Deck 8: Special Topics in Algebra

Question 1

Graph the solution region for the system of inequalities and identify the corners of the region.

- $\left\{\begin{array}{l}-x+y \leq 5 \\x+y \geq 3 \\-3 x+y \geq-1\end{array}\right.$

A)

B)

C)

D)

Answer 1

Question 2

Graph the solution region for the system of inequalities and identify the corners of the region.
$$\left\{ \begin{array} { l } x + 2 y \leq 10 \\2 x + y \leq 8 \\x \geq 0 , y \geq 0\end{array} \right.$$
A)

B)

C)

D)

Answer 2

B

Question 3

Graph the inequality.

- $5 x+y \leq 4$

A)
B)
C)
D)

Answer 3

Question 4

Match the solution of the system of inequalities with the graph.
$$\left\{ \begin{array} { l } y > 2 x - 1 \\y < x + 1\end{array} \right.$$

A)

B)

C)

D)

Question 5

Graph the solution region for the system of inequalities and identify the corners of the region.
$$\left\{ \begin{array} { l } 3 x + 2 y \geq - 12 \\x - 2 y \leq - 4 \\y \leq 6\end{array} \right.$$

A)

B)

C)

D)

Question 6

$\frac { x } { 3 } - \frac { y } { 4 } > - 1$

A)
B)
C)
D)

Question 7

Graph the inequality.

- $2 x+4 y \geq-8$

A)
B)
C)
D)

Question 8

Match the solution of the system of inequalities with the graph.
$$\left\{ \begin{array} { l } 2 x + y \geq 4 \\x + 2 y \geq 5 \\x \geq 0 \\y \geq 0\end{array} \right.$$

A)

B)


C)

D)

Question 9

Graph the inequality.

- $x-y>-2$

A)
B)
C)
D)

Question 10

Graph the solution region for the system of inequalities and identify the corners of the region.

- $\left\{\begin{array}{l}3 y+x>0 \\y+2 x \leq 10 \\y \geq 0\end{array}\right.$

A)

B)

C)

D)

Question 11

Graph the solution region for the system of inequalities and identify the corners of the region.
$$\left\{ \begin{array} { l } y \leq 3 x - 1 \\y \geq - 3 x - 1 \\x \leq 3\end{array} \right.$$

A)

B)

C)

D)

Question 12

Graph the inequality.

- $-2 x-4 y \leq 8$

A)
B)
C)
D)

Question 13

Graph the solution region for the system of inequalities and identify the corners of the region.
$$\left\{ \begin{array} { l } 3 y + x \geq - 6 \\y + 2 x \leq 8 \\y \leq 0 , x \geq 0\end{array} \right.$$

A)

B)

C)

D)

Question 14

The graph of the boundary equations for the system of inequalities is shown with the system. Find the corners of the
solution region.
$$\left\{ \begin{array} { l } x + y \leq 6 \\3 x + y \leq 12\end{array} \right.$$

A) (0, 0), (6, 0), (0, 12), (3, 3)
B) (0, 0), (4, 0), (0, 6), (3, 3)
C) (0, 0), (6, 0), (0, 6), (3, 3)
D) (0, 0), (4, 0), (0, 12), (3, 3)

Question 15

Graph the inequality.

- $x+y<-5$

A)
B)
C)
D)

Question 16

Graph the solution region for the system of inequalities and identify the corners of the region.
$$\left\{ \begin{array} { l } 2 y + x \geq - 2 \\y + 3 x \leq 9 \\y \leq 0 , x \geq 0\end{array} \right.$$

A)

B)

C)
11ecb7d5_61a0_d53a_b9c9_9d81213f8dbc_TB6590_00
D)

Question 17

Graph the solution set of the system of inequalities.
$$\left\{ \begin{array} { l } y > x ^ { 2 } - 4 \\2 y - x < 0\end{array} \right.$$

A)

B)

C)

D)

Question 18

$$y < - 4 x + 1$$

A)

B)

C)

D)

Question 19

Graph the solution region for the system of inequalities and identify the corners of the region.
$$\left\{ \begin{array} { l } 3 y - x < 9 \\y + 2 x < 10 \\y \geq 0\end{array} \right.$$

A)

B)

C)

D)

Question 20

$x+2 y \geq 1$

A)

B)

C)

D)

Question 21

Graph the solution set of the system of inequalities.

- $\left\{\begin{array}{l}y \leq-x^{2} \\x+y \geq-2\end{array}\right.$

A)

B)

C)

D)

Question 22

Graph the region that satisfies the constraints.
Bubba's Computer World sells personal computers. They want to try out a new advertising campaign with x one-minute spots on local television at a cost of $225 per minute, and y one-minute spots on radio, at a cost of
$180 per minute. For the first phase of the campaign, the advertising director is given a budget of no more than
$45,000 to spend on a maximum of 225 minutes of advertising. A)

B)

C)

D)

Question 23

Graph the region that satisfies the constraints.
A company produce two types of printers, the Inkjet and the Laserjet. It takes 5 hours to make the Inkjet and 10 hours to make the Laserjet. The company can make at most 150 printers per day and has 1000 labor-hours
Available per day. Let x represent the number of Inkjet printers produced in a day and y represent the number
Of Laserjet printers produced in a day. A)

B)

C)

D)

Question 24

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the
objective function.
$\mathrm { f } = 7 \mathrm { x } + 6 \mathrm { y }$ subject to the constraints
$$\left\{ \begin{array} { l } 3 x + 4 y \leq 165 \\x + 2 y \leq 77 \\x \geq 0 , y \geq 0\end{array} \right.$$

A) 385
B) 405
C) 275
D) 231

Question 25

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the
objective function.
$$f = 4 x + 3 y \text { subject to the constraints }$$

A) 28
B) 21
C) 26
D) 24

Question 26

Graph the solution set of the system of inequalities.
A company manufactures two types of lawn mowers, a gas-powered model and an electric model. It costs $98 to produce each of x gas-powered mowers and $104 to produce each of y electric mowers, and the company has
At most $86,450 per month to use for production. Write the inequality that describes this constraint on monthly
Production. A) $104 x + 98 y \leq 86,450$
B) $98 x + 104 y \geq 86,450$
C) $98 x + 104 y \leq 86,450$
D) $104 x + 98 y \geq 86,450$

Question 27

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the
objective function.
$$\begin{aligned}f = & 3 x + 11 y \text { subject to the constraints } \\& \left\{ \begin{array} { l } 5 x + 4 y \leq 180 \\x + 2 y \leq 66 \\x \geq 0 , y \geq 0\end{array} \right.\end{aligned}$$

A) 343
B) 383
C) 363
D) 323

Question 28

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
$\mathrm { f } = 7 \mathrm { x } + 6 \mathrm { y }$ subject to the constraints
$$\left\{ \begin{array} { l } 3 x + 4 y \leq 165 \\x + 2 y \leq 77 \\x \geq 0 , y \geq 0\end{array} \right.$$

A) 385
B) 231
C) 275
D) 0

Question 29

Graph the solution set of the system of inequalities.
$$\left\{ \begin{array} { l } y \leq - x ^ { 2 } - 6 x - 4 \\y \geq x ^ { 2 } + 6 x + 4\end{array} \right.$$

A)

B)

C)

D)

Question 30

Graph the solution set of the system of inequalities.
A sushi restaurant charges $8.95 for its lunch buffet and $12.95 for its dinner buffet. In order for the restaurant to turn a profit, its buffets must generate daily revenue of at least $2190. Write an inequality that describes this
Requirement. Let x represent the number of lunch buffet customers and y represent the number of dinner buffet
Customers. A) $8.95 x + 12.95 y \neq 2190$
B) $8.95 x + 12.95 y \geq 2190$
C) $8.95 x + 12.95 y \leq 2190$
D) $8.95 x + 12.95 y = 2190$

Question 31

Graph the region that satisfies the constraints.
Bubba's Computer World sells personal computers. To advertise its computers to target groups, they advertise with x one-minute spots on local television at a cost of $264 per minute, and y one-minute spots on radio, at a
Cost of $220 per minute. Research shows that they sell one computer for every 3 minutes of television
Advertising, and one computer for every 6 minutes of radio advertising. Suppose the company has at most
$55,000 to spend on advertising and that they sell at least 50 computers per month from this advertising. A)

B)

C)

D)

Question 32

Write the inequalities that describe the constraints on production.
The Pen-Ink Company manufactures two ballpoint pens: silver and gold. The silver requires 7 minutes in a grinder and 12 minutes in a bonder. The gold requires 7 minutes in a grinder and 9 minutes in a bonder. The
Grinder can be run no more than 610 minutes per day and the bonder no more than 230 minutes per day. Let x
Represent the silver pens and let y represent the gold pens. A) $0 \leq 19 x + 16 y \leq 840 , x \geq 0 , y \geq 0$
B) $7 x + 7 y \leq 610,12 x + 9 y \leq 230 , x \geq 0 , y \geq 0$
C) $x + y \leq 610 , x + y \leq 230 , x + y \leq 840 , x \geq 0 , y \geq 0$
D) $7 x + 12 y \leq 610,7 x + 9 y \leq 230 , x \geq 0 , y \geq 0$

Question 33

Graph the region that satisfies the constraints.
A contractor builds two models of homes, the Raskolnikov and the Karamazov. The Raskolnikov requires 180 worker-days of labor and $300,000 in capital, while the Karamazov requires 270 worker-days of labor and
$200,000 in capital. The contractor has a total of 5400 worker-days and $6,000,000 in capital available per
Month. Let x represent the number of Raskolnikov models and y represent the number of Karmazov models. A)

B)

C)

D)

Question 34

Graph the region that satisfies the constraints.
A rectangular enclosure must have an area of at least 6300 square yards. If 320 yards of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie? A) $0 \leq w \leq 70$
B) $70 \leq w \leq 90$
C) $80 \leq w \leq 90$
D) $70 \leq w \leq 80$

Question 35

Write the inequalities that describe the constraints on production.
The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. The company can produce up to 84 rings each day, using up to 210 total man-hours of labor. It takes 3 man-hours to make one
VIP ring and 7 man-hours to make one SST ring. Let x represent the number of VIP rings, and let y represent
The number of SST rings. A) $0 \leq x \leq 84,0 \leq y \leq 84,7 x + 3 y \leq 210$
B) $x + y \leq 84,7 x + 3 y \leq 210 , x \geq 0 , y \geq 0$
C) $0 \leq x \leq 84,0 \leq y \leq 84,3 x + 7 y \leq 210$
D) $x + y \leq 84,3 x + 7 y \leq 210 , x \geq 0 , y \geq 0$

Question 36

Graph the region determined by the inequality in the context of the application.
In order to make a profit an automobile dealer must sell at least 200 vehicles a month. The dealer plans to sell x units of one model and y units of another model. This situation can be modeled by the inequality $$x + y \geq 200$$ A)

B)

C)

D)

Question 37

Graph the region determined by the inequality in the context of the application.
A hardware store has room for 300 bags of fertilizer. The fertilizer manufacturer plans to ship x bags of fertilizer with a weed killer and y bags of fertilizer without the weed killer. This can be represented by $$\text { by } x + y \leq 300$$ A)

B)

C)

D)

Question 38

Graph the solution set of the system of inequalities.
$$\left\{ \begin{array} { l } y \geq - x ^ { 2 } - 6 x - 4 \\y \geq x ^ { 2 } + 6 x + 4\end{array} \right.$$

A)

B)

C)

D)

Question 39

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the
objective function.
$f = 5 x + 6 y$ subject to the constraints
$$\left\{ \begin{array} { l } x + 2 y \leq 14 \\3 x + 2 y \leq 18 \\- x + 2 y \leq 12 \\x \geq 0 , y \geq 0\end{array} \right.$$

A) 36
B) 40
C) 46
D) 44

Question 40

Graph the solution set of the system of inequalities.
A company manufactures two types of lawn mowers, a gas-powered model and an electric model. The company's production plan calls for the production of at least 940 mowers per month. Write the inequality that
Describes the production plan, if x represents the number of gas-powered mowers and y represents the number
Of electric mowers.

A) $x + y \leq 940$
B) $x - y \leq 940$
C) $x + y \geq 940$
D) $x - y \geq 940$

Question 41

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2
Man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the
Company's profit, if the profit on a VIP ring is $30 and on an SST ring is $40?

A) 16 VIP and 8 SST
B) 0 VIP and 24 SST
C) 12 VIP and 12 SST
D) 8 VIP and 16 SST

Question 42

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
$f = 4 x + 3 y$ subject to the constraints
$$\left\{ \begin{array} { l } 2 x + y \leq 12 \\x + 2 y \leq 14 \\x + y \leq 8 \\x \geq 0 , y \geq 0\end{array} \right.$$

A) 24
B) 21
C) 0
D) 26

Question 43

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
$\mathrm { f } = 3 \mathrm { x } + 11 \mathrm { y }$ subject to the constraints
$$\left\{ \begin{array} { l } 5 x + 4 y \geq 180 \\x + 2 y \leq 66 \\y \geq 0\end{array} \right.$$

A) 323
B) 108
C) 198
D) 0

Question 44

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2
Man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the
Company's profit, if the profit on a VIP ring is $50 and on an SST ring is $10?

A) 20 VIP and 4 SST
B) 24 VIP and 0 SST
C) 20 VIP and 0 SST
D) 24 VIP and 4 SST

Question 45

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
$f = 5 x + 6 y$ subject to the constraints
$$\left\{ \begin{array} { l } x + 2 y \geq 14 \\3 x + 2 y \geq 18 \\- x + 2 y \leq 12 \\y \geq 0\end{array} \right.$$

A) 46
B) 48
C) 0
D) 70

Question 46

A certain area of forest is populated by two species of animals, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as $\mathrm { F } _ { 1 }$ and $\mathrm { F } _ { 2 }$ . For one year, species A requires $1.45$ units of $\mathrm { F } _ { 1 }$ and 1 units of $\mathrm { F } _ { 2 }$ . Species $B$ requires $2.0$ units of $\mathrm { F } _ { 1 }$ and $1.9$ units of $\mathrm { F } _ { 2 }$ . The forest can normally supply at most 833 units of $F _ { 1 }$ and 453 units of $F _ { 2 }$ per year. What is the maximum total number of these animals that the forest can support?

A) 453 animals
B) 184 animals
C) 886 animals
D) 312 animals

Question 47

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2
Man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the
Company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?

A) 18 VIP and 6 SST
B) 20 VIP and 0 SST
C) 0 VIP and 24 SST
D) 12 VIP and 12 SST

Question 48

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
Find the minimum possible value of $g = 4 x + 5 y$ subject to the following constraints:
$$\left\{ \begin{array} { l } x - 2 y \leq 5 \\2 x + y \geq 15 \\x \geq 0 , y \geq 0\end{array} \right.$$

A) 39
B) 20
C) 75
D) 33

Question 49

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
Find the minimum possible value of $\mathrm { f } = 2 \mathrm { x } + 4 \mathrm { y }$ subject to the following constraints:
$$\left\{ \begin{array} { l } x + 2 y \geq 10 \\3 x + y \geq 10 \\x \geq 0 , y \geq 0\end{array} \right.$$

A) 20
B) 0
C) 10
D) 30

Question 50

Zach is planning to invest up to $50,000 in corporate and municipal bonds. The least he will invest in corporate bonds is $9000 and he does not want to invest more than $27,000 in corporate bonds. He also does not want to
Invest more than $34,307 in municipal bonds. The interest is 8.2% on corporate bonds and 6.2% on municipal
Bonds. This is simple interest for one year. What is the maximum income?

A) $3640
B) $26,640
C) $4788
D) $30,640

Question 51

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
Find the values of $x$ and $y$ that give the maximum possible value of $g = 8 x + 12 y$ subject to the following constraints:
$$\left\{ \begin{array} { l } 40 x + 80 y \leq 560 \\6 x + 8 y \leq 72 \\x \geq 0 , y \geq 0\end{array} \right.$$

A) $x = 8 , y = 3$
B) $x = 14 , y = 0$
C) $x = 12 , y = 0$
D) $x = 0 , y = 9$

Question 52

Suppose that Janine desires 46 grams of protein and 38 grams of dietary fiber daily. One serving of kidney beans has 8 grams of protein and 6 grams of dietary fiber. One serving of refried pinto beans has 6 grams of
Protein and 6 grams of dietary fiber. If a serving of kidney beans costs $0.45 and a serving of refried pinto beans
Costs $0.35, then how many servings of each should Janine eat to minimize cost and still meet her requirements?
Fractional servings are allowed. A) 4 servings of refried pinto beans and $\frac { 7 } { 3 }$ servings of kidney beans
B) $\frac { 23 } { 3 }$ servings of refried pinto beans and 0 servings of kidney beans
C) $\frac { 7 } { 3 }$ servings of refried pinto beans and 4 servings of kidney beans
D) $\frac { 19 } { 3 }$ servings of kidney beans and 0 servings of refried pinto beans

Question 53

Find the first five terms of the sequence defined by the given general term.
$$a _ { n } = n - 5$$

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

Question 54

An airline with two types of airplans, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers . for a certain trip, airplane P1 costs $10,00 to operate and can accommodate 20 first class, 50 tourist class, 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 rourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

A) 20 P1 plans and 0 P2 plans
B) 11 P1 plans and 7 P2 plans
C) 7P1 plans and 11 P2 plans
D) 9 P1 plans and 13 P2 plans

Question 55

Suppose an animal feed to be mixed from soybean meal and oats must contain at least 100 lb of protein, 20 lb of fat, and 12 lb of mineral ash. Each 100-lb sack of soybean meal costs $20 and contains 50 lb of protein, 10 lb of
Fat, and 8 lb of mineral ash. Each 100-lb sack of alfalfa costs $11 and contains 30 lb of protein, 8 lb of fat, and 3 lb
Of mineral ash. How many sacks of each should be used to satisfy the minimum requirements at minimum cost?
Fractional sacks are allowed. A) 2 sacks of soybeans and 0 sacks of alfalfa
B) $\frac { 18 } { 17 }$ sacks of soybeans and $\frac { 20 } { 17 }$ sacks of alfalfa
C) $\frac { 2 } { 3 }$ sack of soybeans and $\frac { 20 } { 9 }$ sacks of alfalfa
D) 0 sacks of soybeans and 4 sacks of alfalfa

Question 56

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
Find the maximum possible value of $f = 6 x + 7 y$ subject to the following constraints:
$$\left\{ \begin{array} { l } 2 x + 3 y \leq 12 \\2 x + y \leq 8 \\x \geq 0 , y \geq 0\end{array} \right.$$

A) 32
B) 52
C) 13
D) 24

Question 57

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
Find the values of $x$ and $y$ that give the minimum possible value of $f = 6 x + 8 y$ subject to the following constraint $\left\{ \begin{array} { l } 2 x + 4 y \geq 12 \\ 2 x + y \geq 8 \\ x \geq 0 , y \geq 0 \end{array} \right.$

A) $x = 0 , y = 3$
B) $x = 0 , y = 0$
C) $x = \frac { 10 } { 3 } , y = \frac { 4 } { 3 }$
D) $x = 6 , y = 0$

Question 58

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
Find the maximum possible value of $f = 2 x + 5 y$ subject to the following constraints:
$$\left\{ \begin{array} { l } 3 x + 2 y \leq 6 \\- 2 x + 4 y \leq 8 \\x \geq 0 , y \geq 0\end{array} \right.$$

A) 19
B) $\frac { 34 } { 3 }$
C) $\frac { 49 } { 4 }$
D) 10

Question 59

Suppose an animal feed to be mixed from soybean meal and oats must contain at least 100 lb of protein, 20 lb of fat, and 9 lb of mineral ash. Each 100-lb sack of soybean meal costs $20 and contains 50 lb of protein, 10 lb of fat,
And 8 lb of mineral ash. Each 100-lb sack of oats costs $10 and contains 20 lb of protein, 5 lb of fat, and 1 lb of
Mineral ash. How many sacks of each should be used to satisfy the minimum requirements at minimum cost?
Fractional sacks are allowed. A) 2 sacks of soybeans and 0 sacks of oats
B) 0 sacks of soybeans and 4 sacks of oats
C) $\frac { 14 } { 11 }$ sacks of soybeans and $\frac { 20 } { 11 }$ sacks of oats
D) $\frac { 7 } { 3 }$ sacks of soybeans and $\frac { 5 } { 6 }$ sacks of oats

Question 60

An airline with two types of airplans, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers . for a certain trip, airplane P1 costs $10,00 to operate and can accommodate 20 first class, 50 tourist class, 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 rourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

A) 14 P1 plans and 7 P2 plans
B) 9 P1 plans and 12 P2 plans
C) 5 P1 plans and 22 P2 plans
D) 9 P1 plans and 13 P2 plans

Question 61

Write four additional terms of the geometric sequence.
Find the 6 th term of the geometric sequence with first term $\frac { 1 } { 2 }$ and common ratio $\frac { 1 } { 4 }$ .

A) $\frac { 1 } { 512 }$
B) $\frac { 1 } { 8192 }$
C) $\frac { 1 } { 128 }$
D) $\frac { 1 } { 2048 }$

Question 62

$a _ { n } = \frac { 1 } { n ^ { 2 } }$

A) $\frac { 1 } { 4 } , \frac { 2 } { 9 } , \frac { 3 } { 16 } , \frac { 4 } { 25 } , \frac { 5 } { 36 }$
B) $\frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \frac { 1 } { 36 }$
C) $1 , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 }$
D) $1 , \frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 1 } { 4 } , \frac { 1 } { 5 }$

Question 63

Find the next three terms of the arithmetic sequence.
Find term 25 of the arithmetic sequence with first term 5 and common difference $- \frac { 3 } { 4 }$ .

A) 23
B) $\frac { 95 } { 4 }$
C) $- \frac { 55 } { 4 }$
D) $- 13$

Question 64

Write four additional terms of the geometric sequence.
Find the first six terms of the sequence with first term $- 1$ and nth term $a _ { n } = 3 - a _ { n - 1 }$ .

A) $- 1,4 , - 1,4 , - 1,4$
B) $- 1 , - 4,1 , - 4 , - 1 , - 4$
C) $- 1,2,1,2,1,2$
D) $- 1,2 , - 1,2 , - 1,2$

Question 65

Find the next three terms of the arithmetic sequence.
Find the 25 th term of the arithmetic sequence with first term $- 3$ and common difference $- 4$ .

A) 93
B) 97
C) $- 99$
D) $- 103$

Question 66

Write four additional terms of the geometric sequence.
Find the first six terms of the sequence with first term 3 and nth term $a _ { n } = 1 - \frac { 1 } { a _ { n } - 1 }$ .

A) $3 , - \frac { 2 } { 3 } , \frac { 5 } { 2 } , \frac { 3 } { 5 } , - \frac { 2 } { 3 } , \frac { 5 } { 3 }$
B) $3 , \frac { 2 } { 3 } , \frac { 1 } { 2 } , - 1,2 , \frac { 1 } { 2 }$
C) $3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 } , 3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 }$
D) $3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 } , - 3 , \frac { 4 } { 3 } , \frac { 1 } { 4 }$

Question 67

$a _ { n } = ( - 1 ) ^ { n + 5}$

A) 1,1,1,1,1
B) 1,-1,1,-1,1
C) -1,1,-1,1,-1
D) -1,-1,-1,-1,-1

Question 68

Write four additional terms of the geometric sequence.
Find the first four terms of the sequence with first term 9 and nth term $$a _ { n } = a _ { n - 1 } + 4$$

A) 13, 17, 21, 25
B) 0, 4, 8, 12
C) 9, 4, 8, 12
D) 9, 13, 17, 21

Question 69

Find the next three terms of the arithmetic sequence.
Find the 9 th term of the arithmetic sequence with first term 8 and common difference $\frac { 1 } { 2 }$ .

A) 12
B) 4
C) $\frac { 25 } { 2 }$
D) $\frac { 7 } { 2 }$

Question 70

Write four additional terms of the geometric sequence.
Find the 6th term of the geometric sequence with first term 4 and common ratio $- 3$ .

A) $- 2187$
B) $- 972$
C) 324
D) $- 72$

Question 71

Find the first five terms of the sequence defined by the given general term.
$$f ( n ) = 2 n - 2$$

A) $0,1,2,3,4$
B) $0,2,4,6,8$
C) $4,6,8,10,12$
D) $0 , - 2 , - 4 , - 6 , - 8$

Question 72

Write four additional terms of the geometric sequence.
Find the first five terms of the sequence with first term 8 and nth term $$a _ { n } = 2 a _ { n - 1 }$$

A) 16, 32, 64, 128, 256
B) 8, 16, 32, 64, 128
C) 8, 40, 45, 50, 55
D) 0, 5, 40, 45, 50

Question 73

Find the next three terms of the arithmetic sequence.
Find the eighth term of the arithmetic sequence with first term $- 5$ and common difference 4 .

A) $- 33$
B) 27
C) 23
D) $- 37$

Question 74

Find the first five terms of the sequence defined by the given general term.
$$f ( n ) = 3 ^ { n }$$

A) 9, 27, 81, 243, 729
B) 1, 3, 9, 27, 81
C) 1, 8, 27, 64, 125
D) 3, 9, 27, 81, 243

Question 75

Find the first five terms of the sequence defined by the given general term.
$$a _ { n } = n ^ { 2 } - n$$

A) $1,4,9,16,25$
B) $2,6,12,20,30$
C) $0,2,6,12,20$
D) $0,3,8,15,24$

Question 76

Find the next three terms of the arithmetic sequence.
$3,1 , - 1 , \ldots$

A) $- 6 , - 7 , - 10$
B) $- 3 , - 5 , - 7$
C) $1,3,5$
D) $- 3 , - 6 , - 9$

Question 77

Write four additional terms of the geometric sequence.
$6 , - 18,54 , \ldots$

A) $- 162 , - 486 , - 1458 , - 4374$
B) $162 , - 486,1458 , - 4374$
C) $162,486,1458,4374$
D) $- 162,486 , - 1458,4374$

Question 78

Write four additional terms of the geometric sequence.
6, 18, 54, . . .

A) 162, 486, 1458, 4374
B) 216, 864, 3456, 13,824
C) 162, 486, 1468, 4399
D) 108, 216, 432, 864

Question 79

Find the next three terms of the arithmetic sequence.
3, 9, 15, 21, . . .

A) 27, 33, 39
B) 21, 27, 33
C) 27, 34, 40
D) 27, 39, 45

Question 80

Write four additional terms of the geometric sequence.
8, 12, 18, . . .

A) 45, 112.5, 291.25, 728.125
B) 27, 40.5, 60.75, 91.125
C) 27, 40.5, 1954, 5857
D) 45, 112.5, 281.25, 703.125