Question 1

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

Accepted Answer

A) 0, 3, 8, 15, 24 
B) 1, 4, 9, 16, 25 
C) 0, 2, 6, 12, 20 
D) 2, 6, 12, 20, 30 
A) 0, 3, 8, 15, 24 
B) 1, 4, 9, 16, 25 
C) 0, 2, 6, 12, 20 
D) 2, 6, 12, 20, 30

Question 2

Solve the problem.
-A die is rolled. Find the odds against rolling a multiple of 3.

Accepted Answer

A) 2:1 
B) 1:2 
C) 1:3 
D) 3:1 
A) 2:1 
B) 1:2 
C) 1:3 
D) 3:1

Question 3

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.
-$a _ { 1 } = 1 , d = 3$

Accepted Answer

A)  $a _ { n } = n + 3$ 
B)  $a _ { n } = 2 n - 3$ 
C)  $a _ { n } = 3 n - 2$ 
D)  $a _ { n } = 3 n + 2$ 
A)  $a _ { n } = n + 3$ 
B)  $a _ { n } = 2 n - 3$ 
C)  $a _ { n } = 3 n - 2$ 
D)  $a _ { n } = 3 n + 2$

Question 4

Find the indicated term of the geometric sequence.
-a1 = 4, r = 3; find ${ a } _{11}$

Accepted Answer

A) 708,588 
B) 236,200 
C) 34 
D) 236,196 
A) 708,588 
B) 236,200 
C) 34 
D) 236,196

Question 5

Find the indicated term of the geometric sequence.
-a $a _ { 1 } = 2000 , r = \frac { 1 } { 3 } ; \text { find } a _ { 11 }$

Accepted Answer

A)  $\frac { 2000 } { 59049 }$ 
B)  $\frac { 2000 } { 531441 }$ 
C)  $\frac { 2000 } { 177147 }$ 
D)  $\frac { 6010 } { 3 }$ 
A)  $\frac { 2000 } { 59049 }$ 
B)  $\frac { 2000 } { 531441 }$ 
C)  $\frac { 2000 } { 177147 }$ 
D)  $\frac { 6010 } { 3 }$

Question 6

Find the indicated sum.
-$a _ { 1 } = \frac { 1 } { 8 } , r = - 2 ; \text { find } s _ { 13 }$

Accepted Answer

A)  $\frac { 2725 } { 8 }$ 
B)  $\frac { 2729 } { 8 }$ 
C)  $\frac { 1369 } { 4 }$ 
D)  $\frac { 2731 } { 8 }$ 
A)  $\frac { 2725 } { 8 }$ 
B)  $\frac { 2729 } { 8 }$ 
C)  $\frac { 1369 } { 4 }$ 
D)  $\frac { 2731 } { 8 }$

Question 7

Solve the problem.
-The odds against the horse Teabag winning a race are 3:14. i)Find the probability that Teabag wins.
Ii)Find the probability that Teabag loses.

Accepted Answer

A)  i) $\frac { 17 } { 14 }$

ii) $\frac { 17 } { 3 }$ 
B)  i) $\frac { 17 } { 3 }$

ii) $\frac { 17 } { 14 }$ 
C)  i) $\frac { 14 } { 17 }$

ii) $\frac { 3 } { 17 }$ 
D)  i) $\frac { 3 } { 17 }$

ii) $\frac { 14 } { 17 }$ 
A)  i) $\frac { 17 } { 14 }$

ii) $\frac { 17 } { 3 }$ 
B)  i) $\frac { 17 } { 3 }$

ii) $\frac { 17 } { 14 }$ 
C)  i) $\frac { 14 } { 17 }$

ii) $\frac { 3 } { 17 }$ 
D)  i) $\frac { 3 } { 17 }$

ii) $\frac { 14 } { 17 }$

Question 8

Find the indicated term of the sequence whose nth term is shown.
-$a _ { n } = \frac { n } { 2 } - 5 \text {, eighth term }$

Accepted Answer

A) -1 
B) 9 
C) 3 
D) 11 
A) -1 
B) 9 
C) 3 
D) 11

Question 9

Solve the problem.
-A traffic light is red for 50 seconds, yellow for 5 seconds, and green for 40 seconds. Find the probability: P(the light is not yellow)

Accepted Answer

A)  $\frac { 18 } { 19 }$ 
B)  $\frac { 1 } { 14 }$ 
C)  $\frac { 94 } { 95 }$ 
D)  $\frac { 9 } { 14 }$ 
A)  $\frac { 18 } { 19 }$ 
B)  $\frac { 1 } { 14 }$ 
C)  $\frac { 94 } { 95 }$ 
D)  $\frac { 9 } { 14 }$

Question 10

Solve the problem.
-A spinner is spun. Assuming that the spinner cannot land on a line, find the probability of landing on a color that is yellow or green.

Accepted Answer

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

Question 11

Evalutate the series.
-$$\sum _ { n = 3 } ^ { 5 } \left( n ^ { 2 } - 4 \right)$$

Accepted Answer

A) 35 
B) 38 
C) 0 
D) 12 
A) 35 
B) 38 
C) 0 
D) 12

Question 12

Find the common difference of the sequence.
-$a _ { 1 } = - 12 , a _ { 4 } = - 24 ; \text { find } d$

Accepted Answer

A) -8 
B) -4 
C) -12 
D) 12 
A) -8 
B) -4 
C) -12 
D) 12

Question 13

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum.
-$a _ { n } = n ^ { 7 },$ fifth partial sum

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 4 } i ^ { 7 }$ 
B)  $\sum _ { i = 0 } ^ { 4 } i ^ { 7 }$ 
C)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \mathrm { i } ^ { 7 }$ 
D)  $\sum _ { \mathrm { i } = 0 } ^ { 5 } \mathrm { i } ^ { 7 }$ 
A)  $\sum _ { i = 1 } ^ { 4 } i ^ { 7 }$ 
B)  $\sum _ { i = 0 } ^ { 4 } i ^ { 7 }$ 
C)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \mathrm { i } ^ { 7 }$ 
D)  $\sum _ { \mathrm { i } = 0 } ^ { 5 } \mathrm { i } ^ { 7 }$

Question 14

For the geometric sequence, find the common ratio, r.
-2, 0.8, 0.32, 0.128, . . .

Accepted Answer

A) 4 
B) 0.04 
C) 0.4 
D) 0.8 
A) 4 
B) 0.04 
C) 0.4 
D) 0.8

Question 15

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
-$\frac { 1 } { 7 } , \frac { 1 } { 49 } , \frac { 1 } { 343 } , \frac { 1 } { 2401 } , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 7 } + \frac { 1 } { 7 } ( n - 1 )$ 
B)  $a _ { n } = \left( \frac { 1 } { 7 } \right) ^ { n - 1 } - \frac { 6 } { 49 }$ 
C)  $a _ { n } = \frac { 1 } { 7 } - \frac { 6 } { 49 } ( n - 1 )$ 
D)  $\mathrm { a } _ { \mathrm { n } } = \frac { 1 } { 7 } \left( \frac { 1 } { 7 } \right) ^ { n - 1 }$ 
A)  $a _ { n } = \frac { 1 } { 7 } + \frac { 1 } { 7 } ( n - 1 )$ 
B)  $a _ { n } = \left( \frac { 1 } { 7 } \right) ^ { n - 1 } - \frac { 6 } { 49 }$ 
C)  $a _ { n } = \frac { 1 } { 7 } - \frac { 6 } { 49 } ( n - 1 )$ 
D)  $\mathrm { a } _ { \mathrm { n } } = \frac { 1 } { 7 } \left( \frac { 1 } { 7 } \right) ^ { n - 1 }$

Question 16

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.
-$$1 + \frac { 1 } { 5 } + \frac { 1 } { 5 ^ { 2 } } + \ldots + \frac { 1 } { 5 ^ { n - 1 } } = \frac { 5 } { 4 } \left( 1 - \frac { 1 } { 5 ^ { n } } \right)$$

Accepted Answer

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

Question 17

Evalutate the series.
-$$\sum _ { n = 1 } ^ { 4 } \left( - \frac { 1 } { 4 } \right) ^ { n }$$

Accepted Answer

A)  $- \frac { 47 } { 256 }$ 
B)  $\frac { 85 } { 256 }$ 
C)  $- \frac { 51 } { 256 }$ 
D)  $\frac { 51 } { 256 }$ 
A)  $- \frac { 47 } { 256 }$ 
B)  $\frac { 85 } { 256 }$ 
C)  $- \frac { 51 } { 256 }$ 
D)  $\frac { 51 } { 256 }$

Question 18

Write the first five terms of the sequence whose nth term is shown.
-$a _ { n } = ( - 4 ) ^ { n }$

Accepted Answer

A) 16, -64, 256, -1024, 4096 
B) -4, 16, -64, 256, -1024 
C) 4, 16, 64, 256, 1024 
D) -4, -8, -12, -16, -20 
A) 16, -64, 256, -1024, 4096 
B) -4, 16, -64, 256, -1024 
C) 4, 16, 64, 256, 1024 
D) -4, -8, -12, -16, -20

Question 19

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum.
-$a _ { n } = 2 - 6 n,$ third partial sum

Accepted Answer

A)  $\sum _ { i = 1 } ^ { n } 2 - 6 i$ 
B)  $\sum _ { i = 1 } ^ { 3 } 2 - 6 i$ 
C)  $\sum _ { i = 0 } ^ { 2 } 2 - 6 i$ 
D)  $\sum _ { i = 0 } ^ { 3 } 2 - 6 i$ 
A)  $\sum _ { i = 1 } ^ { n } 2 - 6 i$ 
B)  $\sum _ { i = 1 } ^ { 3 } 2 - 6 i$ 
C)  $\sum _ { i = 0 } ^ { 2 } 2 - 6 i$ 
D)  $\sum _ { i = 0 } ^ { 3 } 2 - 6 i$

Question 20

Solve the problem.
-A card is selected at random from a deck of cards. Find the probability: P(selecting the 8 of spades)

Accepted Answer

A)  $\frac { 1 } { 13 }$ 
B)  $\frac { 4 } { 13 }$ 
C)  $\frac { 1 } { 26 }$ 
D)  $\frac { 1 } { 52 }$ 
A)  $\frac { 1 } { 13 }$ 
B)  $\frac { 4 } { 13 }$ 
C)  $\frac { 1 } { 26 }$ 
D)  $\frac { 1 } { 52 }$

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

Solve the problem. -A die is rolled. Find the odds against rolling a multiple of 3.

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence. - $a _ { 1 } = 1 , d = 3$

Find the indicated term of the geometric sequence. -a1 = 4, r = 3; find ${ a } _{11}$

Find the indicated term of the geometric sequence. -a $a _ { 1 } = 2000 , r = \frac { 1 } { 3 } ; \text { find } a _ { 11 }$

Find the indicated sum. - $a _ { 1 } = \frac { 1 } { 8 } , r = - 2 ; \text { find } s _ { 13 }$

Solve the problem. -The odds against the horse Teabag winning a race are 3:14. i)Find the probability that Teabag wins. Ii)Find the probability that Teabag loses.

Find the indicated term of the sequence whose nth term is shown. - $a _ { n } = \frac { n } { 2 } - 5 \text {, eighth term }$

Solve the problem. -A traffic light is red for 50 seconds, yellow for 5 seconds, and green for 40 seconds. Find the probability: P(the light is not yellow)

Solve the problem. -A spinner is spun. Assuming that the spinner cannot land on a line, find the probability of landing on a color that is yellow or green.

Evalutate the series. - $\sum _ { n = 3 } ^ { 5 } \left( n ^ { 2 } - 4 \right)$

Find the common difference of the sequence. - $a _ { 1 } = - 12 , a _ { 4 } = - 24 ; \text { find } d$

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum. - $a _ { n } = n ^ { 7 },$ fifth partial sum

For the geometric sequence, find the common ratio, r. -2, 0.8, 0.32, 0.128, . . .

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence. - $\frac { 1 } { 7 } , \frac { 1 } { 49 } , \frac { 1 } { 343 } , \frac { 1 } { 2401 } , \ldots$

Evalutate the series. - $\sum _ { n = 1 } ^ { 4 } \left( - \frac { 1 } { 4 } \right) ^ { n }$

Write the first five terms of the sequence whose nth term is shown. - $a _ { n } = ( - 4 ) ^ { n }$

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum. - $a _ { n } = 2 - 6 n,$ third partial sum

Solve the problem. -A card is selected at random from a deck of cards. Find the probability: P(selecting the 8 of spades)

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Exam 12: Sequences, Series, and Probability

Write the first five terms of the sequence whose nth term is shown. - an=n2−na _ { n } = n ^ { 2 } - nan​=n2−n