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)  $- 4 , - 12 , - 20 , - 28 , - 36$

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

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

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)  $\frac { 1 } { 2 }$

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

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)  $\frac { 2 } { 5 }$

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)  $5,10,20,40,80$

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)  $- \frac { 1 } { 9 } , \frac { 1 } { 10 } , - \frac { 1 } { 11 } , \frac { 1 } { 12 }$

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

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

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

Question 12

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

Accepted Answer

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)  $a _ { n } = 13 n + 5 , a _ { 20 } = 265$

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)  $- 2 , - 6 , - 10 , - 14$

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

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.

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)  $\frac { 1 } { 7 }$

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

The answer of A statement Sn about the positive integers...

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

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

Exam 11: Sequences, Induction, and Probability

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 - $\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 }$

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

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 - a1=2;r=5\mathrm { a } _ { 1 } = 2 ; \mathrm { r } = 5a1​=2;r=5

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

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 - ∑k=24k(k−4) \sum _ { k = 2 } ^ { 4 } k ( k - 4 ) ∑k=24​k(k−4)

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an\mathbf { a } _ { \mathbf { n } }an​ to find a20a _ { 20 }a20​ , the 20th term of the sequence. - an=an−1+5,a1=18a _ { n } = a _ { n - 1 } + 5 , a _ { 1 } = 18an​=an−1​+5,a1​=18

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

Use the Formula for the Sum of an Infinite Geometric Series - 75+15+3+35+…75 + 15 + 3 + \frac { 3 } { 5 } + \ldots75+15+3+53​+…

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

Find the Probability of One Event or a Second Event Occurring -One digit from the number 8,161,4418,161,4418,161,441 is written on each of seven cards. What is the probability of drawing a card that shows 8 or 4 ?

Use the Permutations Formula -How many 3-letter codes can be formed using the letters A,B,C,DA , B , C , DA,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 - 43,83,163,323,643\frac { 4 } { 3 } , \frac { 8 } { 3 } , \frac { 16 } { 3 } , \frac { 32 } { 3 } , \frac { 64 } { 3 }34​,38​,316​,332​,364​