Deck 8: Sequences, Series, and Probability

Question 1

Write the first five terms of the sequence. (Assume that n begins with 0.)

Answer 1

A

Question 2

Answer 2

A

Question 3

Answer 3

B

Question 4

Use mathematical induction to prove that 80 is a factor of 6 for all positive n.

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Use mathematical induction to prove the property for all positive integers n.

Question 16

Question 17

Evaluate using a graphing utility:

A) 15,504
B) 116,280
C) 1,860,480
D) 100
E) undefined

Question 18

Question 19

Use mathematical induction to prove the following for every positive integer n.

Question 20

Question 21

Question 22

Question 23

Question 24

Determine whether the sequence is arithmetic. If so, find the common difference. 7, 8, 9, 10, 11

A) 6
B) 1
C) 7
D) -1
E) not arithmetic

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 32

Question 33

Question 34

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing four green, six yellow, and five red marbles such that both
Marbles are yellow.

Question 35

Question 36

Write the first five terms of the arithmetic sequence.

A) 5, 12, 19, 26, 33
B) 5, -2, -9, -16, -23
C) 12, 19, 26, 33, 40
D) 5, 35, 245, 1715, 12005
E) 5, 12, 17, 22, 27

Question 37

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Question 40

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Question 43

Write the first five terms of the sequence defined recursively. Use the pattern to write the nth term of the sequence as a function of n. (Assume that n begins with 1.)

Question 44

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Question 46

Question 47

Use the Binomial Theorem to expand the complex number. Simplify your result.

Question 48

Question 49

Question 50

Question 51

Write the first five terms of the geometric sequence.

Question 52

Question 53

Question 54

Question 55

Question 56

Expand the following expression in the difference quotient and simplify.

Question 57

Question 58

Find a formula for the nth term of the following geometric sequence, then find the 4th term of the sequence.

Question 59

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Question 79

Question 80