Deck 9: Sequences; Induction; the Binomial Theorem

Question 1

Write out the first five terms of the sequence.

A)
B)c
C)
D)

Answer 1

Question 2

Evaluate the factorial expression.

A)12
B)
C)
D)4

Answer 2

12

Question 3

Write out the first five terms of the sequence.

A)
B)
C)
D)

Answer 3

Question 4

Write out the first five terms of the sequence.

A)
B)
C)s
D)

Question 5

Write out the first five terms of the sequence.

A)
B)
C)
D)

Question 6

Evaluate the factorial expression.

A)479,001,600
B)132
C)24
D)16

Question 7

Evaluate the factorial expression.

A)4
B)1
C)
D)

Question 8

Write out the first five terms of the sequence.

A)
B)
C)
D)

Question 9

Evaluate the factorial expression.

A)2,016
B)
C)336
D)

Question 10

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
-1 , 1 , 3 , 5 , 7 , ...

A)
B)
C)
D)

Question 11

Evaluate the factorial expression.

A)21
B)7
C)0
D)1

Question 12

Write out the first five terms of the sequence.

A)
B)
C)
D)

Question 13

Write out the first five terms of the sequence.

A)
B)
C)
D)

Question 14

Write out the first five terms of the sequence.

A)
B)
C)
D)

Question 15

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
6 , 14, 22, 30, 38, ...

A)a
B)a
C)
D)

Question 16

Write out the first five terms of the sequence.

A)
B)
C)
D)

Question 17

Evaluate the factorial expression.

A)
B)20
C)
D)

Question 18

Write out the first five terms of the sequence.

A)
B)
C)
D)

Question 19

Write out the first five terms of the sequence.

A)
B)
C)
D)

Question 20

Evaluate the factorial expression.

A)252
B)504
C)30,240
D)126

Question 21

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
2, -4, 6, -8, ...

A)
B)
C)
D)

Question 22

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.

A)
B)
C)
D)

Question 23

The sequence is defined recursively. Write the first four terms.

A)
B)a
C)
D)

Question 24

Solve.
The number of students in a school in year n is estimated by the model . About howmany students are in the school in each of the first three years?

A)98, 123, 156
B)111, 136, 169
C)102, 123, 156
D)98, 123, 144

Question 25

The sequence is defined recursively. Write the first four terms.

A)
B)
C)
D)

Question 26

Solve.
Given that what is the fifth term of this recursively definedsequence?

A)
B)
C)
D)

Question 27

The sequence is defined recursively. Write the first four terms.

A)
B)
C)
D)

Question 28

Solve.
During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth yearare $160,000, then what are the profits for each of the first four years?

A)$10,000, $20,000, $40,000, $80,000
B)$10,000, $20,000, $40,000, $100,000
C)$11,000, $22,000, $44,000, $86,000
D)$10,000, $20,000, $30,000, $40,000

Question 29

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
3 , 9 , 27, 81, 243 , ...

A)
B)
C)
D)

Question 30

The sequence is defined recursively. Write the first four terms.

A)
B)
C)
D)

Question 31

The sequence is defined recursively. Write the first four terms.

A)
B)
C)
D)

Question 32

Write the word or phrase that best completes each statement or answers the question.
Jake bought a truck by taking out a loan for $26,500 at 0.25% interest per month. Jakeʹs regular monthlypayment is $567, but he decides to pay an extra $75 toward the balance each month. His balance each monthafter making his payment, is given by the recursively defined sequence Determine Jakeʹs balance after making the first payment. That is, determine

Question 33

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.

A)
B)
C)
D)

Question 34

The sequence is defined recursively. Write the first four terms.

A)
B)
C)
D)

Question 35

The sequence is defined recursively. Write the first four terms.

A)
B)
C)
D)

Question 36

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.

A)
B)
C)
D)n(n + 3)

Question 37

The sequence is defined recursively. Write the first four terms.

A)
B)
C)
D)

Question 38

Write the word or phrase that best completes each statement or answers the question.
Karen has a balance of $1000 on a department store credit card that charges 1.5% interest per month onany unpaid balance. She can afford to pay $150 toward the balance each month. Her balance each month,after making a $150 payment, is given by the recursively defined sequence Determine Karenʹs balance after making the first payment. That is, determine

Question 39

Write the word or phrase that best completes each statement or answers the question.
A wildlife refuge currently has 100 deer in it. A local wildlife society decides to add an additional 2 deereach month. It is already known that the deer population is growing 12% per year. The size of thepopulation is given by the recursively defined sequence How many deer are in the wildlife refuge at the end of the second month? That is, what is

Question 40

The sequence is defined recursively. Write the first four terms.

A)
B)a
C)
D)

Question 41

Write out the sum.

A)1 + 3 + 5 + ... + (2n - 1)
B)3 + 5 + 7 + ... + (2n - 1)
C)1 + 3 + 5 + ... + (2n + 1)
D)3 + 5 +7+ ... + (2n + 1)

Question 42

Express the sum using summation notation.

A)
B)
C)
D)

Question 43

Express the sum using summation notation.

A)
B)
C)
D)

Question 44

Write out the sum.

A)20 + 21 + 22 + ... + (n + 19)
B)n + 19
C)19 + 20 + 21 + ... + (n + 19)
D)1 + 2 + 3 + ... + n

Question 45

Express the sum using summation notation.
3 + 6 + 9 + ... + 21

A)
B)
C)
D)

Question 46

Write the word or phrase that best completes each statement or answers the question.
Maria deposited $1500 in an independent retirement account at her bank. She earns 0.5% interest permonth on the balance. Each month, she deposits $100 in the account. Her balance each month after makinga $100 deposit, is given by the recursively defined sequence If she made the initial deposit on September 30, and makes each monthly deposit on the last day of the monhow much money will be in the account at the end of the year for Maria to count as a deduction for that yeafederal income taxes? That is, determine

Question 47

Express the sum using summation notation.

A)
B)
C)
D)

Question 48

Write out the sum.

A)
B)
C)
D)

Question 49

Write out the sum.

A)
B)
C)3 + 12 + 27 + ... +
D)1 + 2 + 3 + ... + n

Question 50

Write out the sum.

A)
B)
C)
D)0 + 1 + 2 + 3 + ... + n

Question 51

Express the sum using summation notation.

A)
B)
C)
D)

Question 52

Express the sum using summation notation.

A)
B)
C)
D)

Question 53

Write out the sum.

A)12 + 15 + 18 + ... + (3n + 9)
B)3n + 9
C)9 +12 + 15 + ... + (3n + 9)
D)1 + 2 + 3 + ... + n

Question 54

Express the sum using summation notation.

A)
B)
C)
D)

Question 55

Write out the sum.

A)
B)
C)0
D)

Question 56

Write the word or phrase that best completes each statement or answers the question.
Lexington Reservoir has 300 million gallons of water. About 0.07% of the water is lost to evaporation everyweek. About 150,000 gallons of water enter the reservoir every week. The amount of water in the reservoirat the end of each week is given by the recursively defined sequence Determine the amount of water in the reservoir at the beginning of the second week. That is, determine

Question 57

Express the sum using summation notation.
3 + 12 + 27 + . . . + 108

A)
B)
C)
D)

Question 58

Express the sum using summation notation.

A)
B)
C)
D)

Question 59

Express the sum using summation notation.

A)
B)
C)
D)

Question 60

Find the sum of the sequence.

A)84
B)7
C)12
D)5

Question 61

Find the sum of the sequence.

A)26
B)15
C)0
D)-12

Question 62

Find the sum of the sequence.

A)30
B)18
C)14
D)20

Question 63

Determine whether the sequence is arithmetic.
1, 4, 7, 10, 13, ...

A)Arithmetic
B)Not arithmetic

Question 64

Find the sum of the sequence.

A)384
B)53
C)272
D)400

Question 65

An arithmetic sequence is given. Find the common difference and write out the first four terms.
{5n + 8}

A)d = 5; 13, 18, 23, 28
B)d = 5; 5, 13, 18, 23
C)d = 8; 13, 18, 23, 28
D)d = 8; 5, 13, 18, 23

Question 66

Find the sum of the sequence.

A)176
B)56
C)88
D)120

Question 67

Find the sum of the sequence.

A)
B)
C)
D)

Question 68

An arithmetic sequence is given. Find the common difference and write out the first four terms.
{8 - 4n}

A)d = -4; 4, 0, -4, -8
B)d = -4; -4, -8, -12, -16
C)d = 4; 4, 8 , 12 , 16
D)d = -4; 4, 2 , -2 , -6

Question 69

Determine whether the sequence is arithmetic.
5, -15, 45, -135, 405, ...

A)Arithmetic
B)Not arithmetic

Question 70

Find the sum of the sequence.

A)64
B)54
C)66
D)34

Question 71

An arithmetic sequence is given. Find the common difference and write out the first four terms.

A)
B)
C)
D)

Question 72

Find the sum of the sequence.

A)-10
B)-4
C)-3
D)-12

Question 73

Find the sum of the sequence.

A)20
B)6
C)8
D)14

Question 74

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference,
d, are given.

A)
B)
C)
D)

Question 75

Determine whether the sequence is arithmetic.
2, 4, 6, 10, 12, ...

A)Arithmetic
B)Not arithmetic

Question 76

Determine whether the sequence is arithmetic.
4, 12, 36, 108, 972, ...

A)Arithmetic
B)Not arithmetic

Question 77

Find the sum of the sequence.

A)-8
B)40
C)-40
D)256

Question 78

Determine whether the sequence is arithmetic.
2, -1, -4, -7, -10, ...

A)Arithmetic
B)Not arithmetic

Question 79

Find the sum of the sequence.

A)101
B)110
C)68
D)42

Question 80

Determine whether the sequence is arithmetic.
2, -3, -8, -13, -18, ...

A)Arithmetic
B)Not arithmetic