Question 1

Write the first five terms of the sequence whose general term is given.
-$a _ { n } = 2 n - 1$

Accepted Answer

A)  $3,5,7,9,11$ 
B)  $1,3,5,7,9$ 
C)  $- 1 , - 3 , - 5 , - 7 , - 9$ 
D)  $1,2,3,4,5$ 
A)  $3,5,7,9,11$ 
B)  $1,3,5,7,9$ 
C)  $- 1 , - 3 , - 5 , - 7 , - 9$ 
D)  $1,2,3,4,5$

Question 2

Evaluate the expression.
-$\sum _ { i = 8 } ^ { 11 } \frac { 1 } { i - 3 }$

Accepted Answer

A)  26 
B)  $\frac { 533 } { 840 }$ 
C)  $\frac { 701 } { 1320 }$ 
D)  $- \frac { 1755 } { 4096 }$ 
A)  26 
B)  $\frac { 533 } { 840 }$ 
C)  $\frac { 701 } { 1320 }$ 
D)  $- \frac { 1755 } { 4096 }$

Question 3

Use Pascal's triangle to expand the binomial.
-$( x - y ) ^ { 6 }$

Accepted Answer

A)  $x ^ { 6 } - x ^ { 5 } y + x ^ { 4 } y ^ { 2 } - x ^ { 3 } y ^ { 3 } + x ^ { 2 } y ^ { 4 } - x y ^ { 5 } + y ^ { 6 }$ 
B)  $x ^ { 6 } - 6 x ^ { 5 } y + 15 x ^ { 4 } y ^ { 2 } - 20 x ^ { 3 } y ^ { 3 } + 15 x ^ { 2 } y ^ { 4 } - 6 x y ^ { 5 } + y ^ { 6 }$ 
C)  $x ^ { 6 } - 6 x ^ { 5 } y - 15 x ^ { 4 } y ^ { 2 } - 20 x ^ { 3 } y ^ { 3 } - 15 x ^ { 2 } y ^ { 4 } - 6 x y ^ { 5 } - y ^ { 6 }$ 
D)  $x ^ { 6 } - y ^ { 6 }$ 
A)  $x ^ { 6 } - x ^ { 5 } y + x ^ { 4 } y ^ { 2 } - x ^ { 3 } y ^ { 3 } + x ^ { 2 } y ^ { 4 } - x y ^ { 5 } + y ^ { 6 }$ 
B)  $x ^ { 6 } - 6 x ^ { 5 } y + 15 x ^ { 4 } y ^ { 2 } - 20 x ^ { 3 } y ^ { 3 } + 15 x ^ { 2 } y ^ { 4 } - 6 x y ^ { 5 } + y ^ { 6 }$ 
C)  $x ^ { 6 } - 6 x ^ { 5 } y - 15 x ^ { 4 } y ^ { 2 } - 20 x ^ { 3 } y ^ { 3 } - 15 x ^ { 2 } y ^ { 4 } - 6 x y ^ { 5 } - y ^ { 6 }$ 
D)  $x ^ { 6 } - y ^ { 6 }$

Question 4

Find the partial sum.
-Find the sum of the first three terms of the sequence whose general term is $a _ { n } = ( n + 1 ) ( n - 5 )$.

Accepted Answer

A)  25 
B)  65 
C)  $- 17$ 
D)  $- 25$ 
A)  25 
B)  65 
C)  $- 17$ 
D)  $- 25$

Question 5

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l l } 
\text { general term } & \text { common difference } & \text { finite sequence } & \text { common ratio } \
\text { Pascal's triangle } & \text { infinite sequence } & \text { factorial of } \mathbf { n } & \text { series } \
\text { geometric sequence } & \text { arithmetic sequence } & &
\end{array}$$
-A(n)__________is a function whose domain is the set of natural numbers $\{ 1,2,3 , \ldots , n \}$, where $n$ is some natural number.

Accepted Answer

A)  factorial of $n$ 
B)  finite sequence 
C)  series 
D)  infinite sequence 
A)  factorial of $n$ 
B)  finite sequence 
C)  series 
D)  infinite sequence

Question 6

Find the indicated term(s) of the given sequence.
-The general term of the sequence $- 3,9 , - 27,81 , \ldots$

Accepted Answer

A)  $a _ { n } = ( - 1 ) ^ { n } 3 ^ { n }$ 
B)  $a _ { n } = 3 ^ { n }$ 
C)  $a _ { n } = 3 ^ { n + 1 }$ 
D)  $a _ { n } = ( - 1 ) ^ { n + 1 } 3 ^ { n + 1 }$ 
A)  $a _ { n } = ( - 1 ) ^ { n } 3 ^ { n }$ 
B)  $a _ { n } = 3 ^ { n }$ 
C)  $a _ { n } = 3 ^ { n + 1 }$ 
D)  $a _ { n } = ( - 1 ) ^ { n + 1 } 3 ^ { n + 1 }$

Question 7

Evaluate the expression.
-$\frac { 5 ! } { 3 ! }$

Accepted Answer

A)  $\frac { 5 } { 3 }$ 
B)  20 
C)  2 ! 
D)  5 
A)  $\frac { 5 } { 3 }$ 
B)  20 
C)  2 ! 
D)  5

Question 8

Solve the problem.
-In 2007 , business analysts estimated that the number of skilled carpenters working in a certain city was decreasing each year. The number of employed carpenters in a given year is $24 - 4 n$ hundred fewer than the previous year. Find the decrease in employed carpenters in 2010, if year 1 is $2007 .$ Find how many total hundred carpenters became unemployed from 2007 through 2010 .

Accepted Answer

A)  12 hundred carpenters; 48 hundred carpenters 
B)  8 hundred carpenters; 36 hundred carpenters 
C)  8 hundred carpenters; 56 hundred carpenters 
D)  8 hundred carpenters; 48 hundred carpenters 
A)  12 hundred carpenters; 48 hundred carpenters 
B)  8 hundred carpenters; 36 hundred carpenters 
C)  8 hundred carpenters; 56 hundred carpenters 
D)  8 hundred carpenters; 48 hundred carpenters

Question 9

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given.
-$a _ { 1 } = 5 ; d = - 1$

Accepted Answer

A)  $5,4,2,2,1$ 
B)  $4,3,2,1,0$ 
C)  $5,4,3,2,1$ 
D)  $6,5,4,3,2$ 
A)  $5,4,2,2,1$ 
B)  $4,3,2,1,0$ 
C)  $5,4,3,2,1$ 
D)  $6,5,4,3,2$

Question 10

Use the binomial formula to expand the binomial.
-$( x + 3 ) ^ { 5 }$

Accepted Answer

A)  $x ^ { 5 } + 15 x ^ { 4 } + 180 x ^ { 3 } + 540 x ^ { 2 } + 405 x + 243$ 
B)  $x ^ { 5 } + 15 x ^ { 4 } + 180 x ^ { 3 } + 540 x ^ { 2 } + 405 x + 3$ 
C)  $x ^ { 5 } + 15 x ^ { 4 } + 90 x ^ { 3 } + 270 x ^ { 2 } + 405 x + 243$ 
D)  $x ^ { 5 } + 15 x ^ { 4 } + 90 x ^ { 3 } + 270 x ^ { 2 } + 405 x + 3$ 
A)  $x ^ { 5 } + 15 x ^ { 4 } + 180 x ^ { 3 } + 540 x ^ { 2 } + 405 x + 243$ 
B)  $x ^ { 5 } + 15 x ^ { 4 } + 180 x ^ { 3 } + 540 x ^ { 2 } + 405 x + 3$ 
C)  $x ^ { 5 } + 15 x ^ { 4 } + 90 x ^ { 3 } + 270 x ^ { 2 } + 405 x + 243$ 
D)  $x ^ { 5 } + 15 x ^ { 4 } + 90 x ^ { 3 } + 270 x ^ { 2 } + 405 x + 3$

Question 11

Solve the problem.
-A financial planner predicts that a certain stock will increase in value $17 \%$ each year. Thus, the yearly stock values can be modeled by a geometric sequence whose common ratio $r$ is $1.17$. If the initial stock value was $\$ 33$, write the first five terms of the sequence. Round to the nearest cent, if necessary.

Accepted Answer

A)  $\$ 33 , \$ 45.17 , \$ 52.85 , \$ 61.84 , \$ 72.35$ 
B)  $\$ 33 , \$ 34.17 , \$ 35.34 , \$ 36.51 , \$ 37.68$ 
C)  $\$ 38.61 , \$ 45.17 , \$ 52.85 , \$ 61.84 , \$ 72.35$ 
D)  $\$ 33 , \$ 38.61 , \$ 45.17 , \$ 52.85 , \$ 61.84$ 
A)  $\$ 33 , \$ 45.17 , \$ 52.85 , \$ 61.84 , \$ 72.35$ 
B)  $\$ 33 , \$ 34.17 , \$ 35.34 , \$ 36.51 , \$ 37.68$ 
C)  $\$ 38.61 , \$ 45.17 , \$ 52.85 , \$ 61.84 , \$ 72.35$ 
D)  $\$ 33 , \$ 38.61 , \$ 45.17 , \$ 52.85 , \$ 61.84$

Question 12

Find the indicated term of the sequence.
-If the third term of a geometric progression is 3 and the fourth term is $- 6$, find $a _ { 1 }$ and $r$.

Accepted Answer

A)  $a _ { 1 } = 12 ; r = - 2$ 
B)  $a _ { 1 } = - \frac { 3 } { 2 } ; r = - 2$ 
C)  $a _ { 1 } = - \frac { 3 } { 4 } ; r = 2$ 
D)  $\mathrm { a } _ { 1 } = \frac { 3 } { 4 } ; \mathrm { r } = - 2$ 
A)  $a _ { 1 } = 12 ; r = - 2$ 
B)  $a _ { 1 } = - \frac { 3 } { 2 } ; r = - 2$ 
C)  $a _ { 1 } = - \frac { 3 } { 4 } ; r = 2$ 
D)  $\mathrm { a } _ { 1 } = \frac { 3 } { 4 } ; \mathrm { r } = - 2$

Question 13

Solve the problem.
-Use the formula $S _ { \infty }$ to write $0.49 \overline { 49 }$ as a fraction.

Accepted Answer

A)  $\frac { 49 } { 99 }$ 
B)  $\frac { 49 } { 1000 }$ 
C)  $\frac { 4900 } { 99 }$ 
D)  $\frac { 49 } { 100 }$ 
A)  $\frac { 49 } { 99 }$ 
B)  $\frac { 49 } { 1000 }$ 
C)  $\frac { 4900 } { 99 }$ 
D)  $\frac { 49 } { 100 }$

Question 14

Find the indicated term of the sequence.
-The sixth term of the geometric sequence 4, 20, 100, ...

Accepted Answer

A)  3125 
B)  100 
C)  12,500 
D)  62,500 
A)  3125 
B)  100 
C)  12,500 
D)  62,500

Question 15

Provide an appropriate response.
-Find the term containing $x ^ { 2 }$ in the expansion of $( \sqrt { x } + \sqrt { 3 } ) ^ { 8 }$.

Accepted Answer

A)  $70 \sqrt { 3 } x ^ { 2 }$ 
B)  $630 x ^ { 2 }$ 
C)  $- 630 x ^ { 2 }$ 
D)  $- 70 \sqrt { 3 } x ^ { 2 }$ 
A)  $70 \sqrt { 3 } x ^ { 2 }$ 
B)  $630 x ^ { 2 }$ 
C)  $- 630 x ^ { 2 }$ 
D)  $- 70 \sqrt { 3 } x ^ { 2 }$

Question 16

Find a general term an for the sequence whose first four terms are given.
-$\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { n ^ { 2 } }$ 
B)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = \frac { 1 } { 3 n - 2 }$ 
D)  $a _ { n } = \frac { 1 } { n ^ { n - 1 } }$ 
A)  $a _ { n } = \frac { 1 } { n ^ { 2 } }$ 
B)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = \frac { 1 } { 3 n - 2 }$ 
D)  $a _ { n } = \frac { 1 } { n ^ { n - 1 } }$

Question 17

Find the partial sum.
-Find the sum of the first four terms of the sequence whose general term is $a _ { n } = - \frac { n } { 11 }$.

Accepted Answer

A)  $\frac { 10 } { 11 }$ 
B)  $- \frac { 10 } { 11 }$ 
C)  $- \frac { 6 } { 11 }$ 
D)  $\frac { 2 } { 11 }$ 
A)  $\frac { 10 } { 11 }$ 
B)  $- \frac { 10 } { 11 }$ 
C)  $- \frac { 6 } { 11 }$ 
D)  $\frac { 2 } { 11 }$

Question 18

The notation $\left( \frac { \mathbf { n } } { \mathrm { r } } \right) \text { means } \left( \frac { \mathrm { n } ! } { \mathrm { r } ! ( \mathrm { n } - \mathrm { r } ) ! } \right) \text {. Evaluate the expression. }$
-$\left( \begin{array} { c } 236 \ 3 \end{array} \right)$

Accepted Answer

A)  $\frac { 236 ! } { 233 ! }$ 
B)  233 
C)  $2,162,940$ 
D)  $12,977,640$ 
A)  $\frac { 236 ! } { 233 ! }$ 
B)  233 
C)  $2,162,940$ 
D)  $12,977,640$

Question 19

Solve the problem.
-When students at the local university held a food drive, 320 cans of food were collected on the first day of the drive, 160 the second day, 80 the third day, and so on. Find the total number of cans
Collected the first five days.

Accepted Answer

A)  630 cans 
B)  620 cans 
C)  600 cans 
D)  850 cans 
A)  630 cans 
B)  620 cans 
C)  600 cans 
D)  850 cans

Question 20

Find the partial sum.
-Find the sum of the first four terms of the sequence whose general term is $a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { 3 n }$.

Accepted Answer

A)  $- \frac { 7 } { 36 }$ 
B)  $\frac { 7 } { 36 }$ 
C)  $- \frac { 25 } { 36 }$ 
D)  $\frac { 25 } { 36 }$ 
A)  $- \frac { 7 } { 36 }$ 
B)  $\frac { 7 } { 36 }$ 
C)  $- \frac { 25 } { 36 }$ 
D)  $\frac { 25 } { 36 }$

Write the first five terms of the sequence whose general term is given. - $a _ { n } = 2 n - 1$

Evaluate the expression. - $\sum _ { i = 8 } ^ { 11 } \frac { 1 } { i - 3 }$

Use Pascal's triangle to expand the binomial. - $( x - y ) ^ { 6 }$

Find the partial sum. -Find the sum of the first three terms of the sequence whose general term is $a _ { n } = ( n + 1 ) ( n - 5 )$ .

Find the indicated term(s) of the given sequence. -The general term of the sequence $- 3,9 , - 27,81 , \ldots$

Evaluate the expression. - $\frac { 5 ! } { 3 ! }$

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given. - $a _ { 1 } = 5 ; d = - 1$

Use the binomial formula to expand the binomial. - $( x + 3 ) ^ { 5 }$

Find the indicated term of the sequence. -If the third term of a geometric progression is 3 and the fourth term is $- 6$ , find $a _ { 1 }$ and $r$ .

Solve the problem. -Use the formula $S _ { \infty }$ to write $0.49 \overline { 49 }$ as a fraction.

Find the indicated term of the sequence. -The sixth term of the geometric sequence 4, 20, 100, ...

Provide an appropriate response. -Find the term containing $x ^ { 2 }$ in the expansion of $( \sqrt { x } + \sqrt { 3 } ) ^ { 8 }$ .

Find a general term an for the sequence whose first four terms are given. - $\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \ldots$

Find the partial sum. -Find the sum of the first four terms of the sequence whose general term is $a _ { n } = - \frac { n } { 11 }$ .

The notation $\left( \frac { \mathbf { n } } { \mathrm { r } } \right) \text { means } \left( \frac { \mathrm { n } ! } { \mathrm { r } ! ( \mathrm { n } - \mathrm { r } ) ! } \right) \text {. Evaluate the expression. }$ - $\left( \begin{array} { c } 236 \\ 3 \end{array} \right)$

Solve the problem. -When students at the local university held a food drive, 320 cans of food were collected on the first day of the drive, 160 the second day, 80 the third day, and so on. Find the total number of cans Collected the first five days.

Find the partial sum. -Find the sum of the first four terms of the sequence whose general term is $a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { 3 n }$ .

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Filters

Exam 14: Sequences, Series, and the Binomial Theorem

Write the first five terms of the sequence whose general term is given. - an=2n−1a _ { n } = 2 n - 1an​=2n−1

Evaluate the expression. - ∑i=8111i−3\sum _ { i = 8 } ^ { 11 } \frac { 1 } { i - 3 }∑i=811​i−31​

Use Pascal's triangle to expand the binomial. - (x−y)6( x - y ) ^ { 6 }(x−y)6

Find the partial sum. -Find the sum of the first three terms of the sequence whose general term is an=(n+1)(n−5)a _ { n } = ( n + 1 ) ( n - 5 )an​=(n+1)(n−5) .

Find the indicated term(s) of the given sequence. -The general term of the sequence −3,9,−27,81,…- 3,9 , - 27,81 , \ldots−3,9,−27,81,…

Evaluate the expression. - 5!3!\frac { 5 ! } { 3 ! }3!5!​

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given. - a1=5;d=−1a _ { 1 } = 5 ; d = - 1a1​=5;d=−1

Use the binomial formula to expand the binomial. - (x+3)5( x + 3 ) ^ { 5 }(x+3)5

Find the indicated term of the sequence. -If the third term of a geometric progression is 3 and the fourth term is −6- 6−6 , find a1a _ { 1 }a1​ and rrr .

Solve the problem. -Use the formula S∞S _ { \infty }S∞​ to write 0.4949‾0.49 \overline { 49 }0.4949 as a fraction.