Deck 13: Sequences

Question 1

Write the first five terms of the sequence with the following general term.

A) -2, 10, -26, 83, -241
B) -2, 10, -26, 82, -242
C) -2, 10, -25, 84, -240
D) -2, 10, -25, 83, -241
E) -2, 10, -27, 82, -242

Answer 1

B

Question 2

Write the first five terms of the sequence with the following general term.

A)
B)
C)
D)
E)

Answer 2

C

Question 3

Write the first ten terms of the sequence defined by the recursion formula.

A)
B)
C)
D)
E)

Answer 3

C

Question 4

Write the first five terms of the sequence with the following general term.

A) , , , ,
B) , , , ,
C) , , , ,
D) , , , ,
E) , , , ,

Question 5

Write the first five terms of the sequence defined by the recursion formula.

A) 6, 2, -1, -5, -9
B) 6, 2, -2, -6, -10
C) 6, 2, -2, -6, -18
D) 6, 2, -2, -10, -14
E) 6, 2, -2, -5, -8

Question 6

Determine the general term for the following sequence.

A)
B)
C)
D)
E)

Question 7

Write the first five terms of the sequence with the following general term.

A)
B)
C)
D)
E)

Question 8

To save money for holiday presents, a person deposits $5 in a savings account on January 1, and then deposits an additional $5 every week thereafter until Christmas. If there are 50 weeks from January 1 to Christmas, how much money will be available for spending on Christmas presents?

A) $200
B) $245
C) $441
D) $250
E) $450

Question 9

Write the first five terms of the sequence defined by the recursion formula.

A) 1, -3, 9, -27, 81
B) 1, -3, 9, -27, 82
C) 1, 3, -9, 27, -81
D) 1, -3, 9, -27, -81
E) 1, 3, 9, 27, 81

Question 10

Determine the general term for the sequence.

A)
B)
C)
D)
E)

Question 11

Write the first five terms of the sequence defined by the recursion formula.

A) -5, -10, -20, -40, -80
B) -5, -8, -16, -32, -64
C) -5, -10, 20, 40, -80
D) 5, 10, 23, 46, 92
E) -5, -10, -20, -39, -78

Question 12

Write the first five terms of the sequence with the following general term.

A) -3, 10, -25, 83, -241
B) -3, 12, -24, 84, -240
C) -3, 9, -27, 81, -243
D) -3, 9, -22, 86, -238
E) -3, 11, -24, 85, -238

Question 13

Write the first ten terms of the sequence defined by the recursion formula.

A)
B)
C)
D)
E)

Question 14

Determine the general term for the sequence.

A)
B)
C)
D)
E)

Question 15

Determine the general term for the sequence.

A)
B)
C)
D)
E)

Question 16

Write the first five terms of the sequence defined by the recursion formula.

A) 2, 5, 11, 23, 47
B) -2, -7, -14, -29, -59
C) -2, -6, -13, -27, -54
D) -2, -5, -10, -21, -43
E) -2, -5, -11, -23, -47

Question 17

If a boulder fell from the top of in Hawaii, the distance, in feet, the boulder would fall in each consecutive second would be modeled by a sequence whose general term is where represents the number of seconds. What is the total distance the boulder fell in 4 seconds?

A) 276 feet
B) 251 feet
C) 241 feet
D) 246 feet
E) 256 feet

Question 18

Write the first five terms of the sequence with the following general term.

A) 1, 2, 3, 4, 5
B) - 2, - 3, - 4, - 5, - 6
C) - 2, - 3, - 4, - 4, - 5
D) - 3, - 4, - 5, - 6, - 7
E) 2, 3, 4, 5, 6

Question 19

The total national health expenditures, in billions of dollars, increased by approximately $50 billion from 1995 to 1996 and from 1996 to 1997. The total national health expenditures for 1997 was approximately $1,092 billion (U.S. Census Bureau, Nation Health Expenditures). If health expenditures continue to increase at this approximate rate, what would the expected expenditures be in 2005?

A) $1,492 billion
B) $1,742 billion
C) $1,442 billion
D) $1,392 billion
E) $1,692 billion

Question 20

Write the first five terms of the sequence defined by the recursion formula.

A) 1, 2, 4, 8, 16
B) 1, 3, 6, 13, 27
C) 1, 1, 1, 1, 1
D) 1, 0, 1, 0, 1
E) 1, 2, 4, 9, 19

Question 21

Write the first five terms of the sequence defined by the recursion formula.

Question 22

The total national health expenditures, in billion of dollars, increased by approximately $50 billion from 1995 to 1996 and from 1996 to 1997. The total national health expenditures for 1997 was approximately $1,092 billion (U.S. Census Bureau, Nation Health Expenditures). If the same approximate increase is assumed to continue, what would be the estimated total expenditures for 1998, 1999, and 2000? __________ Write the general term for the sequence, where represents the number of years since 1997. __________ If health expenditures continue to increase at this approximate rate, what would the expected expenditures be in 2008? $ __________

Question 23

Write the first five terms of the sequence defined by the recursion formula.

Question 24

Write the first five terms of the sequence defined by the recursion formula.

Question 25

Write the first ten terms of the sequence defined by the recursion formula.

Question 26

Write the first ten terms of the sequence defined by the recursion formula.

Question 27

Write the first five terms of the sequence with the following general term.

Question 28

Write the first five terms of the sequence defined by the recursion formula.

Question 29

Determine the general term for the following sequence.

Question 30

Write the first five terms of the sequence defined by the recursion formula.

Question 31

Write the first five terms of the sequence with the following general term.

Question 32

Write the first five terms of the sequence with the following general term.

Question 33

If a boulder fell from the top of in Hawaii, the distance, in feet, the boulder would fall in each consecutive second would be modeled by a sequence whose general term is where represents the number of seconds. Write a sequence for the first 5 seconds the boulder falls. __________ What is the total distance the boulder fell in 5 seconds? __________ ft If is approximately 420 feet high, will the boulder hit the ground within 8 seconds? Answer yes or no . __________

Question 34

Write the first five terms of the sequence with the following general term.

Question 35

To save money for holiday presents, a person deposits $4 in a savings account on January 1, and then deposits an additional $4 every week thereafter until Christmas. Write a sequence for the money in that savings account for the first 10 weeks of the year. __________ Write the general term for the sequence above. __________ If there are 50 weeks from January 1 to Christmas, how much money will be available for spending on Christmas presents? $ __________

Question 36

Determine the general term for the sequence.

Question 37

Write the first five terms of the sequence with the following general term.

Question 38

Write the first five terms of the sequence with the following general term.

Question 39

Determine the general term for the sequence.

Question 40

Determine the general term for the sequence.

Question 41

Write the sum with summation notation.

A)
B)
C)
D)
E)

Question 42

Expand and simplify.

A) 44
B) 43
C) 42
D) 47
E) 46

Question 43

Write the sum with summation notation.

A)
B)
C)
D)
E)

Question 44

Write the sum with summation notation. Do not calculate the sum.

A)
B)
C)
D)
E)

Question 45

Expand

A)
B)
C)
D)
E)

Question 46

Write the sum with summation notation. Do not calculate the sum.

A)
B)
C)
D)
E)

Question 47

After 1 day, a colony of 40 bacteria reproduces to become 200 bacteria. After 2 days, they reproduce to become 1,000 bacteria. If they continue to reproduce at this rate, how many bacteria will be present after 6 days?

A) 626,000 bacteria
B) 625,800 bacteria
C) 625,500 bacteria
D) 625,000 bacteria
E) 624,900 bacteria

Question 48

A pendulum swings 9 feet left to right on its first swing, and on each swing following the first, swings of the previous swing. The distance the pendulum traveled in 7 seconds can be expressed in summation notation . Expand the summation notation and simplify.

A) 34.0 feet
B) 35.6 feet
C) 26.5 feet
D) 27.9 feet
E) 28.5 feet

Question 49

Write the sum with summation notation. Do not calculate the sum.

A)
B)
C)
D)
E)

Question 50

Expand and simplify.

A)
B)
C)
D)
E)

Question 51

Expand and simplify.

A)
B)
C)
D)
E)

Question 52

Solve the equation for

A)
B)
C)
D)
E)

Question 53

Expand and simplify.

A) 38
B) 51
C) 48
D) 50
E) 49

Question 54

Expand and simplify.

A) 23
B) 14
C) 37
D) 39
E) 33

Question 55

Write the sum with summation notation.

A)
B)
C)
D)
E)

Question 56

Expand

A)
B)
C)
D)
E)

Question 57

Any repeating, nonterminating decimal may be viewed as a series. For instance, Write the following fraction as a series.

A) 0.29 + 0.0029 + 0.000029 + 0.00000029 + ...
B) 0.13 + 0.0013 + 0.000013 + 0.00000013 + ...
C) 0.6 + 0.06 + 0.006 + 0.0006 + ...
D) 0.7 + 0.07 + 0.007 + 0.0007 + ...
E) 0.8 + 0.08 + 0.008 + 0.0008 + ...

Question 58

Expand and simplify.

A) 460
B) 438
C) 310
D) 550
E) 278

Question 59

Expand and simplify.

A)
B)
C)
D)
E)

Question 60

Expand

A)
B)
C)
D)
E)

Question 61

Write the following sum in summation notation. Do not calculate the sum.

Question 62

Consider the following finite series: For which values of i does the following summation notation hold true? must range from __________ to __________ .

Question 63

A pendulum swings 11 feet left to right on its first swing, and on each swing following the first, swings of the previous swing. The distance the pendulum traveled in 5 seconds can be expressed in summation notation . Expand the summation notation and simplify. Round your final answer to the nearest tenth. __________ feet

Question 64

Consider the following finite series: For which values of i does the following summation notation hold true and what constant must be added in the denominator? must range from __________ to __________. __________

Question 65

Expand

Question 66

After 1 day, a colony of 40 bacteria reproduces to become 200 bacteria. After 2 days, they reproduce to become 1,000 bacteria. If they continue to reproduce at this rate, how many bacteria will be present after 6 days? __________ bacteria

Question 67

Expand and simplify.

Question 68

Expand

Question 69

Expand and simplify.

Question 70

Expand and simplify.

Question 71

Write the following sum in summation notation. Do not calculate the sum.

Question 72

Expand and simplify.

Question 73

Expand and simplify.

Question 74

Write the sum with summation notation. Do not calculate the sum.

Question 75

Expand and simplify.

Question 76

Write the following sum in summation notation. Do not calculate the sum.

Question 77

Any repeating, nonterminating decimal may be viewed as a series. For instance, . Use this fact to express the following series as a fraction.

Question 78

Expand

Question 79

Solve the equation for

Question 80

Expand and simplify.