Question 1

Find the second term in the expansion of $\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 50 }$

Accepted Answer

$- 50 x ^ { 97 }$

Question 2

How much money should be invested monthly at $6 \%$ per year, compounded monthly, in order to have $\$ 10,000$ in two years?

Accepted Answer

$10,000 = R \frac { ( 1.005 ) ^ { 24 } - 1 } { 0.005 }$ $\Rightarrow$  $R = 10,000 \frac { 0.005 } { ( 1.005 ) ^ { 24 } - 1 } \approx \$ 393.21$

Question 3

Determine the common ratio, the fifth, and the $n ^ { t h }$ terms of the geometric sequence. $9,9 \sqrt { 3 } , 27,27 \sqrt { 3 } , \dots$

Accepted Answer

A)  $a _ { n } = 9 ( 3 ) ^ { - \cdots }$ 
B)  $a _ { n } = 6 ( \sqrt { 3 } ) ^ { n - 1 }$ 
C)  $a _ { n } = 9 ( \sqrt { 3 } ) ^ { n - 1 }$ 
D)  $a _ { n } = ( \sqrt { 3 } ) ^ { n + 1 }$ 
E) none 
A)  $a _ { n } = 9 ( 3 ) ^ { - \cdots }$ 
B)  $a _ { n } = 6 ( \sqrt { 3 } ) ^ { n - 1 }$ 
C)  $a _ { n } = 9 ( \sqrt { 3 } ) ^ { n - 1 }$ 
D)  $a _ { n } = ( \sqrt { 3 } ) ^ { n + 1 }$ 
E) none C

Question 4

Expand the expression $( 1 - x ) ^ { 3 }$

Accepted Answer

The answer of Expand the expression \(( 1 - x...

Question 5

Find the values of a and b for which the sequence $2 , a , b , 17 , \ldots$ is arithmetic

Accepted Answer

A)  $a = 7 , b = 12$ 
B)  $a = 6 , b = 12$ 
C)  $a = 8 , b = 12$ 
D)  $a = 10 , b = 12$ 
E)  $a = 8 , b = 15$ 
A)  $a = 7 , b = 12$ 
B)  $a = 6 , b = 12$ 
C)  $a = 8 , b = 12$ 
D)  $a = 10 , b = 12$ 
E)  $a = 8 , b = 15$

Question 6

Find the second term in the expansion of $\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 45 }$

Accepted Answer

The answer of Find the second term in the expansion...

Question 7

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

Accepted Answer

A)  $a _ { 1 000 } = - \frac { 501 } { 500 }$ 
B)  $a _ { 1000 } = \frac { 251 } { 250 }$ 
C)  $a _ { 1000 } = \frac { 126 } { 125 }$ 
D)  $a _ { 1000} = - \frac { 126 } { 125 }$ 
E)  $a _ { 1000 } = \frac { 501 } { 500 }$ 
A)  $a _ { 1 000 } = - \frac { 501 } { 500 }$ 
B)  $a _ { 1000 } = \frac { 251 } { 250 }$ 
C)  $a _ { 1000 } = \frac { 126 } { 125 }$ 
D)  $a _ { 1000} = - \frac { 126 } { 125 }$ 
E)  $a _ { 1000 } = \frac { 501 } { 500 }$

Question 8

The common ratio of a geometric sequence is $\frac { 3 } { 7 }$ and the fourth term is $\frac { 1 } { 7 }$ Find the third term

Accepted Answer

A)  $a _ { 1 } = \frac { 1 } { 3 }$ 
B)  $a _ { 1 } = \frac { 7 } { 3 }$ 
C)  $a _ { 1 } = \frac { 3 } { 7 }$ 
D)  $a _ { 1 } = \frac { 5 } { 3 }$ 
E)  $a _ { 1 } = \frac { 2 } { 7 }$ 
A)  $a _ { 1 } = \frac { 1 } { 3 }$ 
B)  $a _ { 1 } = \frac { 7 } { 3 }$ 
C)  $a _ { 1 } = \frac { 3 } { 7 }$ 
D)  $a _ { 1 } = \frac { 5 } { 3 }$ 
E)  $a _ { 1 } = \frac { 2 } { 7 }$

Question 9

Find the sum of the infinite geometric series. $a + a x ^ { 2 } + a x ^ { 4 } + a x ^ { 6 } + \ldots$

Accepted Answer

A)  $S = \frac { x } { 1 - \alpha ^ { 2 } }$ 
B)  $S = \frac { \alpha } { 1 - x ^ { 4 } }$ 
C)  $S = \frac { x ^ { 2 } } { 1 - a ^ { 2 } }$ 
D)  $S = \frac { 1 } { 1 + x ^ { 2 } }$ 
E)  $S = \frac { \alpha } { 1 - x ^ { 2 } }$ 
A)  $S = \frac { x } { 1 - \alpha ^ { 2 } }$ 
B)  $S = \frac { \alpha } { 1 - x ^ { 4 } }$ 
C)  $S = \frac { x ^ { 2 } } { 1 - a ^ { 2 } }$ 
D)  $S = \frac { 1 } { 1 + x ^ { 2 } }$ 
E)  $S = \frac { \alpha } { 1 - x ^ { 2 } }$

Question 10

Find the coefficient of $a ^ { 4 } b ^ { 4 }$  in the expansion of $( b - a ) ^ { 3 }$

Accepted Answer

The answer of Find the coefficient of \(a ^ {...

Question 11

A man gets a job with a salary of $50,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period

Accepted Answer

A)  $\$ 518,000$ 
B)  $\$ 851,000$ 
C)  $\$ 1,581,000$ 
D)  $\$ 481,000$ 
E) none of these 
A)  $\$ 518,000$ 
B)  $\$ 851,000$ 
C)  $\$ 1,581,000$ 
D)  $\$ 481,000$ 
E) none of these

Question 12

The common ratio of a geometric sequence is $\frac { 3 } { 7 }$ and the fourth term is $\frac { 1 } { 7 }$ 
 Find the third term.

Accepted Answer

The answer of The common ratio of a geometric sequence...

Question 13

Find the $n ^ { \text {th} }$  term of the sequence whose first several terms are $3$ , $9$ , $27$ , $81$ ,.....

Accepted Answer

The answer of Find the \(n ^ { \text {th}...

Question 14

The first four terms of a sequence are given. Determine whether they can be terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic find the common difference. If the sequence is geometric find the common ratio. $- 5 , - 2 s , - 3 s , - 4 s , K$

Accepted Answer

A)  $\text { arithmetic, } d  = - s$ 
B)  $\text { arithmetic, } d = - \frac { 1 } { 2 }$ 
C)  $\text { geometric, } \gamma = \frac { 35 } { 2 }$ 
D)  $\text { geometric, } \gamma = - \frac { 5 } { 4 }$ 
E)  neither 
A)  $\text { arithmetic, } d  = - s$ 
B)  $\text { arithmetic, } d = - \frac { 1 } { 2 }$ 
C)  $\text { geometric, } \gamma = \frac { 35 } { 2 }$ 
D)  $\text { geometric, } \gamma = - \frac { 5 } { 4 }$ 
E)  neither

Question 15

Express the repeating decimal $0.1 \overline { 38 }$ as a fraction.

Accepted Answer

The answer of Express the repeating decimal \(0.1 \overline {...

Question 16

Write the sum using sigma notation. $1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } + 4 ^ { 2 } + \ldots + 101 ^ { 2 }$

Accepted Answer

The answer of Write the sum using sigma notation. \(1...

Question 17

Write the sum without using sigma notation. Do not evaluate. $\sum _ { n = 2 } ^ { 100 } \frac { 1 } { n - 1 }$

Accepted Answer

The answer of Write the sum without using sigma notation....

Question 18

Find the coefficient of $- a ^ { \dot { 3 } } b ^ { 3 }$ in the expansion of $( b - a ) ^ { 3 }$

Accepted Answer

The answer of Find the coefficient of \(- a ^...

Question 19

A man gets a job with a salary of $40,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period.

Accepted Answer

The answer of A man gets a job with a...

Question 20

Expand the expression $( 1 - y ) ^ { 4 }$ 
.

Accepted Answer

The answer of Expand the expression \(( 1 - y...

Find the second term in the expansion of $\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 50 }$

How much money should be invested monthly at $6 \%$ per year, compounded monthly, in order to have $\$ 10,000$ in two years?

Determine the common ratio, the fifth, and the $n ^ { t h }$ terms of the geometric sequence. $9,9 \sqrt { 3 } , 27,27 \sqrt { 3 } , \dots$

Expand the expression $( 1 - x ) ^ { 3 }$

Find the values of a and b for which the sequence $2 , a , b , 17 , \ldots$ is arithmetic

Find the second term in the expansion of $\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 45 }$

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

The common ratio of a geometric sequence is $\frac { 3 } { 7 }$ and the fourth term is $\frac { 1 } { 7 }$ Find the third term

Find the sum of the infinite geometric series. $a + a x ^ { 2 } + a x ^ { 4 } + a x ^ { 6 } + \ldots$

Find the coefficient of $a ^ { 4 } b ^ { 4 }$ in the expansion of $( b - a ) ^ { 3 }$

A man gets a job with a salary of $50,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period

The common ratio of a geometric sequence is $\frac { 3 } { 7 }$ and the fourth term is $\frac { 1 } { 7 }$ Find the third term.

Find the $n ^ { \text {th} }$ term of the sequence whose first several terms are $3$ , $9$ , $27$ , $81$ ,.....

The first four terms of a sequence are given. Determine whether they can be terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic find the common difference. If the sequence is geometric find the common ratio. $- 5 , - 2 s , - 3 s , - 4 s , K$

Express the repeating decimal $0.1 \overline { 38 }$ as a fraction.

Write the sum using sigma notation. $1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } + 4 ^ { 2 } + \ldots + 101 ^ { 2 }$

Write the sum without using sigma notation. Do not evaluate. $\sum _ { n = 2 } ^ { 100 } \frac { 1 } { n - 1 }$

Find the coefficient of $- a ^ { \dot { 3 } } b ^ { 3 }$ in the expansion of $( b - a ) ^ { 3 }$

A man gets a job with a salary of $40,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period.

Expand the expression $( 1 - y ) ^ { 4 }$ .

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Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

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Exam 13: Sequences and Series

Find the second term in the expansion of (x2−1x)50\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 50 }(x2−x1​)50

How much money should be invested monthly at 6%6 \%6% per year, compounded monthly, in order to have $10,000\$ 10,000$10,000 in two years?

Determine the common ratio, the fifth, and the nthn ^ { t h }nth terms of the geometric sequence. 9,93,27,273,…9,9 \sqrt { 3 } , 27,27 \sqrt { 3 } , \dots9,93​,27,273​,…

Expand the expression (1−x)3( 1 - x ) ^ { 3 }(1−x)3

Find the values of a and b for which the sequence 2,a,b,17,…2 , a , b , 17 , \ldots2,a,b,17,… is arithmetic

Find the second term in the expansion of (x2−1x)45\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 45 }(x2−x1​)45

Find the 1000th1000 ^ { \mathrm { th } }1000th term of the sequence an=(−1)nn+2na _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }an​=(−1)nnn+2​

The common ratio of a geometric sequence is 37\frac { 3 } { 7 }73​ and the fourth term is 17\frac { 1 } { 7 }71​ Find the third term

Find the sum of the infinite geometric series. a+ax2+ax4+ax6+…a + a x ^ { 2 } + a x ^ { 4 } + a x ^ { 6 } + \ldotsa+ax2+ax4+ax6+…

Find the coefficient of a4b4a ^ { 4 } b ^ { 4 }a4b4 in the expansion of (b−a)3( b - a ) ^ { 3 }(b−a)3

A man gets a job with a salary of $50,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period

The common ratio of a geometric sequence is 37\frac { 3 } { 7 }73​ and the fourth term is 17\frac { 1 } { 7 }71​ Find the third term.

Find the nthn ^ { \text {th} }nth term of the sequence whose first several terms are 333 , 999 , 272727 , 818181 ,.....

Express the repeating decimal 0.138‾0.1 \overline { 38 }0.138 as a fraction.

Write the sum using sigma notation. 12+22+32+42+…+10121 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } + 4 ^ { 2 } + \ldots + 101 ^ { 2 }12+22+32+42+…+1012

Write the sum without using sigma notation. Do not evaluate. ∑n=21001n−1\sum _ { n = 2 } ^ { 100 } \frac { 1 } { n - 1 }∑n=2100​n−11​

Find the coefficient of −a3˙b3- a ^ { \dot { 3 } } b ^ { 3 }−a3˙b3 in the expansion of (b−a)3( b - a ) ^ { 3 }(b−a)3

A man gets a job with a salary of $40,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period.

Expand the expression (1−y)4( 1 - y ) ^ { 4 }(1−y)4 .

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Counting and Probability

Filters

Find the second term in the expansion of $\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 50 }$

How much money should be invested monthly at $6 \%$ per year, compounded monthly, in order to have $\$ 10,000$ in two years?

Determine the common ratio, the fifth, and the $n ^ { t h }$ terms of the geometric sequence. $9,9 \sqrt { 3 } , 27,27 \sqrt { 3 } , \dots$

Expand the expression $( 1 - x ) ^ { 3 }$

Find the values of a and b for which the sequence $2 , a , b , 17 , \ldots$ is arithmetic

Find the second term in the expansion of $\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 45 }$

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

The common ratio of a geometric sequence is $\frac { 3 } { 7 }$ and the fourth term is $\frac { 1 } { 7 }$ Find the third term

Find the sum of the infinite geometric series. $a + a x ^ { 2 } + a x ^ { 4 } + a x ^ { 6 } + \ldots$

Find the coefficient of $a ^ { 4 } b ^ { 4 }$ in the expansion of $( b - a ) ^ { 3 }$

The common ratio of a geometric sequence is $\frac { 3 } { 7 }$ and the fourth term is $\frac { 1 } { 7 }$ Find the third term.

Find the $n ^ { \text {th} }$ term of the sequence whose first several terms are $3$ , $9$ , $27$ , $81$ ,.....

Express the repeating decimal $0.1 \overline { 38 }$ as a fraction.

Write the sum using sigma notation. $1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } + 4 ^ { 2 } + \ldots + 101 ^ { 2 }$

Write the sum without using sigma notation. Do not evaluate. $\sum _ { n = 2 } ^ { 100 } \frac { 1 } { n - 1 }$

Find the coefficient of $- a ^ { \dot { 3 } } b ^ { 3 }$ in the expansion of $( b - a ) ^ { 3 }$

Expand the expression $( 1 - y ) ^ { 4 }$ .