Deck 11: Miscellaneous Topics

Question 1

Hun puts $90 into a safety deposit box. Each month she puts in an additional $50. Find the size of her savings after 4 years.

A) $2,490
B) $1,135
C) $1,950
D) $4,805

Answer 1

$2,490

Question 2

For the given arithmetic sequence, find the sum of the specified number of terms. The first 20 terms of

Answer 2

610

Question 3

Each term of a(n) __________ sequence is found by adding the same number to the previous term.

Question 4

Find the sum: $\sum _ { k = 1 } ^ { 7 } \left( k ^ { 2 } - 4 \right)$

A) 0
B) 54
C) 45
D) 112

Question 5

For the given arithmetic sequence, find the sum of the specified number of terms. The first 17 terms of

Question 6

The first three terms of an arithmetic sequence are 9, 15, and 21. Find the $500 ^ { \text {th } }$ term.

A) 3,009
B) 7,071
C) 5,161
D) 3,003

Question 7

Find the $55 ^ { \text {th } }$ term of the arithmetic sequence with $a _ { 1 } = - 2$ and $d = 6$ .

A) 326
B) 460
C) 201
D) 322

Question 8

A(n) __________ is a function whose domain is the set of natural numbers.

Question 9

Insert two arithmetic means between 20 and 30 .

A) $\frac { 50 } { 3 } , \frac { 55 } { 3 }$
B) $\frac { 38 } { 3 } , \frac { 53 } { 3 }$
C) $\frac { 100 } { 9 } , \frac { 100 } { 7 }$
D) $\frac { 70 } { 3 } , \frac { 80 } { 3 }$

Question 10

Which of the following Greek letters is used for summation notation?

A) θ
B) $\sigma$
C) $\beta$
D) $\Sigma$

Question 11

A sequence with an unlimited number of terms is called a(n) __________ sequence.

Question 12

Find the sum.

Question 13

Find the first term of the arithmetic sequence with a common difference of if its 27th term is . __________

Question 14

The sum of the terms of an arithmetic sequence is called a(n) __________ series.

Question 15

In a grocery store, a display of cans of vegetables has 24 cans on the bottom row, 21 cans on the next row up, 18 cans on the next row up, and so on until there is 3 cans on the top row. At the end of the day, all cans in the top 6 rows have been sold. Exactly how many cans of vegetables are needed to restock the display?

A) 117
B) 176
C) 63
D) 41

Question 16

Find the sum of the first 35 terms of the sequence 2, 6, 10, 14, 18, . . .

A) 182
B) 2,450
C) 4,808
D) 2,760

Question 17

Select the sequence that is an arithmetic sequence.

A) $1,1,2,3,5,8 \ldots$
B) $3,9,27,81$
C) $0 , \frac { 3 } { 2 } , 3 , \frac { 9 } { 2 } , 6 , \ldots$
D) $3 , - 1,3 , - 1$

Question 18

If a single number is inserted between a and b to form an arithmetic sequence, the number is called the arithmetic __________ between a and b .

Question 19

Write the first 3 terms of the arithmetic sequence where $d = 6$ and sixth term is 22 .

A) $6,12,18 , \ldots$
B) $- 8 , - 2,4 , \ldots$
C) $10,16,22 , \ldots$
D) $4,10,16 ,$

Question 20

The formula for the sum of the first n terms of an arithmetic sequence is _______.

A) $\frac { n \left( a _ { 1 } - a _ { n } \right) } { 2 }$
B) $\frac { n \left( a _ { 1 } + a _ { n - 1 } \right) } { 2 }$
C) $a _ { 1 } + ( n - 1 ) d$
D) $\frac { n \left( a _ { 1 } + a _ { n } \right) } { 2 }$

Question 21

Write the series associated with the summation.

Question 22

Match each sum with the corresponding summation notation.

- $\sum _ { k = 5 } ^ { 9 } k ^ { 2 }$

A) $16 + 25 + 36 + 49 + 64$
B) $25 + 36 + 49 + 64 + 81$
C) $1 + 4 + 9 + 16 + 25 + 36$

Question 23

A sequence with a specific number of terms is called a(n) _________ sequence.

Question 24

Find the first term of the arithmetic sequence with a common difference of if its th term is .

Question 25

For the given arithmetic sequence, find the sum of the specified number of terms. The first 30 terms of

Question 26

Insert three arithmetic means between and .

Question 27

Write the first five terms of the arithmetic sequence with the given properties and find the specified term. Find the term.

Question 28

In the symbol , k is called the __________ of summation.

Question 29

Each term of a(n) __________ sequence is found by adding the same number to the previous term.

Question 30

Match each sum with the corresponding summation notation.

- $\sum _ { k = 4 } ^ { 8 } k ^ { 2 }$

A) $16 + 25 + 36 + 49 + 64$
B) $25 + 36 + 49 + 64 + 81$
C) $1 + 4 + 9 + 16 + 25 + 36$

Question 31

A sequence with an unlimited number of terms is called a(n) ___________ sequence.

Question 32

Write the first five terms of the arithmetic sequence with the given properties. The 6th term is 30.

Question 33

Match each sum with the corresponding summation notation.

- $\sum _ { k = 1 } ^ { 6 } k ^ { 2 }$

A) $16 + 25 + 36 + 49 + 64$
B) $25 + 36 + 49 + 64 + 81$
C) $1 + 4 + 9 + 16 + 25 + 36$

Question 34

Write the first five terms of the arithmetic sequence with the given properties and find the specified term. Find the 20th term.

Question 35

The sum of the terms of an arithmetic sequence is called an arithmetic ___________.

Question 36

Find the sum.

Question 37

Write the summation notation for the sum.

Question 38

If a single number is inserted between a and b to form a(n) __________ sequence, the number is called the arithmetic mean between a and b .

Question 39

For the given arithmetic sequence, find the sum of the specified number of terms. The first 17 terms of

Question 40

A(n) ___________ is a function whose domain is the set of natural numbers.

Question 41

Find the sum of the first seven terms of $64,32,16 , \ldots$

A) 124
B) 126
C) 127
D) 130

Question 42

Find the common ratio of the geometric sequence with a first term of 18 and a $7 ^ { \text {th } }$ term of $\frac { 2 } { 81 }$ .

A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 81 }$
C) $\frac { 1 } { 9 }$
D) $\frac { 1 } { 27 }$

Question 43

Find the $10 ^ { \text {th } }$ term of the geometric sequence with $a _ { 1 } = 243$ and $r = \frac { 1 } { 3 }$

A) $\frac { 1 } { 243 }$
B) $\frac { 1 } { 729 }$
C) $\frac { 1 } { 81 }$
D) $\frac { 1 } { 9 }$

Question 44

Write $0 . \overline { 4 }$ in fraction form.

A) $\frac { 2 } { 5 }$
B) $\frac { 4 } { 9 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 5 } { 11 }$

Question 45

Find the fourth term of a geometric sequence with a first term of and a common ratio of

A)
B)
C)
D)

Question 46

Find two geometric means between $\frac { 1 } { 32 }$ and $\frac { 1 } { 4 }$ .

A) 2 and 16
B) $\frac { 1 } { 2 }$ and $\frac { 1 } { 16 }$
C) 8 and 16
D) $\frac { 1 } { 8 }$ and $\frac { 1 } { 16 }$

Question 47

Write the first five terms of the arithmetic sequence with the given properties and find the specified term. Find the 20th term. = __________ = __________ = __________ = __________ = __________ = __________

Question 48

Insert three arithmetic means between and .

Question 49

Write the series associated with the summation. __________ + __________ + __________

Question 50

If an open barrel contains 60 gallons of a liquid, and each day $\frac { 1 } { 10 }$ of the barrel s contents evaporate. How many gallons are left in the barrel after 15 days?

A) 27.2 gallons
B) 35.4 gallons
C) 12.4 gallons
D) 10.8 gallons

Question 51

Find the sum of the infinite geometric series: $\frac { 5 } { 2 } + \frac { 1 } { 2 } + \frac { 1 } { 10 } + \frac { 1 } { 50 } + \ldots$

A) $\frac { 5 } { 2 }$
B) 3
C) sum is not possible
D) $\frac { 25 } { 8 }$

Question 52

Yasmeen puts $70 into a safety deposit box. After each succeeding month, she puts $30 more in the box. Write the first six terms of an arithmetic sequence that gives the monthly amounts in her savings. = $__________ = $__________ = $__________ = $__________ = $__________ = $__________ Find her savings after 10 years. $__________

Question 53

Yasmeen puts $ into a safety deposit box. After each succeeding month, she puts $ more in the box. Write the first six terms of an arithmetic sequence that gives the monthly amounts in her savings, and find her savings after years.

Question 54

Write the summation notation for

Question 55

Write the first five terms of the arithmetic sequence with the following properties. The 6th term is 32. __________ __________ __________ __________ __________

Question 56

Write the summation notation for .

Question 57

Write the first five terms of the arithmetic sequence with the given properties and find the specified term. Find the term. = __________ = __________ = __________ = __________ = __________ = __________

Question 58

A ball is dropped from a height of 3 feet. On each bounce, it returns to a height that is two-thirds of the distance it fell. Find the total vertical distance the ball travels.

A) 9 feet
B) 6 feet
C) 15 feet
D) 38 feet

Question 59

Find the sum of the infinite geometric series: $3 + \frac { 15 } { 4 } + \frac { 75 } { 16 } + \ldots$

A) $\frac { 7 } { 4 }$
B) 20
C) 50
D) no sum is possible

Question 60

Write the first 4 terms of the geometric sequence with $a _ { 1 } = \frac { 1 } { 5 }$ , $r > 0$ , $6 ^ { \text {th } }$ term is $\frac { 32 } { 5 }$ .

A) $\frac { 1 } { 5 } , \frac { 2 } { 5 } , \frac { 4 } { 5 } , \frac { 8 } { 5 }$
B) $\frac { 1 } { 5 } , \frac { - 2 } { 5 } , \frac { 4 } { 5 } , \frac { - 8 } { 5 }$
C) $\frac { 1 } { 5 } , \frac { 2 } { 5 } , 2 , \frac { 4 } { 5 }$
D) $\frac { 1 } { 5 } , \frac { - 2 } { 5 } , 2 , \frac { - 4 } { 5 }$

Question 61

Write the first five terms of each geometric sequence with the given properties and then find the specified term. First term: Common ratio: Find the 8th term.

Question 62

Find the positive geometric mean between 4 and 54 .

A) $\sqrt { 6 }$
B) 6
C) $- 16$
D) $6 \sqrt { 6 }$

Question 63

Find the sum of the infinite geometric series 1024 + 512 + 256 + …

Question 64

John has $10,000 in a safe deposit box. Each year, he spends 10% of what is left in the box. How much will be in the box after 16 years?
Please round the answer to the nearest cent. $__________

Question 65

Find the sum of the first terms of the geometric sequence.

Question 66

Write the first five terms of each geometric sequence with the given properties and then find the specified term. First term: 2 Common ratio: 3 Find the 9th term.

Question 67

Find the sum of each infinite geometric series, if possible. 72 + 24 + 8 + . . .

Question 68

Write $0 . \overline { 2 }$ as an infinite geometric series.

A) $22 + 2.2 + 2.22 + 2.222 + \ldots$
B) $0.2 + 0.02 + 0.002 + \ldots$
C) $0.2 + 0.22 + 0.222 + \ldots$
D) $0.02 + 0.002 + 0.002 + \ldots$

Question 69

Find the sum of each infinite geometric series, if possible. 64 + 32 + 16 + . . .

Question 70

8, 16, 32, 64, 128, . . . is an example of a geometric sequence. The first __________ is 8 and the common ratio is 2.

Question 71

If a single number is inserted between a and b to form a geometric sequence, the number is called the geometric __________ between a and b .

Question 72

8, 16, 32, 64, 128, . . . is an example of a __________ sequence. The first term is 8 and the common ratio is 2.

Question 73

Each term of a(n) __________ sequence is found by multiplying the previous term by the same number.

Question 74

The sum of the __________ of a geometric sequence is called a geometric series. The sum of the terms of an infinite geometric sequence is called an infinite geometric series.

Question 75

If a single number is inserted between a and b to form a geometric sequence, the number is called the geometric __________ between a and b .

Question 76

Each term of a(n) __________ sequence is found by multiplying the previous term by the same number.

Question 77

The sum of the terms of a geometric sequence is called a geometric __________ . The sum of the terms of an infinite geometric sequence is called an infinite geometric series.

Question 78

Find the common ratio of the geometric sequence with a first term and a sixth term .

Question 79

Write the first five terms of the geometric sequence with the given properties. The 4th term is .

Question 80

Find the tenth term of the geometric sequence with and .