Question 1

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 2

Find the $n ^ { \text {th } }$ 
term of the sequence whose first several terms are $2,6,10,14 , \ldots$ 
.

Accepted Answer

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

Question 3

The seventh term of an arithmetic sequence is $- 16$  and the seventeenth term is $- 66$ .
 Find the twenty-fourth term.

Accepted Answer

None

Question 4

Find the amount of an annuity that consists of $15$ 
annual payments of $\$ 200$ 
each into an account that pays $12 \%$ 
interest per year.

Accepted Answer

The answer of Find the amount of an annuity that...

Question 5

Express the repeating decimal $0.345345345 \ldots$ 
as a fraction.

Accepted Answer

The answer of Express the repeating decimal $0.345345345 \ldots$ 
as...

Question 6

Write the sum using sigma notation. $\frac { 1 } { 1 \cdot 2 } + \frac { 1 } { 2 \cdot 3 } + \frac { 1 } { 3 \cdot 4 } + \ldots + \frac { 1 } { 999 \cdot 1000 }$

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 1000 } \frac { 1 } { n ( n + 1 ) }$ 
B)  $\sum _ { n = 1 } ^ { 1000 } \frac { 1 } { n ( n - 1 ) }$ 
C)  $\sum _ { n = 1 } ^ { 999 } \frac { 1 } { n ( n + 1 ) }$ 
D)  $\sum _ { n = 1 } ^ { 1001 } \frac { 1 } { n ( n + 1 ) }$ 
E)  $\sum _ { n = 1 } ^ { 999 } \frac { 1 } { n ( n - 1 ) }$ 
A)  $\sum _ { n = 1 } ^ { 1000 } \frac { 1 } { n ( n + 1 ) }$ 
B)  $\sum _ { n = 1 } ^ { 1000 } \frac { 1 } { n ( n - 1 ) }$ 
C)  $\sum _ { n = 1 } ^ { 999 } \frac { 1 } { n ( n + 1 ) }$ 
D)  $\sum _ { n = 1 } ^ { 1001 } \frac { 1 } { n ( n + 1 ) }$ 
E)  $\sum _ { n = 1 } ^ { 999 } \frac { 1 } { n ( n - 1 ) }$

Question 7

The first term of the arithmetic sequence is $\frac {2 } { 3 }$and the common difference is $\left( - \frac { 2 } { 3 } \right\}$Which term of this sequence is $- \frac { 20 } { 3 }$?

Accepted Answer

A)  $10 ^ { \mathrm { th } } \text { term }$ 
B)  $12 ^ { \text {th } } \text { term }$ 
C)  $13 ^ { \text {th } } \text { term }$ 
D)  $16 ^ { \mathrm { th} } \text { term }$ 
E)   $6 ^ { \mathrm { th} } \text { term }$ 
A)  $10 ^ { \mathrm { th } } \text { term }$ 
B)  $12 ^ { \text {th } } \text { term }$ 
C)  $13 ^ { \text {th } } \text { term }$ 
D)  $16 ^ { \mathrm { th} } \text { term }$ 
E)   $6 ^ { \mathrm { th} } \text { term }$

Question 8

An arithmetic sequence has first term $a = - 2$ and common difference $d = 4$ . 
How many terms of this sequence must be added to get $1566$ ?

Accepted Answer

The answer of An arithmetic sequence has first term \(a...

Question 9

Dr. Stevens is considering a 30-year mortgage at 4% interest. She can make payments of $3500 a month. What size loan can she afford?

Accepted Answer

A)  $\$ 831,114.26$ 
B)  $\$ 786,457.35$ 
C)  $\$ 750,114.36$ 
D)  $\$ 833,114.34$ 
E)  $\$ 733,114.34$ 
A)  $\$ 831,114.26$ 
B)  $\$ 786,457.35$ 
C)  $\$ 750,114.36$ 
D)  $\$ 833,114.34$ 
E)  $\$ 733,114.34$

Question 10

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $2 + 4 + 6 + 8 +\dots + 100$

Accepted Answer

The answer of Determine whether the expression is a partial...

Question 11

Find the amount of an annuity that consists of $30$  annual payments of $\$ 500$  each into an account that pays $7 \%$  interest per year.

Accepted Answer

The answer of Find the amount of an annuity that...

Question 12

A city was incorporated in 2004 with a population of 45,000. It is expected that the population will increase at a rate of 2% per year. The population n years after 2004 is given by the sequence $P _ { n } = 45000 ( 1.02 ) ^ { n }$ 
a) Find the first 5 terms of the sequence
b) Find the population in 2014.

Accepted Answer

The answer of A city was incorporated in 2004 with...

Question 13

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 + \dots+ 15625$

Accepted Answer

@#LAT-DLM& , @#LAT-DLM& , so @#LAT-DLM&

Question 14

Find the first four terms and the $10 ^ { \mathrm { ct } }$  term of the sequence $a _ { n } = n - 2$

Accepted Answer

The answer of Find the first four terms and the...

Question 15

Given that the $ 5^{\text {th }} $ term of an arithmetic sequence is $30$and the $7 ^ { \mathrm { ct } }$term is $44$
, find the first term

Accepted Answer

A)  $a _ { 1 } = 7$ 
B)  $a _ { 1 } = 4$ 
C)  $a _ { 1 } = - 4$ 
D)  $a _ { 1 } = - 2$ 
E)  $a _ { 1 } = 2$ 
A)  $a _ { 1 } = 7$ 
B)  $a _ { 1 } = 4$ 
C)  $a _ { 1 } = - 4$ 
D)  $a _ { 1 } = - 2$ 
E)  $a _ { 1 } = 2$

Question 16

How much money must be invested now at $5 \%$ per year, compounded semi-annually, to fund an annuity of $14$
Semi-annual payments of $\$ 100$
Each, the first payment being six months after the initial investment?

Accepted Answer

A)  $\$ 1069.09$ 
B)  $\$ 2455.09$ 
C)  $\$ 2169.09$ 
D)  $\$ 2545.49$ 
E)  $\$ 1169.09$ 
A)  $\$ 1069.09$ 
B)  $\$ 2455.09$ 
C)  $\$ 2169.09$ 
D)  $\$ 2545.49$ 
E)  $\$ 1169.09$

Question 17

Find the first four terms and the $10 ^ { \mathrm { ct } }$ 
term of the sequence $a _ { n } = n - 2$ 
.

Accepted Answer

The answer of Find the first four terms and the...

Question 18

Find the $n ^ { \text {th } }$ term of the sequence whose first several terms are $\frac { 1 } { 4 } , - \frac { 1 } { 9 } , \frac { 1 } { 16 } , - \frac { 1 } { 25 } , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { n ^ { 2 } }$ 
B)  $a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { ( n + 1 ) ^ { 2 } }$ 
C)  $a _ { \mathrm { n } } = \frac { ( n + 1 ) ^ { n } } { 4 ^ { 2 } }$ 
D)  $a _ { n } = \frac { ( 1 ) ^ { n } } { ( 2 n ) ^ { 2 } }$ 
E)  none of these 
A)  $a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { n ^ { 2 } }$ 
B)  $a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { ( n + 1 ) ^ { 2 } }$ 
C)  $a _ { \mathrm { n } } = \frac { ( n + 1 ) ^ { n } } { 4 ^ { 2 } }$ 
D)  $a _ { n } = \frac { ( 1 ) ^ { n } } { ( 2 n ) ^ { 2 } }$ 
E)  none of these

Question 19

Dr. Stevens is considering a 30-year mortgage at 4% interest. She can make payments of $3500 a month. What size loan can she afford?

Accepted Answer

The answer of Dr. Stevens is considering a 30-year mortgage...

Question 20

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

Accepted Answer

A)  $- 28$ 
B)  $28$ 
C)  $- 56$ 
D)  $56$ 
E)  $70$ 
A)  $- 28$ 
B)  $28$ 
C)  $- 56$ 
D)  $56$ 
E)  $70$

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

Find the $n ^ { \text {th } }$ term of the sequence whose first several terms are $2,6,10,14 , \ldots$ .

The seventh term of an arithmetic sequence is $- 16$ and the seventeenth term is $- 66$ . Find the twenty-fourth term.

Find the amount of an annuity that consists of $15$ annual payments of $\$ 200$ each into an account that pays $12 \%$ interest per year.

Express the repeating decimal $0.345345345 \ldots$ as a fraction.

Write the sum using sigma notation. $\frac { 1 } { 1 \cdot 2 } + \frac { 1 } { 2 \cdot 3 } + \frac { 1 } { 3 \cdot 4 } + \ldots + \frac { 1 } { 999 \cdot 1000 }$

The first term of the arithmetic sequence is $\frac {2 } { 3 }$ and the common difference is $\left( - \frac { 2 } { 3 } \right\}$ Which term of this sequence is $- \frac { 20 } { 3 }$ ?

An arithmetic sequence has first term $a = - 2$ and common difference $d = 4$ . How many terms of this sequence must be added to get $1566$ ?

Dr. Stevens is considering a 30-year mortgage at 4% interest. She can make payments of $3500 a month. What size loan can she afford?

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $2 + 4 + 6 + 8 +\dots + 100$

Find the amount of an annuity that consists of $30$ annual payments of $\$ 500$ each into an account that pays $7 \%$ interest per year.

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 + \dots+ 15625$

Find the first four terms and the $10 ^ { \mathrm { ct } }$ term of the sequence $a _ { n } = n - 2$

Given that the $5^{\text {th }}$ term of an arithmetic sequence is $30$ and the $7 ^ { \mathrm { ct } }$ term is $44$ , find the first term

How much money must be invested now at $5 \%$ per year, compounded semi-annually, to fund an annuity of $14$ Semi-annual payments of $\$ 100$ Each, the first payment being six months after the initial investment?

Find the first four terms and the $10 ^ { \mathrm { ct } }$ term of the sequence $a _ { n } = n - 2$ .

Find the $n ^ { \text {th } }$ term of the sequence whose first several terms are $\frac { 1 } { 4 } , - \frac { 1 } { 9 } , \frac { 1 } { 16 } , - \frac { 1 } { 25 } , \ldots$

Dr. Stevens is considering a 30-year mortgage at 4% interest. She can make payments of $3500 a month. What size loan can she afford?

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

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

Exam 13: Sequences and Series

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

Find the nth n ^ { \text {th } }nth term of the sequence whose first several terms are 2,6,10,14,…2,6,10,14 , \ldots2,6,10,14,… .

The seventh term of an arithmetic sequence is −16- 16−16 and the seventeenth term is −66- 66−66 . Find the twenty-fourth term.

Find the amount of an annuity that consists of 151515 annual payments of $200\$ 200$200 each into an account that pays 12%12 \%12% interest per year.

Express the repeating decimal 0.345345345…0.345345345 \ldots0.345345345… as a fraction.

Write the sum using sigma notation. 11⋅2+12⋅3+13⋅4+…+1999⋅1000\frac { 1 } { 1 \cdot 2 } + \frac { 1 } { 2 \cdot 3 } + \frac { 1 } { 3 \cdot 4 } + \ldots + \frac { 1 } { 999 \cdot 1000 }1⋅21​+2⋅31​+3⋅41​+…+999⋅10001​

The first term of the arithmetic sequence is 23\frac {2 } { 3 }32​ and the common difference is (−23}\left( - \frac { 2 } { 3 } \right\}(−32​} Which term of this sequence is −203- \frac { 20 } { 3 }−320​ ?

An arithmetic sequence has first term a=−2a = - 2a=−2 and common difference d=4d = 4d=4 . How many terms of this sequence must be added to get 156615661566 ?

Dr. Stevens is considering a 30-year mortgage at 4% interest. She can make payments of $3500 a month. What size loan can she afford?

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. 2+4+6+8+⋯+1002 + 4 + 6 + 8 +\dots + 1002+4+6+8+⋯+100

Find the amount of an annuity that consists of 303030 annual payments of $500\$ 500$500 each into an account that pays 7%7 \%7% interest per year.

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. 5+25+125+⋯+156255 + 25 + 125 + \dots+ 156255+25+125+⋯+15625

Find the first four terms and the 10ct10 ^ { \mathrm { ct } }10ct term of the sequence an=n−2a _ { n } = n - 2an​=n−2

Given that the 5th 5^{\text {th }} 5th term of an arithmetic sequence is 303030 and the 7ct7 ^ { \mathrm { ct } }7ct term is 444444 , find the first term

How much money must be invested now at 5%5 \%5% per year, compounded semi-annually, to fund an annuity of 141414 Semi-annual payments of $100\$ 100$100 Each, the first payment being six months after the initial investment?

Find the first four terms and the 10ct10 ^ { \mathrm { ct } }10ct term of the sequence an=n−2a _ { n } = n - 2an​=n−2 .

Find the nth n ^ { \text {th } }nth term of the sequence whose first several terms are 14,−19,116,−125,…\frac { 1 } { 4 } , - \frac { 1 } { 9 } , \frac { 1 } { 16 } , - \frac { 1 } { 25 } , \ldots41​,−91​,161​,−251​,…

Dr. Stevens is considering a 30-year mortgage at 4% interest. She can make payments of $3500 a month. What size loan can she afford?

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

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

Find the $n ^ { \text {th } }$ term of the sequence whose first several terms are $2,6,10,14 , \ldots$ .

The seventh term of an arithmetic sequence is $- 16$ and the seventeenth term is $- 66$ . Find the twenty-fourth term.

Find the amount of an annuity that consists of $15$ annual payments of $\$ 200$ each into an account that pays $12 \%$ interest per year.

Express the repeating decimal $0.345345345 \ldots$ as a fraction.

Write the sum using sigma notation. $\frac { 1 } { 1 \cdot 2 } + \frac { 1 } { 2 \cdot 3 } + \frac { 1 } { 3 \cdot 4 } + \ldots + \frac { 1 } { 999 \cdot 1000 }$

The first term of the arithmetic sequence is $\frac {2 } { 3 }$ and the common difference is $\left( - \frac { 2 } { 3 } \right\}$ Which term of this sequence is $- \frac { 20 } { 3 }$ ?

An arithmetic sequence has first term $a = - 2$ and common difference $d = 4$ . How many terms of this sequence must be added to get $1566$ ?

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $2 + 4 + 6 + 8 +\dots + 100$

Find the amount of an annuity that consists of $30$ annual payments of $\$ 500$ each into an account that pays $7 \%$ interest per year.

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 + \dots+ 15625$

Find the first four terms and the $10 ^ { \mathrm { ct } }$ term of the sequence $a _ { n } = n - 2$

Given that the $5^{\text {th }}$ term of an arithmetic sequence is $30$ and the $7 ^ { \mathrm { ct } }$ term is $44$ , find the first term

How much money must be invested now at $5 \%$ per year, compounded semi-annually, to fund an annuity of $14$ Semi-annual payments of $\$ 100$ Each, the first payment being six months after the initial investment?

Find the first four terms and the $10 ^ { \mathrm { ct } }$ term of the sequence $a _ { n } = n - 2$ .

Find the $n ^ { \text {th } }$ term of the sequence whose first several terms are $\frac { 1 } { 4 } , - \frac { 1 } { 9 } , \frac { 1 } { 16 } , - \frac { 1 } { 25 } , \ldots$

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