3 }$

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.) $a _ { 1 } = 2500 , r = 1.005 , n = 60$

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A₁ = 3 a_n = an_{- 1} - n

Use the Binomial Theorem to expand the complex number.Simplify your result. $( 5 + i ) ^ { 4 }$

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

Select the first five terms of the sequence.(Assume that n begins with 1.) an=(−1)n(nn+11)a _ { n } = ( - 1 ) ^ { n } \left( \frac { n } { n + 11 } \right)an​=(−1)n(n+11n​)

Find pk + 1 for the given pk . pk=k2(k+4)28p _ { k } = \frac { k ^ { 2 } ( k + 4 ) ^ { 2 } } { 8 }pk​=8k2(k+4)2​

Find the indicated nth term of the geometric sequence. 7th term : 3,21,147,…3,21,147 , \ldots3,21,147,…

Determine whether the sequence is geometric.If so, find the common ratio. 7,1.4,0.28,0.056,…7,1.4,0.28,0.056 , \ldots7,1.4,0.28,0.056,…

Determine whether the sequence is arithmetic.If so, find the common difference. 3, 114\frac { 11 } { 4 }411​ , 52\frac { 5 } { 2 }25​ , 94\frac { 9 } { 4 }49​ , 2,...

Find the indicated nth partial sum of the arithmetic sequence. 1.5, 3.1, 4.7, 6.3, ...., n = 40

Calculate the binomial coefficient. 29C29{ } _ { 29 } C _ { 29 }29​C29​

Find the sum using the formulas for the sums of powers of integers. ∑n=17n5\sum _ { n = 1 } ^ { 7 } n ^ { 5 }∑n=17​n5

Use sigma notation to write the sum. 13(1)+13(2)+13(3)+…+13(9)\frac { 1 } { 3 ( 1 ) } + \frac { 1 } { 3 ( 2 ) } + \frac { 1 } { 3 ( 3 ) } + \ldots + \frac { 1 } { 3 ( 9 ) }3(1)1​+3(2)1​+3(3)1​+…+3(9)1​

Use the binomial theorem to expand the binomial. (z2+b)4\left( \frac { z } { 2 } + b \right) ^ { 4 }(2z​+b)4

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ . 7P4{ } _ { 7 } P _ { 4 }7​P4​

Use mathematical induction to solve for all positive integers n. 16+34+52+70+…+(18n−2)=?16 + 34 + 52 + 70 + \ldots + ( 18 n - 2 ) = ?16+34+52+70+…+(18n−2)=?

How many four-digit numbers can be formed under the following condition? ​ The leading digit cannot be zero and the number must be less than 7,000. ​

In how many ways can seven people sit in a seven-passenger car? ​

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A1 = 2 An = an - 1 + 2

Evaluate nCr{ } _ { n } C _ { r }n​Cr​ using the formula from this section. 5C3{ } _ { 5 } C _ { 3 }5​C3​

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.) a1=2500,r=1.005,n=60a _ { 1 } = 2500 , r = 1.005 , n = 60a1​=2500,r=1.005,n=60

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A1 = 3 an = an - 1 - n

Use the Binomial Theorem to expand the complex number.Simplify your result. (5+i)4( 5 + i ) ^ { 4 }(5+i)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

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = ( - 1 ) ^ { n } \left( \frac { n } { n + 11 } \right)$

Find pk_{+ 1} for the given pk. $p _ { k } = \frac { k ^ { 2 } ( k + 4 ) ^ { 2 } } { 8 }$

Find the indicated nth term of the geometric sequence. 7th term : $3,21,147 , \ldots$

Determine whether the sequence is geometric.If so, find the common ratio. $7,1.4,0.28,0.056 , \ldots$

Determine whether the sequence is arithmetic.If so, find the common difference. 3, $\frac { 11 } { 4 }$ , $\frac { 5 } { 2 }$ , $\frac { 9 } { 4 }$ , 2,...

Calculate the binomial coefficient. ${ } _ { 29 } C _ { 29 }$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 7 } n ^ { 5 }$

Use sigma notation to write the sum. $\frac { 1 } { 3 ( 1 ) } + \frac { 1 } { 3 ( 2 ) } + \frac { 1 } { 3 ( 3 ) } + \ldots + \frac { 1 } { 3 ( 9 ) }$

Use the binomial theorem to expand the binomial. $\left( \frac { z } { 2 } + b \right) ^ { 4 }$

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 7 } P _ { 4 }$

Use mathematical induction to solve for all positive integers n. $16 + 34 + 52 + 70 + \ldots + ( 18 n - 2 ) = ?$

How many four-digit numbers can be formed under the following condition? The leading digit cannot be zero and the number must be less than 7,000.

In how many ways can seven people sit in a seven-passenger car?

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A₁ = 2 A_n = an_{- 1} + 2

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 5 } C _ { 3 }$

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places.) $a _ { 1 } = 2500 , r = 1.005 , n = 60$

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A₁ = 3 a_n = an_{- 1} - n

Use the Binomial Theorem to expand the complex number.Simplify your result. $( 5 + i ) ^ { 4 }$