Question 1

Find the probability.
-What is the probability that the arrow will land on 2 or 1?

Accepted Answer

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

Question 2

Solve the problem.
-Suppose 5 cards are drawn from a deck of 52 cards. What is the probability of drawing 4 aces with any other card?

Accepted Answer

A)  $\frac { 1 } { 54,145 }$ 
B)  $\frac { 1 } { 5,997,600 }$ 
C)  $\frac { 1 } { 676 }$ 
D)  $\frac { 1 } { 10,829 }$ 
A)  $\frac { 1 } { 54,145 }$ 
B)  $\frac { 1 } { 5,997,600 }$ 
C)  $\frac { 1 } { 676 }$ 
D)  $\frac { 1 } { 10,829 }$

Question 3

Provide an appropriate response.
-Determine the general term of the sequence $6 , - 15 , \frac { 75 } { 2 } , - \frac { 375 } { 4 } , \ldots$

Accepted Answer

A)  $a _ { n } = 6 \left( - \frac { 5 } { 2 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = \frac { 5 } { 2 } ( 6 ) ^ { n - 1 }$ 
C)  $a _ { n } = - 6 \left( \frac { 5 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 6 \left( - \frac { 5 } { 2 } \right) ^ { n }$ 
A)  $a _ { n } = 6 \left( - \frac { 5 } { 2 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = \frac { 5 } { 2 } ( 6 ) ^ { n - 1 }$ 
C)  $a _ { n } = - 6 \left( \frac { 5 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 6 \left( - \frac { 5 } { 2 } \right) ^ { n }$

Question 4

Write a formula for the general term, or nth term, for the given sequence.
-2 , 10 , 18 , 26 , 34 , . . .

Accepted Answer

A)  $a _ { n } = 2 ( 8 ) ^ { n - 1 }$ 
B)  $a _ { n } = 8 n - 3$ 
C)  $a _ { n } = 8 n - 6$ 
D)  $a _ { n } = 6 n - 8$ 
A)  $a _ { n } = 2 ( 8 ) ^ { n - 1 }$ 
B)  $a _ { n } = 8 n - 3$ 
C)  $a _ { n } = 8 n - 6$ 
D)  $a _ { n } = 6 n - 8$

Question 5

Find the general term of the arithmetic sequence.
-$3,9,15,21,27 , \ldots$

Accepted Answer

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

Question 6

Provide an appropriate response.
-Determine the general term of the sequence 5, 20, 80, 320, . . . .

Accepted Answer

A)  $a _ { n } = 5 ( 4 ) ^ { n }$ 
B)  $a _ { n } = 5 ( 4 ) ^ { n - 1 }$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 4 ( 5 ) ^ { \mathrm { n } }$ 
D)  $a _ { n } = 4 ( 5 ) ^ { n - 1 }$ 
A)  $a _ { n } = 5 ( 4 ) ^ { n }$ 
B)  $a _ { n } = 5 ( 4 ) ^ { n - 1 }$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 4 ( 5 ) ^ { \mathrm { n } }$ 
D)  $a _ { n } = 4 ( 5 ) ^ { n - 1 }$

Question 7

Find the probability.
-What is the probability that a card drawn from a deck of 52 cards is not black?

Accepted Answer

A)  2 
B)  $\frac { 25 } { 52 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  2 
B)  $\frac { 25 } { 52 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 1 } { 2 }$

Question 8

Use the Binomial Theorem to expand the binomial.
-$$( 2 x - 2 y ) ^ { 3 }$$

Accepted Answer

A)  $8 x ^ { 3 } - 24 x ^ { 2 } y + 24 x y ^ { 2 } - 8 y ^ { 3 }$ 
B)  $4 x ^ { 3 } y - 8 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$ 
C)  $4 x ^ { 3 } y - 4 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$ 
D)  $8 x ^ { 3 } - 8 x ^ { 2 } y + 8 x y ^ { 2 } - 8 y ^ { 3 }$ 
A)  $8 x ^ { 3 } - 24 x ^ { 2 } y + 24 x y ^ { 2 } - 8 y ^ { 3 }$ 
B)  $4 x ^ { 3 } y - 8 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$ 
C)  $4 x ^ { 3 } y - 4 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$ 
D)  $8 x ^ { 3 } - 8 x ^ { 2 } y + 8 x y ^ { 2 } - 8 y ^ { 3 }$

Question 9

Find the sum of the geometric series.
-$\sum _ { \mathrm { i } = 1 } ^ { 11 } \frac { 1 } { 5 } ( - 3 ) ^ { \mathrm { i } - 1 } \quad$ Express the answer as a fraction.

Accepted Answer

A)  $\frac { 44,294 } { 5 }$ 
B)  $\frac { 44,281 } { 5 }$ 
C)  8857 
D)  $\frac { 44,287 } { 5 }$ 
A)  $\frac { 44,294 } { 5 }$ 
B)  $\frac { 44,281 } { 5 }$ 
C)  8857 
D)  $\frac { 44,287 } { 5 }$

Question 10

Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.
-$$S _ { n } : 6 + 12 + 18 + \ldots + 6 n = 3 n ( n + 1 )$$

Accepted Answer

\[\begin{aligned}
& ? \
\mathrm {~S} _

Question 11

Write the first four terms of the sequence.
-$$\mathrm { a } _ { \mathrm { n } } = 4 ( \mathrm { n } + 2 ) !$$

Accepted Answer

A)  $8,48,288,1920$ 
B)  $8,24,96,480$ 
C)  $24,192,1440,11,520$ 
D)  $24,96,480,2880$ 
A)  $8,48,288,1920$ 
B)  $8,24,96,480$ 
C)  $24,192,1440,11,520$ 
D)  $24,96,480,2880$

Question 12

Write the first four terms of the sequence.
-$$a _ { n } = 4 n - 1$$

Accepted Answer

A) 3, 7, 11, 15 
B) 5, 9, 13, 17 
C) 3, 4, 5, 6 
D) -3, -7, -11, -15 
A) 3, 7, 11, 15 
B) 5, 9, 13, 17 
C) 3, 4, 5, 6 
D) -3, -7, -11, -15

Question 13

Write the first five terms of the geometric sequence with the given information.
-$$a _ { n } = 7 a _ { n - 1 } ; a _ { 1 } = 4$$

Accepted Answer

A)  $4,11,18,25,32$ 
B)  $7,28,196,1372,9604$ 
C)  $4,28,196,1372,9604$ 
D)  $28,196,1372,9604,67,228$ 
A)  $4,11,18,25,32$ 
B)  $7,28,196,1372,9604$ 
C)  $4,28,196,1372,9604$ 
D)  $28,196,1372,9604,67,228$

Question 14

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
-Find $a _ { n }$ and $a _ { 21 }$.

Accepted Answer

A)  $a _ { n } = n + 3 ; a _ { 21 } = 24$ 
B)  $a _ { n } = 4 - n ; a _ { 21 } = - 17$ 
C)  $a _ { n } = n - 4 ; a _ { 21 } = 17$ 
D)  $a _ { n } = n + 2 ; a _ { 21 } = 23$ 
A)  $a _ { n } = n + 3 ; a _ { 21 } = 24$ 
B)  $a _ { n } = 4 - n ; a _ { 21 } = - 17$ 
C)  $a _ { n } = n - 4 ; a _ { 21 } = 17$ 
D)  $a _ { n } = n + 2 ; a _ { 21 } = 23$

Question 15

Find the indicated sum.
-7 + 3 - 1 + . . . - 153

Accepted Answer

A) -144 
B) -2993 
C) -2920 
D) -146 
A) -144 
B) -2993 
C) -2920 
D) -146

Find the probability. -What is the probability that the arrow will land on 2 or 1?

Solve the problem. -Suppose 5 cards are drawn from a deck of 52 cards. What is the probability of drawing 4 aces with any other card?

Provide an appropriate response. -Determine the general term of the sequence $6 , - 15 , \frac { 75 } { 2 } , - \frac { 375 } { 4 } , \ldots$

Write a formula for the general term, or nth term, for the given sequence. -2 , 10 , 18 , 26 , 34 , . . .

Find the general term of the arithmetic sequence. - $3,9,15,21,27 , \ldots$

Provide an appropriate response. -Determine the general term of the sequence 5, 20, 80, 320, . . . .

Find the probability. -What is the probability that a card drawn from a deck of 52 cards is not black?

Use the Binomial Theorem to expand the binomial. - $( 2 x - 2 y ) ^ { 3 }$

Find the sum of the geometric series. - $\sum _ { \mathrm { i } = 1 } ^ { 11 } \frac { 1 } { 5 } ( - 3 ) ^ { \mathrm { i } - 1 } \quad$ Express the answer as a fraction.

Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n. - $S _ { n } : 6 + 12 + 18 + \ldots + 6 n = 3 n ( n + 1 )$

Write the first four terms of the sequence. - $\mathrm { a } _ { \mathrm { n } } = 4 ( \mathrm { n } + 2 ) !$

Write the first four terms of the sequence. - $a _ { n } = 4 n - 1$

Write the first five terms of the geometric sequence with the given information. - $a _ { n } = 7 a _ { n - 1 } ; a _ { 1 } = 4$

Find the indicated sum. -7 + 3 - 1 + . . . - 153

Equations, Inequalities, and Applications

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Exam 9: Sequences and Series; Counting and Probability