Question 1

Find the arithmetic meaic mean $\bar { x },$ , of , ofthe following set of data.
-3, 9, 27, 81, 243

Accepted Answer

A) 90.75 
B) 363 
C) 72.6 
D) 60.5 
A) 90.75 
B) 363 
C) 72.6 
D) 60.5

Question 2

Solve the problem.
-There are 2 key lime pies, 5 pints of butter pecan ice cream, and 4 pineapple upside down cakes in the cooler. Irving selects one dessert at random. Find the probability that it is a pint of butter pecan ice cream.

Accepted Answer

A)  $\frac { 8 } { 65 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 28 }$ 
D)  $\frac { 2 } { 11 }$ 
A)  $\frac { 8 } { 65 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 28 }$ 
D)  $\frac { 2 } { 11 }$

Question 3

Write out the series.
-$$\sum _ { n = 1 } ^ { 4 } ( n + 3 )$$

Accepted Answer

A) 7 + 8 + 9 + 10 
B) 4 + 5 + 6 + 7 + ... 
C) 3 + 4 + 5 + 6 
D) 4 + 5 + 6 + 7 
A) 7 + 8 + 9 + 10 
B) 4 + 5 + 6 + 7 + ... 
C) 3 + 4 + 5 + 6 
D) 4 + 5 + 6 + 7

Question 4

Determine the first five terms of the geometric sequence.
-$a _ { 1 } = 4 , r = \frac { 1 } { 3 }$

Accepted Answer

A)  $4 , \frac { 4 } { 3 } , \frac { 4 } { 9 } , \frac { 4 } { 27 } , \frac { 4 } { 81 }$ 
B)  $4 , \frac { 13 } { 3 } , \frac { 14 } { 3 } , 5 , \frac { 16 } { 3 }$ 
C)  $4,12,36,108,324$ 
D)  $\frac { 4 } { 3 } , \frac { 4 } { 9 } , \frac { 4 } { 27 } , \frac { 4 } { 81 } , \frac { 4 } { 243 }$ 
A)  $4 , \frac { 4 } { 3 } , \frac { 4 } { 9 } , \frac { 4 } { 27 } , \frac { 4 } { 81 }$ 
B)  $4 , \frac { 13 } { 3 } , \frac { 14 } { 3 } , 5 , \frac { 16 } { 3 }$ 
C)  $4,12,36,108,324$ 
D)  $\frac { 4 } { 3 } , \frac { 4 } { 9 } , \frac { 4 } { 27 } , \frac { 4 } { 81 } , \frac { 4 } { 243 }$

Question 5

Solve the problem.
-One person is selected at random from a class of 40 males and 28 females. Find the odds against selecting a male.

Accepted Answer

A) 7:10 
B) 10:17 
C) 17:10 
D) 10:7 
A) 7:10 
B) 10:17 
C) 17:10 
D) 10:7

Question 6

Solve the problem.
-D.J Bob, a disc jockey has 34 records that he wants to play during the next hour, but he has time to play only 12 of them. Write the expression used to determine how many different ways he can select a group of 12 records to
Play.

Accepted Answer

A)  $\frac { 34 ! } { 22 ! }$ 
B)  $\frac { 34 ! } { 22 ! \cdot 12 ! }$ 
C)  $\frac { 34 ! } { 12 ! }$ 
D)  $\frac { 34 } { 22 }$ 
A)  $\frac { 34 ! } { 22 ! }$ 
B)  $\frac { 34 ! } { 22 ! \cdot 12 ! }$ 
C)  $\frac { 34 ! } { 12 ! }$ 
D)  $\frac { 34 } { 22 }$

Question 7

Solve the problem.
-A card is selected at random from a deck of cards. Find the probability: P(selecting a card that is not a king)

Accepted Answer

A)  $\frac { 12 } { 13 }$ 
B)  $\frac { 1 } { 13 }$ 
C)  $\frac { 10 } { 13 }$ 
D)  $\frac { 5 } { 13 }$ 
A)  $\frac { 12 } { 13 }$ 
B)  $\frac { 1 } { 13 }$ 
C)  $\frac { 10 } { 13 }$ 
D)  $\frac { 5 } { 13 }$

Question 8

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
-5, 10, 20, 40, 80,. . .

Accepted Answer

A)  $a _ { n } = 5 ( 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = 5 ( 2 n )$ 
C)  $a _ { n } = a _ { 1 } + 2 ^ { n }$ 
D)  $a _ { n } = 5 ( 2 ) ^ { n }$ 
A)  $a _ { n } = 5 ( 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = 5 ( 2 n )$ 
C)  $a _ { n } = a _ { 1 } + 2 ^ { n }$ 
D)  $a _ { n } = 5 ( 2 ) ^ { n }$

Question 9

Find the indicated term of the geometric sequence.
-a1 = -6, r = -2; find $a_8$

Accepted Answer

A) -20 
B) 772 
C) -1536 
D) 768 
A) -20 
B) 772 
C) -1536 
D) 768

Question 10

Write the first five terms of the arithmetic sequence with the given term and common difference.
-$a _ { 1 } = \frac { 3 } { 8 } , d = - \frac { 1 } { 8 }$

Accepted Answer

A)  $\frac { 3 } { 8 } , \frac { 1 } { 4 } , \frac { 5 } { 8 } , 0 , \frac { 7 } { 8 }$ 
B)  $\frac { 3 } { 8 } , \frac { 1 } { 2 } , \frac { 5 } { 8 } , \frac { 3 } { 4 } , \frac { 7 } { 8 }$ 
C)  $\frac { 3 } { 8 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , 0 , - \frac { 1 } { 8 }$ 
D)  $\frac { 3 } { 8 } , \frac { 3 } { 4 } , \frac { 9 } { 8 } , \frac { 3 } { 2 } , \frac { 15 } { 8 }$ 
A)  $\frac { 3 } { 8 } , \frac { 1 } { 4 } , \frac { 5 } { 8 } , 0 , \frac { 7 } { 8 }$ 
B)  $\frac { 3 } { 8 } , \frac { 1 } { 2 } , \frac { 5 } { 8 } , \frac { 3 } { 4 } , \frac { 7 } { 8 }$ 
C)  $\frac { 3 } { 8 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , 0 , - \frac { 1 } { 8 }$ 
D)  $\frac { 3 } { 8 } , \frac { 3 } { 4 } , \frac { 9 } { 8 } , \frac { 3 } { 2 } , \frac { 15 } { 8 }$

Question 11

Write the word or phrase that best completes each statement or answers the question.
Use mathematical induction to prove the following statement for all positive integers n.
-$$6 + 6 ^ { 2 } + \ldots + 6 ^ { n } = 6 \left( \frac { 6 ^ { n } - 1 } { 5 } \right)$$

Accepted Answer

Condition 1:For n = 1, we get 6 = 6. Thi

Question 12

Solve the problem.
-A die is rolled. Find the odds against rolling a 5.

Accepted Answer

A) 1:6 
B) 6:1 
C) 5:1 
D) 1:5 
A) 1:6 
B) 6:1 
C) 5:1 
D) 1:5

Question 13

Find the first and third partial sums, s1 and s3, for the sequence
-$a _ { n } = \frac { n ^ { 2 } } { n + 4 }$

Accepted Answer

A)  $\frac { 1 } { 5 } , \frac { 9 } { 7 }$ 
B)  $\frac { 1 } { 5 } , \frac { 1 } { 15 }$ 
C)  $\frac { 1 } { 5 } , \frac { 226 } { 105 }$ 
D)  $\frac { 1 } { 5 } , \frac { 7 } { 5 }$ 
A)  $\frac { 1 } { 5 } , \frac { 9 } { 7 }$ 
B)  $\frac { 1 } { 5 } , \frac { 1 } { 15 }$ 
C)  $\frac { 1 } { 5 } , \frac { 226 } { 105 }$ 
D)  $\frac { 1 } { 5 } , \frac { 7 } { 5 }$

Question 14

Find the common difference of the sequence.
-$\mathrm { a } _ { 1 } = 3.82 , \mathrm { a } _ { 4 } = 12.16 ; \text { find } \mathrm { d }$

Accepted Answer

A) 8.34 
B) 2.78 
C) 3.82 
D) 2.085 
A) 8.34 
B) 2.78 
C) 3.82 
D) 2.085

Question 15

Evaluate the expression.
-${ } _ { 10 } \mathrm { C } _ { 5 }$

Accepted Answer

A) 1 
B) 252 
C) 5 
D) 30,240 
A) 1 
B) 252 
C) 5 
D) 30,240

Question 16

Write the first five terms of the sequence whose nth term is shown.
-$a _ { n } = \frac { 3 } { n ^ { 2 } }$

Accepted Answer

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

Question 17

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.
-Find the sum of the first 90 positive even integers.

Accepted Answer

A) 8190 
B) 8095 
C) 8194 
D) 8099 
A) 8190 
B) 8095 
C) 8194 
D) 8099

Question 18

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
--8, -24, -72, -216, -648,. . .

Accepted Answer

A)  $a _ { n } = - 8 ( 3 ) ^ { n }$ 
B)  $a _ { n } = - 8 ( 3 n )$ 
C)  $a _ { n } = - 8 ( 3 ) ^ { n - 1 }$ 
D)  $a _ { n } = a _ { 1 } + 3 ^ { n }$ 
A)  $a _ { n } = - 8 ( 3 ) ^ { n }$ 
B)  $a _ { n } = - 8 ( 3 n )$ 
C)  $a _ { n } = - 8 ( 3 ) ^ { n - 1 }$ 
D)  $a _ { n } = a _ { 1 } + 3 ^ { n }$

Question 19

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.
-$a _ { 1 } = - 12 , d = - 4$

Accepted Answer

A)  $a _ { n } = - 4 n - 12$ 
B)  $a _ { n } = 4 n + 8$ 
C)  $a _ { n } = 4 n + 12$ 
D)  $a _ { n } = - 4 n - 8$ 
A)  $a _ { n } = - 4 n - 12$ 
B)  $a _ { n } = 4 n + 8$ 
C)  $a _ { n } = 4 n + 12$ 
D)  $a _ { n } = - 4 n - 8$

Question 20

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
-3, 9, 27, 81, 243,. . .

Accepted Answer

A)  $a _ { n } = 3 ^ { n }$ 
B)  $a _ { n } = 3 ^ { n - 1 } + 3$ 
C)  $a _ { n } = 6 n$ 
D)  $a _ { n } = 3 + 6 ( n - 1 )$ 
A)  $a _ { n } = 3 ^ { n }$ 
B)  $a _ { n } = 3 ^ { n - 1 } + 3$ 
C)  $a _ { n } = 6 n$ 
D)  $a _ { n } = 3 + 6 ( n - 1 )$

Find the arithmetic meaic mean $\bar { x },$ , of , ofthe following set of data. -3, 9, 27, 81, 243

Solve the problem. -There are 2 key lime pies, 5 pints of butter pecan ice cream, and 4 pineapple upside down cakes in the cooler. Irving selects one dessert at random. Find the probability that it is a pint of butter pecan ice cream.

Write out the series. - $\sum _ { n = 1 } ^ { 4 } ( n + 3 )$

Determine the first five terms of the geometric sequence. - $a _ { 1 } = 4 , r = \frac { 1 } { 3 }$

Solve the problem. -One person is selected at random from a class of 40 males and 28 females. Find the odds against selecting a male.

Solve the problem. -D.J Bob, a disc jockey has 34 records that he wants to play during the next hour, but he has time to play only 12 of them. Write the expression used to determine how many different ways he can select a group of 12 records to Play.

Solve the problem. -A card is selected at random from a deck of cards. Find the probability: P(selecting a card that is not a king)

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence. -5, 10, 20, 40, 80,. . .

Find the indicated term of the geometric sequence. -a1 = -6, r = -2; find $a_8$

Write the first five terms of the arithmetic sequence with the given term and common difference. - $a _ { 1 } = \frac { 3 } { 8 } , d = - \frac { 1 } { 8 }$

Write the word or phrase that best completes each statement or answers the question. Use mathematical induction to prove the following statement for all positive integers n. - $6 + 6 ^ { 2 } + \ldots + 6 ^ { n } = 6 \left( \frac { 6 ^ { n } - 1 } { 5 } \right)$

Solve the problem. -A die is rolled. Find the odds against rolling a 5.

Find the first and third partial sums, s1 and s3, for the sequence - $a _ { n } = \frac { n ^ { 2 } } { n + 4 }$

Find the common difference of the sequence. - $\mathrm { a } _ { 1 } = 3.82 , \mathrm { a } _ { 4 } = 12.16 ; \text { find } \mathrm { d }$

Evaluate the expression. - ${ } _ { 10 } \mathrm { C } _ { 5 }$

Write the first five terms of the sequence whose nth term is shown. - $a _ { n } = \frac { 3 } { n ^ { 2 } }$

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence. -Find the sum of the first 90 positive even integers.

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence. --8, -24, -72, -216, -648,. . .

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence. - $a _ { 1 } = - 12 , d = - 4$

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence. -3, 9, 27, 81, 243,. . .

Basic Concepts

Equations and Inequalities

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Systems of Equations and Inequalities

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Exam 12: Sequences, Series, and Probability

Find the arithmetic meaic mean xˉ,\bar { x },xˉ, , of , ofthe following set of data. -3, 9, 27, 81, 243