Question 1

Write Terms of a Geometric Sequence
-$$a _ { n } = - 8 a _ { n - 1 } ; a _ { 1 } = - 4$$

Accepted Answer

A)  $- 4,32 , - 256,2048 , - 16,384$ 
B)  $32 , - 256,2048 , - 16,384,131,072$ 
C)  $- 8 , - 32 , - 256 , - 2048 , - 16,384$ 
D)  $- 4 , - 12 , - 20 , - 28 , - 36$ 
A)  $- 4,32 , - 256,2048 , - 16,384$ 
B)  $32 , - 256,2048 , - 16,384,131,072$ 
C)  $- 8 , - 32 , - 256 , - 2048 , - 16,384$ 
D)  $- 4 , - 12 , - 20 , - 28 , - 36$

Question 2

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-A brick staircase has a total of 18 steps The bottom step requires 101 bricks. Each successive step requires 4 fewer bricks than the prior one. How many bricks are required to build the staircase?

Accepted Answer

A)  1206 bricks 
B)  2430 bricks 
C)  2412 bricks 
D)  1170 bricks 
A)  1206 bricks 
B)  2430 bricks 
C)  2412 bricks 
D)  1170 bricks

Question 3

Distinguish Between Permutation Problems and Combination Problems
-From 9 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible?

Accepted Answer

A)  permutations 
B)  combinations 
A)  permutations 
B)  combinations

Question 4

Find the Probability that an Event Will Not Occur
-A bag contains 20 marbles, of which 3 are blue and 7 are green. One marble is drawn from the bag. What is the probability that the marble drawn is not blue?

Accepted Answer

A)  $\frac { 17 } { 20 }$ 
B)  $\frac { 3 } { 20 }$ 
C)  $\frac { 3 } { 10 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  $\frac { 17 } { 20 }$ 
B)  $\frac { 3 } { 20 }$ 
C)  $\frac { 3 } { 10 }$ 
D)  $\frac { 1 } { 2 }$

Question 5

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-As part of her retirement savings plan, Patricia deposited $250 in a bank account during her first year in the workforce. During each subsequent year, she deposited $35 more than the previous year. Find how much she deposited during her twentieth year in the workforce. Find the total amount deposited in the twenty years.

Accepted Answer

A)  $915; $11,650 
B)  $950; $12,000 
C)  $915; $23,300 
D)  $950; $24,000 
A)  $915; $11,650 
B)  $950; $12,000 
C)  $915; $23,300 
D)  $950; $24,000

Question 6

Find the Probability that an Event Will Not Occur
-What is the probability that a card drawn from a deck of 52 cards is not a heart?

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 4 } { 13 }$ 
D)  $\frac { 2 } { 5 }$ 
A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 4 } { 13 }$ 
D)  $\frac { 2 } { 5 }$

Question 7

Write Terms of a Geometric Sequence
-$$\mathrm { a } _ { 1 } = 2 ; \mathrm { r } = 5$$

Accepted Answer

A)  $2,10,50,250,1250$ 
B)  $10,50,250,1250,6250$ 
C)  $2,7,12,17,22$ 
D)  $5,10,20,40,80$ 
A)  $2,10,50,250,1250$ 
B)  $10,50,250,1250,6250$ 
C)  $2,7,12,17,22$ 
D)  $5,10,20,40,80$

Question 8

Write the first four terms of the sequence whose general term is given.
-$$\mathrm { a } _ { \mathrm { n } } = \frac { ( - 1 ) ^ { \mathrm { n } + 1 } } { \mathrm { n } + 7 }$$

Accepted Answer

A)  $\frac { 1 } { 8 } , - \frac { 1 } { 9 } , \frac { 1 } { 10 } , - \frac { 1 } { 11 }$ 
B)  $- \frac { 1 } { 8 } , \frac { 1 } { 9 } , - \frac { 1 } { 10 } , \frac { 1 } { 11 }$ 
C)  $\frac { 1 } { 8 } , - \frac { 1 } { 18 } , \frac { 1 } { 30 } , - \frac { 1 } { 44 }$ 
D)  $- \frac { 1 } { 9 } , \frac { 1 } { 10 } , - \frac { 1 } { 11 } , \frac { 1 } { 12 }$ 
A)  $\frac { 1 } { 8 } , - \frac { 1 } { 9 } , \frac { 1 } { 10 } , - \frac { 1 } { 11 }$ 
B)  $- \frac { 1 } { 8 } , \frac { 1 } { 9 } , - \frac { 1 } { 10 } , \frac { 1 } { 11 }$ 
C)  $\frac { 1 } { 8 } , - \frac { 1 } { 18 } , \frac { 1 } { 30 } , - \frac { 1 } { 44 }$ 
D)  $- \frac { 1 } { 9 } , \frac { 1 } { 10 } , - \frac { 1 } { 11 } , \frac { 1 } { 12 }$

Question 9

Find the Probability of One Event or a Second Event Occurring
-A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 8 ?

Accepted Answer

A)  $\frac { 2 } { 13 }$ 
B)  $\frac { 9 } { 26 }$ 
C)  $\frac { 13 } { 2 }$ 
D)  9 
A)  $\frac { 2 } { 13 }$ 
B)  $\frac { 9 } { 26 }$ 
C)  $\frac { 13 } { 2 }$ 
D)  9

Question 10

Distinguish Between Permutation Problems and Combination Problems
-The matching section of an exam has 4 questions and 9 possible answers. In how many different ways can a student answer the 4 questions, if none of the answer choices can be repeated?

Accepted Answer

A)  permutations 
B)  combinations 
A)  permutations 
B)  combinations

Question 11

Use the Formula for the Sum of the First n Terms of a Geometric Sequence
-Find the sum of the first six terms of the geometric sequence: 2, 8, 32, . . . .

Accepted Answer

A)  2730 
B)  42 
C)  84 
D)  1365 
A)  2730 
B)  42 
C)  84 
D)  1365

Question 12

Use Summation Notation
-$$\sum _ { k = 2 } ^ { 4 } k ( k - 4 )$$

Accepted Answer

A)  $- 7$ 
B)  $- 10$ 
C)  $- 4$ 
D)  6 
A)  $- 7$ 
B)  $- 10$ 
C)  $- 4$ 
D)  6

Question 13

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $$\mathbf { a } _ { \mathbf { n } }$$ to find $$a _ { 20 }$$ , the 20th term of the sequence.
-$$a _ { n } = a _ { n - 1 } + 5 , a _ { 1 } = 18$$

Accepted Answer

A)  $a _ { n } = 5 n + 13 , a _ { 20 } = 113$ 
B)  $a _ { n } = 18 n - 13 , a _ { 20 } = 347$ 
C)  $a _ { n } = 5 n + 23 , a _ { 20 } = 123$ 
D)  $a _ { n } = 13 n + 5 , a _ { 20 } = 265$ 
A)  $a _ { n } = 5 n + 13 , a _ { 20 } = 113$ 
B)  $a _ { n } = 18 n - 13 , a _ { 20 } = 347$ 
C)  $a _ { n } = 5 n + 23 , a _ { 20 } = 123$ 
D)  $a _ { n } = 13 n + 5 , a _ { 20 } = 265$

Question 14

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = 4 n - 2$$

Accepted Answer

A)  $2,6,10,14$ 
B)  $2,3,4,5$ 
C)  $6,10,14,18$ 
D)  $- 2 , - 6 , - 10 , - 14$ 
A)  $2,6,10,14$ 
B)  $2,3,4,5$ 
C)  $6,10,14,18$ 
D)  $- 2 , - 6 , - 10 , - 14$

Question 15

Use the Formula for the Sum of an Infinite Geometric Series
-$75 + 15 + 3 + \frac { 3 } { 5 } + \ldots$

Accepted Answer

A)  $\frac { 375 } { 4 }$ 
B)  $- \frac { 75 } { 4 }$ 
C)  93 
D)  does not exist 
A)  $\frac { 375 } { 4 }$ 
B)  $- \frac { 75 } { 4 }$ 
C)  93 
D)  does not exist

Question 16

Use Factorial Notation
-$$a _ { n } = \frac { 4 ( n + 1 ) ! } { n ! }$$

Accepted Answer

A)  $8,12,16,20$ 
B)  $8,6 , \frac { 8 } { 3 } , \frac { 5 } { 6 }$ 
C)  $5,6,7,8$ 
D)  $8,6 , \frac { 16 } { 3 } , 5$ Evaluate the factorial expression. 
A)  $8,12,16,20$ 
B)  $8,6 , \frac { 8 } { 3 } , \frac { 5 } { 6 }$ 
C)  $5,6,7,8$ 
D)  $8,6 , \frac { 16 } { 3 } , 5$ Evaluate the factorial expression.

Question 17

Find the Probability of One Event or a Second Event Occurring
-One digit from the number $8,161,441$ is written on each of seven cards. What is the probability of drawing a card that shows 8 or 4 ?

Accepted Answer

A)  $\frac { 3 } { 7 }$ 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 8 } { 7 }$ 
D)  $\frac { 1 } { 7 }$ 
A)  $\frac { 3 } { 7 }$ 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 8 } { 7 }$ 
D)  $\frac { 1 } { 7 }$

Question 18

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these
statements is true.
-$$S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

Accepted Answer

\[\begin{array} { l } 
\mathrm { S } _ {

Question 19

Use the Permutations Formula
-How many 3-letter codes can be formed using the letters $A , B , C , D$, and E? No letter can be used more than once.

Accepted Answer

A)  60 
B)  20 
C)  10 
D)  40 
A)  60 
B)  20 
C)  10 
D)  40

Question 20

Geometric Sequences and Series
1 Find the Common Ratio of a Geometric Sequence
-$$\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 }$$

Accepted Answer

A)  2 
B)  not a geometric sequence 
C)  6 
D)  4 
A)  2 
B)  not a geometric sequence 
C)  6 
D)  4

Write Terms of a Geometric Sequence - $a _ { n } = - 8 a _ { n - 1 } ; a _ { 1 } = - 4$

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. -A brick staircase has a total of 18 steps The bottom step requires 101 bricks. Each successive step requires 4 fewer bricks than the prior one. How many bricks are required to build the staircase?

Distinguish Between Permutation Problems and Combination Problems -From 9 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible?

Find the Probability that an Event Will Not Occur -A bag contains 20 marbles, of which 3 are blue and 7 are green. One marble is drawn from the bag. What is the probability that the marble drawn is not blue?

Find the Probability that an Event Will Not Occur -What is the probability that a card drawn from a deck of 52 cards is not a heart?

Write Terms of a Geometric Sequence - $\mathrm { a } _ { 1 } = 2 ; \mathrm { r } = 5$

Write the first four terms of the sequence whose general term is given. - $\mathrm { a } _ { \mathrm { n } } = \frac { ( - 1 ) ^ { \mathrm { n } + 1 } } { \mathrm { n } + 7 }$

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 8 ?

Distinguish Between Permutation Problems and Combination Problems -The matching section of an exam has 4 questions and 9 possible answers. In how many different ways can a student answer the 4 questions, if none of the answer choices can be repeated?

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first six terms of the geometric sequence: 2, 8, 32, . . . .

Use Summation Notation - $\sum _ { k = 2 } ^ { 4 } k ( k - 4 )$

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $\mathbf { a } _ { \mathbf { n } }$ to find $a _ { 20 }$ , the 20th term of the sequence. - $a _ { n } = a _ { n - 1 } + 5 , a _ { 1 } = 18$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = 4 n - 2$

Use the Formula for the Sum of an Infinite Geometric Series - $75 + 15 + 3 + \frac { 3 } { 5 } + \ldots$

Use Factorial Notation - $a _ { n } = \frac { 4 ( n + 1 ) ! } { n ! }$

Find the Probability of One Event or a Second Event Occurring -One digit from the number $8,161,441$ is written on each of seven cards. What is the probability of drawing a card that shows 8 or 4 ?

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. - $S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$

Use the Permutations Formula -How many 3-letter codes can be formed using the letters $A , B , C , D$ , and E? No letter can be used more than once.

Geometric Sequences and Series 1 Find the Common Ratio of a Geometric Sequence - $\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 }$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 11: Sequences, Induction, and Probability

Write Terms of a Geometric Sequence - an=−8an−1;a1=−4a _ { n } = - 8 a _ { n - 1 } ; a _ { 1 } = - 4an​=−8an−1​;a1​=−4