Deck 10: Infinite Sequences and Series

Question 1

Write the first four elements of the sequence.
sin (n)

A) 1, 0, -1, 0
B) 1, 1, 1, 1
C) 0, 0, 0, 0
D) 0, 1, 0, -1

Answer 1

C

Question 2

Write the first four elements of the sequence.

Answer 2

D

Question 3

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Answer 3

A

Question 4

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Question 5

Find a formula for the nth term of the sequence.

Question 6

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Question 7

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Question 8

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Question 9

Find a formula for the nth term of the sequence.

Question 10

Find a formula for the nth term of the sequence.

Question 11

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Question 12

Write the first four elements of the sequence.

Question 13

Find a formula for the nth term of the sequence.

Question 14

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Question 15

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Question 16

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Question 17

Write the first four elements of the sequence.

Question 18

Find a formula for the nth term of the sequence.

Question 19

Write the first four elements of the sequence.

Question 20

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.

Question 21

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 22

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 23

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 24

Find a formula for the nth term of the sequence.

Question 25

Find the limit of the sequence if it converges; otherwise indicate divergence.

A) 1
B) 32
C) 53
D) Diverges

Question 26

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 27

Find the limit of the sequence if it converges; otherwise indicate divergence.

A) 8
B) 7
C) 7.3
D) Diverges

Question 28

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 29

Find a formula for the nth term of the sequence.

Question 30

Find the limit of the sequence if it converges; otherwise indicate divergence.

A) 8
B) ±8
C) 0
D) Diverges

Question 31

Find a formula for the nth term of the sequence.

Question 32

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 33

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 34

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 35

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 36

Find the limit of the sequence if it converges; otherwise indicate divergence.

A) 2
B) 0
C) 1
D) Diverges

Question 37

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 38

Find a formula for the nth term of the sequence.

Question 39

Find a formula for the nth term of the sequence.

Question 40

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 41

Determine if the sequence is monotonic and if it is bounded.

A) increasing; bounded
B) not monotonic; bounded
C) decreasing; unbounded
D) nonincreasing; bounded

Question 42

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 43

Determine if the sequence is monotonic and if it is bounded.

A) nondecreasing; unbounded
B) nondecreasing; bounded
C) not monotonic; unbounded
D) nonincreasing; unbounded

Question 44

Assume that the sequence converges and find its limit.

Question 45

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 46

Determine if the sequence is monotonic and if it is bounded.

A) not monotonic; bounded
B) nondecreasing; bounded
C) decreasing; bounded
D) decreasing; unbounded

Question 47

Determine if the sequence is monotonic and if it is bounded.

A) nondecreasing; bounded
B) decreasing; bounded
C) increasing; unbounded
D) not monotonic; unbounded

Question 48

Determine whether the nonincreasing sequence converges or diverges.

A) Converges
B) Diverges

Question 49

Determine whether the nonincreasing sequence converges or diverges.

A) Converges
B) Diverges

Question 50

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 51

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 52

Determine whether the nonincreasing sequence converges or diverges.

A) Diverges
B) Converges

Question 53

Assume that the sequence converges and find its limit.

Question 54

Determine whether the nonincreasing sequence converges or diverges.

Question 55

Determine if the sequence is monotonic and if it is bounded.

A) increasing; bounded
B) not monotonic; unbounded
C) nondecreasing; bounded
D) nondecreasing; unbounded

Question 56

Find the limit of the sequence if it converges; otherwise indicate divergence.

Question 57

Determine if the sequence is monotonic and if it is bounded.

A) decreasing; unbounded
B) nondecreasing; bounded
C) nondecreasing; unbounded
D) not monotonic; unbounded

Question 58

Assume that the sequence converges and find its limit.

Question 59

Determine if the sequence is monotonic and if it is bounded.

A) increasing; unbounded
B) not monotonic; bounded
C) decreasing; bounded
D) nondecreasing; bounded

Question 60

Determine if the sequence is monotonic and if it is bounded.

A) not monotonic; bounded
B) nondecreasing; bounded
C) increasing; unbounded
D) decreasing; bounded

Question 61

Find the smallest value of N that will make the inequality hold for all n > N.

A) 31
B) 30
C) 20
D) 21

Question 62

Find the smallest value of N that will make the inequality hold for all n > N.

A) 9907
B) 9891
C) 9883
D) 9899

Question 63

Find the smallest value of N that will make the inequality hold for all n > N.

A) 507
B) 511
C) 509
D) 514

Question 64

Find the smallest value of N that will make the inequality hold for all n > N.

Question 65

Find the smallest value of N that will make the inequality hold for all n > N.
A company's annual revenue for the period since 2000 can be modeled by the function Rn = 2.11(1.06)n, where R is in millions of dollars and n = 0 corresponds to 2000. Assuming the model accurately predicts future
Revenue, find the year in which the revenue first exceeds $3.10 million.

A) 2007
B) 2009
C) 2006
D) 2005

Question 66

Find the smallest value of N that will make the inequality hold for all n > N.

A) L = 0, N = 8
B) L = 0, N = 10
C) L = 0, N = 13
D) diverges

Question 67

Find the smallest value of N that will make the inequality hold for all n > N.

A) 16
B) 13
C) 15
D) 14

Question 68

Find the smallest value of N that will make the inequality hold for all n > N.

A) 27
B) 23
C) 25
D) 20

Question 69

Find the smallest value of N that will make the inequality hold for all n > N.

Question 70

Find the smallest value of N that will make the inequality hold for all n > N.

A) L = 0, N = 8
B) L = ln 4, N = 8
C) L = ln 2, N = 6
D) diverges

Question 71

Find the smallest value of N that will make the inequality hold for all n > N.

Question 72

Find the smallest value of N that will make the inequality hold for all n > N.

A) 17
B) 20
C) 19
D) 18

Question 73

Find the smallest value of N that will make the inequality hold for all n > N.

A) L = 1, N = 28
B) L = 0, N = 28
C) L = 0, N = 37
D) diverges

Question 74

Find the smallest value of N that will make the inequality hold for all n > N.

A) 17
B) 15
C) 16
D) 18

Question 75

Find the smallest value of N that will make the inequality hold for all n > N.

A) L = 0, N = 7
B) L = ln 4, N = 8
C) L = ln 2, N = 6
D) diverges

Question 76

Find the smallest value of N that will make the inequality hold for all n > N.

Question 77

Find the smallest value of N that will make the inequality hold for all n > N.

A) L = 0, N = 1301
B) L = 1, N = 720
C) L = 1, N = 1301
D) diverges

Question 78

Find the smallest value of N that will make the inequality hold for all n > N.

A) 750
B) 731
C) 737
D) 733

Question 79

Find the smallest value of N that will make the inequality hold for all n > N.
At a plant that packages bottled spring water, the water is passed through a sequence of ion-exchange filters to reduce the sodium content prior to bottling. Each filter removes 74% of the sodium present in the water passing
Through it. Determine the number of filters that must be used to reduce the sodium concentration from 22
Parts-per-million to 3.61 parts-per-million.

A) 8 filters
B) 6 filters
C) 7 filters
D) 9 filters

Question 80

Find the smallest value of N that will make the inequality hold for all n > N.

A) L  1.1653, N = 6
B) L  1.153, N = 6
C) L  1.1653, N = 2
D) diverges