Question 1

Find the common difference of the sequence.
-$$a _ { 1 } = 6 , a _ { 4 } = 18 \text {; find } d$$

Accepted Answer

A) -4 
B) -12 
C) 12 
D) 4 
A) -4 
B) -12 
C) 12 
D) 4

Question 2

Solve the problem.
-Suppose that the probability that it will rain today is $\frac { 11 } { 19 } .$ . Find the odds against raining today. Find the odds against raining today

Accepted Answer

A) 11:8 
B) 8:11 
C) 19:8 
D) 8:19 
A) 11:8 
B) 8:11 
C) 19:8 
D) 8:19

Question 3

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.
-$a _ { 1 } = 2 , d = 8$

Accepted Answer

A)  $a _ { n } = 8 n - 6$ 
B)  $a _ { n } = 6 n - 3$ 
C)  $a _ { n } = 6 n - 8$ 
D)  $a _ { n } = 8 n - 3$ 
A)  $a _ { n } = 8 n - 6$ 
B)  $a _ { n } = 6 n - 3$ 
C)  $a _ { n } = 6 n - 8$ 
D)  $a _ { n } = 8 n - 3$

Question 4

Find the indicated sum.
-$a _ { 1 } = 3 , r = \frac { 1 } { 2 } ; \text { find } s _5$

Accepted Answer

A)  $\frac { 93 } { 16 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 3 } { 16 }$ 
D) 93 
A)  $\frac { 93 } { 16 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 3 } { 16 }$ 
D) 93

Question 5

Solve the problem.
-A college identification number consists of a letter followed by 4 digits. How many different identification numbers are possible if repetition is not permitted?

Accepted Answer

A) 144 
B) 468,000 
C) 5690 
D) 3,276,000 
A) 144 
B) 468,000 
C) 5690 
D) 3,276,000

Question 6

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

Accepted Answer

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

Question 7

Determine the first five terms of the geometric sequence.
-a1 = 3, r = 4

Accepted Answer

A) 12, 48, 192, 768, 3072 
B) 3, 7, 11, 15, 19 
C) 3, 12, 48, 192, 768 
D) 4, 12, 36, 108, 324 
A) 12, 48, 192, 768, 3072 
B) 3, 7, 11, 15, 19 
C) 3, 12, 48, 192, 768 
D) 4, 12, 36, 108, 324

Question 8

Solve the problem.
-On a History test, Keith Kepler must write an essay for 2 of the 7 questions in Part 1, and 4 of the 6 questions in Part 2. How many different combinations of questions can he answer?

Accepted Answer

A) 36 
B) 10 
C) 315 
D) 15,120 
A) 36 
B) 10 
C) 315 
D) 15,120

Question 9

Solve the problem.
-On a gambling boat, Gertrude tripled her bet each time she won. If her first winning bet was $6 and she won six consecutive bets, find how much she won on the sixth bet. Find the total amount she won on these six bets.

Accepted Answer

A) $486; $726 
B) $1458; $2184 
C) $4374; $2184 
D) $4374; $6558 
A) $486; $726 
B) $1458; $2184 
C) $4374; $2184 
D) $4374; $6558

Question 10

Evaluate the combination.
-$\left( \begin{array} { c } 
12 \
6
\end{array} \right)$

Accepted Answer

A) 1848 
B) 462 
C) 924 
D) 665,280 
A) 1848 
B) 462 
C) 924 
D) 665,280

Question 11

Write the first five terms of the arithmetic sequence with the given term and common difference.
-$a _ { 1 } = 9 , d = - 3$

Accepted Answer

A) 9, 6, 3, 0, -3 
B) 12, 9, 6, 3, 0 
C) 9, 6, 2, 0, -3 
D) 6, 3, 0, -3, -6 
A) 9, 6, 3, 0, -3 
B) 12, 9, 6, 3, 0 
C) 9, 6, 2, 0, -3 
D) 6, 3, 0, -3, -6

Question 12

For the set of valueses $x _ { 1 } = 1 , x _ { 2 } = 3 , x _ { 3 } = - 2,$ 2, a nd x4 = 6, find the following.
-$\sum _ { i = 1 } ^ { 4 } 5 x _ { i }$

Accepted Answer

A) 41 
B) 8 
C) 40 
D) 35 
A) 41 
B) 8 
C) 40 
D) 35

Question 13

Write the next three terms of the sequence.
-$\frac { 3 } { 4 } , - \frac { 1 } { 4 } , \frac { 1 } { 12 } , - \frac { 1 } { 36 } ,.$ , . . .

Accepted Answer

A)  $- \frac { 1 } { 108 } , \frac { 1 } { 324 } , - \frac { 1 } { 972 }$ 
B)  $\frac { 1 } { 36 } , - \frac { 1 } { 48 } , \frac { 1 } { 60 }$ 
C)  $\frac { 1 } { 108 } , - \frac { 1 } { 324 } , \frac { 1 } { 972 }$ 
D)  $- \frac { 1 } { 36 } , \frac { 1 } { 48 } , - \frac { 1 } { 60 }$ 
A)  $- \frac { 1 } { 108 } , \frac { 1 } { 324 } , - \frac { 1 } { 972 }$ 
B)  $\frac { 1 } { 36 } , - \frac { 1 } { 48 } , \frac { 1 } { 60 }$ 
C)  $\frac { 1 } { 108 } , - \frac { 1 } { 324 } , \frac { 1 } { 972 }$ 
D)  $- \frac { 1 } { 36 } , \frac { 1 } { 48 } , - \frac { 1 } { 60 }$

Question 14

Find the arithmetic meaic mean $\bar { x },$ , of , ofthe following set of data.
-1, 4, 7, 10, 13

Accepted Answer

A) 8.75 
B) 7 
C) 5.83 
D) 35 
A) 8.75 
B) 7 
C) 5.83 
D) 35

Question 15

Solve the problem.
-A marble is taken out of a bag containing 90 marbles: 15 red, 30 blue, 25 green, and 20 orange. Find the probability: P(an orange marble is not chosen)

Accepted Answer

A)  $\frac { 1 } { 6 }$ 
B)  $\frac { 7 } { 9 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 13 } { 18 }$ 
A)  $\frac { 1 } { 6 }$ 
B)  $\frac { 7 } { 9 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 13 } { 18 }$

Question 16

Solve the problem.
-A song is selected at random from a jukebox containing 30 rock/pop songs, 12 country songs, and 7 classical pieces.
Find the probability: P(selecting a country song)

Accepted Answer

A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 1 } { 49 }$ 
C)  $\frac { 1 } { 12 }$ 
D)  $\frac { 12 } { 49 }$ 
A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 1 } { 49 }$ 
C)  $\frac { 1 } { 12 }$ 
D)  $\frac { 12 } { 49 }$

Question 17

Write the next three terms of the sequence.
-4, 16, 64, 256, . . .

Accepted Answer

A) 1024, 4096, 16,384 
B) 4096, 16,384, 65,536 
C) 1280, 1536, 1792 
D) 1025, 4097, 16,385 
A) 1024, 4096, 16,384 
B) 4096, 16,384, 65,536 
C) 1280, 1536, 1792 
D) 1025, 4097, 16,385

Question 18

Solve the problem.
-In a geometric series, $a _ { 3 } = \frac { 8 } { 9 } \text { and } a _ { 5 } = \frac { 8 } { 81 };$ ; find r and find r anda1.

Accepted Answer

The answer of Solve the problem.
-In a geometric series, \(a...

Question 19

Find the common difference of the sequence.
-$a _ { 1 } = \frac { 9 } { 2 } , a _ { 4 } = \frac { 21 } { 2 } ; \text { find } \mathrm { d }$

Accepted Answer

A) 2 
B)  $\frac { 1 } { 2 }$ 
C) 4 
D) 6 
A) 2 
B)  $\frac { 1 } { 2 }$ 
C) 4 
D) 6

Question 20

Write the first five terms of the arithmetic sequence with the given term and common difference.
-a $a _ { 1 } = 10 , d = 4$

Accepted Answer

A) 10, 13, 16, 19, 22 
B) 14, 18, 22, 26, 30 
C) 0, 10, 14, 18, 22 
D) 10, 14, 18, 22, 26 
A) 10, 13, 16, 19, 22 
B) 14, 18, 22, 26, 30 
C) 0, 10, 14, 18, 22 
D) 10, 14, 18, 22, 26

Find the common difference of the sequence. - $a _ { 1 } = 6 , a _ { 4 } = 18 \text {; find } d$

Solve the problem. -Suppose that the probability that it will rain today is $\frac { 11 } { 19 } .$ . Find the odds against raining today. Find the odds against raining today

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence. - $a _ { 1 } = 2 , d = 8$

Find the indicated sum. - $a _ { 1 } = 3 , r = \frac { 1 } { 2 } ; \text { find } s _5$

Solve the problem. -A college identification number consists of a letter followed by 4 digits. How many different identification numbers are possible if repetition is not permitted?

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

Determine the first five terms of the geometric sequence. -a1 = 3, r = 4

Solve the problem. -On a History test, Keith Kepler must write an essay for 2 of the 7 questions in Part 1, and 4 of the 6 questions in Part 2. How many different combinations of questions can he answer?

Solve the problem. -On a gambling boat, Gertrude tripled her bet each time she won. If her first winning bet was $6 and she won six consecutive bets, find how much she won on the sixth bet. Find the total amount she won on these six bets.

Evaluate the combination. - $\left( \begin{array} { c } 12 \\6\end{array} \right)$

Write the first five terms of the arithmetic sequence with the given term and common difference. - $a _ { 1 } = 9 , d = - 3$

For the set of valueses $x _ { 1 } = 1 , x _ { 2 } = 3 , x _ { 3 } = - 2,$ 2, a nd x4 = 6, find the following. - $\sum _ { i = 1 } ^ { 4 } 5 x _ { i }$

Write the next three terms of the sequence. - $\frac { 3 } { 4 } , - \frac { 1 } { 4 } , \frac { 1 } { 12 } , - \frac { 1 } { 36 } ,.$ , . . .

Find the arithmetic meaic mean $\bar { x },$ , of , ofthe following set of data. -1, 4, 7, 10, 13

Solve the problem. -A marble is taken out of a bag containing 90 marbles: 15 red, 30 blue, 25 green, and 20 orange. Find the probability: P(an orange marble is not chosen)

Solve the problem. -A song is selected at random from a jukebox containing 30 rock/pop songs, 12 country songs, and 7 classical pieces. Find the probability: P(selecting a country song)

Write the next three terms of the sequence. -4, 16, 64, 256, . . .

Solve the problem. -In a geometric series, $a _ { 3 } = \frac { 8 } { 9 } \text { and } a _ { 5 } = \frac { 8 } { 81 };$ ; find r and find r anda1.

Find the common difference of the sequence. - $a _ { 1 } = \frac { 9 } { 2 } , a _ { 4 } = \frac { 21 } { 2 } ; \text { find } \mathrm { d }$

Write the first five terms of the arithmetic sequence with the given term and common difference. -a $a _ { 1 } = 10 , d = 4$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

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Exam 12: Sequences, Series, and Probability

Find the common difference of the sequence. - a1=6,a4=18; find da _ { 1 } = 6 , a _ { 4 } = 18 \text {; find } da1​=6,a4​=18; find d

Solve the problem. -Suppose that the probability that it will rain today is 1119.\frac { 11 } { 19 } .1911​. . Find the odds against raining today. Find the odds against raining today

Write the expression for the general (or nth)term,rm, an,a _ { n },an​, , of the arithmetic sequence. - a1=2,d=8a _ { 1 } = 2 , d = 8a1​=2,d=8

Find the indicated sum. - a1=3,r=12; find s5a _ { 1 } = 3 , r = \frac { 1 } { 2 } ; \text { find } s _5a1​=3,r=21​; find s5​