Free Printable Unit 1: Sequences Review

1.

For the given arithmetic formula, find the value of the 8th term.

$a\left(n\right)=-2n+4$

(a)

2.

Determine the common difference of the arithmetic sequence.

Enter only the number (not d= )

-14, -8, -2, 4 ...

(a)

3.

Which formula represents the following arithmetic series?

6, 9, 12, 15, 18 . . .

a)

3+3(n-1)

b)

3n+5

c)

6+3(n-1)

d)

6+6(n-1)

4.

What is the first term in the given arithmetic sequence? Type in the value only.

(a)

5.

For the given arithmetic sequence, what is the common difference?

Type in the value only.

(a)

6.

Given the recursive arithmetic sequence, what is the common difference? Type in the value only.

$a\left(n\right)=a\left(n-1\right)-10;\ a\left(1\right)=21$

(a)

7.

Which formula represents the nth term formula for the sequence?

20, 15, 10, 5 . . .

a)

f(n)=-5(n-1)+25

b)

f(n)=20-5(n-1)

c)

f(n)=f(n-1)-5; f(1)=20

d)

a_n=a_n-1+20; a₁=-5

8.

It is a sequence wherein the terms are generated by adding a constant number called common difference.

a)

Arithmetic Sequence

b)

Fibonacci Sequence

c)

Geometric Sequence

d)

Harmonic Sequence

9.

Complete the Table.

a)

25, 32, 39, 46

b)

7, 32, 57, 82

c)

32, 39, 46, 53

d)

7, 14, 21, 28

10.

Which sequence(s) represent an arithmetic sequence?

a)

a and e

b)

a, b, and e

c)

b, c, and d

d)

b

11.

Write the explicit rule for this situation.

a)

f(n) = 35 + 3(n − 1)

b)

f(n) = 35 −3(n − 1)

c)

f(n) = 3 + 35(n − 1)

d)

f(n) = −3 + 35(n − 1)

12.

What is the 67^th term of the following arithmetic sequence.

13, 22, 31, 40, ...

a)

-445

b)

67

c)

625

d)

607

13.

What is the 76^th term of the following arithmetic sequence?

8, 14, 20, 26,...

a)

76

b)

452

c)

458

d)

476

14.

What is a₁ in the following sequence?

-6, -14, -22, -30, ...

a)

-6

b)

-14

c)

-22

d)

-30

15.

Find the pattern: 29, 21, 13, 5, ...

a)

-10

b)

-9

c)

-8

d)

-7

16.

Find the common ratio for the geometric sequence.

a)

2

b)

-2

c)

1/2

d)

-1/2

17.

Write the explicit formula for the geometric sequence.

a)

g(n) = 10(2)^n-1

b)

g(n) = 2(10)^n-1

c)

g(n) = 10(2)ⁿ

d)

g(n) = 2(10)ⁿ

18.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

19.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

20.

Find the common ratio: 64, -16, 4, -1, ...

a)

r = -8

b)

r = -1/4

c)

r = -4

d)

r = 4

21.

Find the common ratio: 4, -16, 64, -256, ...

a)

r = -4

b)

r = 2

c)

r = -2

d)

r = 4

22.

Write the explicit formula for the geometric sequence.

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

23.

What is the 14th term of the geometric sequence?

a)

14,348,907

b)

4,782,969

c)

1,594,323

d)

45

24.

What is the explicit formula for the sequence?

4, -20, 100, -500, ...

a)

$a_n=4\left(2\right)^{n-1}$

b)

$a_n=4\left(-5\right)^{n-1}$

c)

$a_n=3\left(-5\right)^{n-1}$

d)

$a_n=3\left(2\right)^{n-1}$

25.

What is the explicit formula for the sequence?

-1, 2, -4, 8, ...

a)

$a_n=-\frac{1}{2}\left(2\right)^{n-1}$

b)

$a_n=-\frac{1}{4}\left(2\right)^{n-1}$

c)

$a_n=-2\left(-\frac{1}{2}\right)^{n-1}$

d)

$a_n=-\left(-2\right)^{n-1}$

26.

What is the 6th term in the sequence 2,4,8,...?

a)

32

b)

64

c)

128

d)

256

27.

If the pattern continues in the same way, how many circles will be in the seventh term?

a)

21

b)

25

c)

28

d)

36

28.

What is the position for the last figure in the picture?

a)

2

b)

3

c)

4

d)

5

29.

What do we call this sequence: 1, 31, 61, 91,...

a)

Arithmetic Sequence

b)

Geometric Sequence

c)

Square Number Sequence

d)

Cube Number Sequence

30.

Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...

a)

63, 72, 81

b)

79, 88, 97

c)

70, 79, 88

d)

61, 70, 79

31.

Who is the Political Head of Municipality and Gram Panchayat?

a)

Mayor and Sarpanch

b)

Deputy Collector and Mayor

c)

Sarpanch and Deputy Collector

d)

Mayor and Chief Minister

32.

What do $a_{n-1}$ in subscript notation and $f\left(n-1\right)$ in function notation both mean?

a)

previous term

b)

first term

c)

common difference

d)

the sequence contains only negative numbers

33.

What do $a_n$ in subscript notation and $f\left(n\right)$ in function notation both mean?

a)

the final term in the sequence

b)

first term

c)

Nth term, where n>1

d)

previous term

34.

What do $a_1$ in subscript notation and $f\left(1\right)$ in function notation both mean?

a)

steak sauce

b)

first term

c)

common difference

d)

the sequence starts with the value 1

35.

Sometimes sequences are described in subscript notation.

Given $T\left(1\right)=-5$ and $T\left(n\right)=T\left(n-1\right)+3$ , what are the first 4 terms in the sequence?

a)

-5, -2, 1, 4

b)

-5, -8, -11, -14

c)

3, -2, -7, -12

d)

3, -15, 75, -375

36.

Sometimes sequences are described in function notation.

Given $f\left(1\right)=-32$ and $f\left(n\right)=f\left(n-1\right)+4$ , what are the first 4 terms in the sequence?

a)

4, -28, -60, -92

b)

-32, -36, -40, -44

c)

-32, -28, -24, -20

d)

-28, -24, -20, -16

37.

Sometimes sequences are described in function notation.

Given $f\left(1\right)=5.5$ and $f\left(n\right)=f\left(n-1\right)-0.5$ , what are the first 4 terms in the sequence?

a)

5.5, 6, 6.5, 7

b)

5.5, 2.75, 1.375, 0.6875

c)

-0.5, 5, 10.5, 16

d)

5.5, 5, 4.5, 4

38.

Given the sequence -5, -15, -25, -35..., which recursive formula describes it?

a)

$f\left(1\right)=-5$

$f\left(n\right)=f\left(n-1\right)-10$

b)

$f\left(1\right)=-5$

$f\left(n\right)=f\left(n-1\right)+10$

c)

$f\left(-5\right)=1$

$f\left(n\right)=f\left(-5\right)-10$

39.

Given the sequence 11, 15, 19, 23..., which recursive formula describes it?

a)

$f\left(1\right)=11$

$f\left(n\right)=f\left(n-1\right)+5$

b)

$f\left(1\right)=11$

$f\left(n\right)=f\left(n-1\right)+4$

c)

$f\left(11\right)=1$

$f\left(n\right)=f\left(11\right)+4$

40.

Find the next three terms:
5, 8, 11, 14...

a)

16, 19, 22

b)

17, 19, 21

c)

17, 20, 23

d)

16, 18, 20

41.

What is the next term in the series? 15, 35, 55...

a)

55

b)

15

c)

32

d)

75

42.

What is the 7th term in the series? 15, 35, 55...

a)

155

b)

135

c)

132

d)

75

43.

List the next three terms of the following sequence:
10, 13, 16, .....

a)

20, 25, 31, .....

b)

18, 20, 22, .....

c)

19, 22, 25, ...

d)

22, 25, 28, ......

44.

Identify the common difference.

-6, -3, 0, 3, 6....

a)

d=4

b)

d=3

c)

d=-4

d)

d=-3

45.

The 6th term of the sequence 4,7,10,13 are

a)

19

b)

15

c)

18

d)

16

46.

The next two terms of the sequence 2,-4, 8,-16 are

a)

32, 64

b)

32, -64

c)

-64, 108

d)

32, 20

47.

The sequence 3, 6, 9, 12... is:

a)

Arithmetic

b)

Geometric

c)

Recursive

d)

Explicit

48.

The sequence 6, 18, 54...

a)

Arithmetic

b)

Geometric

c)

Explicit

d)

Recursive

49.

Find the common ratio: 64, -16, 4, -1, ...

a)

r = -8

b)

r = -1/4

c)

r = -4

d)

r = 4

50.

Given the sequence 4, 11, 18, 25...... what is a₃ ?

a)

4

b)

11

c)

18

d)

25

51.

What is the 15th term of the sequence an = -3n+50

a)

95

b)

-5

c)

5

d)

-95

52.

$f\left(n\right)=\ \ 24\ \left(\frac{1}{2}\right)^{\left(n-1\right)}$ Given the explicit formula, find the 3rd term

a)

6

b)

12

c)

3

d)

1.5

53.

If f(x) = 2x + 1, find f(1).

a)

f(1) = 1

b)

f(1) = 4

c)

f(1) = 0

d)

f(1) = 3

54.

Evaluate f(-2) if f(x) = x + 3

a)

-1

b)

1

c)

5

d)

-5

55.

For the function f(x) = -3(x-1) find f(0).

a)

0

b)

-3

c)

3

d)

-1

56.

Given f(x) = -4x - 10 and f(x) = 10. Find x

a)

x = -5

b)

x = 5

c)

x = -50

d)

x = 30

57.

Given f(x) = -4x - 10 and f(x) = 10. Find x

a)

x = -5

b)

x = 5

c)

x = -50

d)

x = 30

58.

Write a recursive formula for the following sequence:

10, 5, 0, -5,...

a)

_{f(1)= 10}

f(n)= f(n-1) - 5

b)

f(1)= 10

f(n)= f(n-1)+ 5

c)

f(1)= 10

f(n)= f(n )(5)

d)

f(1)= 10

f(n)= f(n-1) (5)

59.

If f(x) = 2x + 1, what would be your first step to find f(1)?

a)

Plug a 1 in for all the x's

b)

Set the function equal to 1

c)

Only plug a 1 into the left side

d)

Only plug a 1 into the right side

60.

If f(x) = 2x + 1, find f(1).

a)

f(1) = 1

b)

f(1) = 4

c)

f(1) = 0

d)

f(1) = 3

61.

Evaluate f(-2) if f(x) = x + 3

a)

-1

b)

1

c)

5

d)

-5

62.

For the function f(x) = -3(x-1) find f(0).

a)

0

b)

-3

c)

3

d)

-1

63.

Given f(x) = -4x - 10 and f(x) = 10. Find x

a)

x = -5

b)

x = 5

c)

x = -50

d)

x = 30

64.

If f(x) = -3x - 8, find f(-1).

a)

f(-1) = 5

b)

f(-1) = -5

c)

f(-1) = -12

d)

f(-1) = -10

65.

Given f(x) = x² - 3 + 2x, find f(6).

a)

45

b)

21

c)

33

d)

17

66.

a)

i

b)

ii

c)

iii

d)

iv

67.

a)

i

b)

ii

c)

iii

d)

iv

68.

a)

i

b)

ii

c)

iii

d)

iv

69.

a)

i

b)

ii

c)

iii

d)

iv

70.

(a)

71.

(a)

72.

Determine T₂₀ with the given:

D = 7, and T₁ = 5

T₂₀ = (a)

73.

Determine T₃₀ with the given:

D = 7, and T₁ = 5

T₃₀ = (a)

74.

Determine T₄₀ with the given:

D = 7, and T₁ = 5

T₄₀ = (a)

75.

Determine T₅₀ with the given:

D = 7, and T₁ = 5

T₅₀ = (a)

76.

Determine T₆₀ with the given:

D = 7, and T₁ = 5

T₆₀ = (a)

77.

Determine T₂₀ with the given:

D = 5, and T₁ = 7

T₂₀ = (a)

78.

Determine T₃₀ with the given:

D = 5, and T₁ = 7

T₃₀ = (a)

79.

Determine T₅₀ with the given:

D = 5, and T₁ = 7

T₅₀ = (a)

80.

Determine T₆₀ with the given:

D = 5, and T₁ = 7

T₆₀ = (a)

81.

a)

i

b)

ii

c)

iii

d)

iv

82.

a)

i

b)

ii

c)

iii

d)

iv

83.

a)

i

b)

ii

c)

iii

d)

iv

84.

a)

i

b)

ii

c)

iii

d)

iv

85.

a)

i

b)

ii

c)

iii

d)

iv

86.

(a)

87.

(a)

88.

Given T₁ = 2 and R = 8

Find T₆?

T₆ = (a)

89.

Given T₁ = 3 and R = 7

Find T₆?

T₆ = (a)

90.

Given T₁ = 4 and R = 6

Find T₆?

T₆ = (a)

91.

Given T₁ = 6 and R = 4

Find T₈?

T₈ = (a)

92.

Given T₁ = 7 and R = 3

Find T₈?

T₈ = (a)

93.

Given T(1) = 8 and r = 2

Find T(8)?

T(8) = (a)

94.

Given a sequence {1, 5, 25, 125, ...}

Determine the common ratio r?

r = (a)

95.

Given a sequence {5, 15, 45, 135, ...}

Determine the common ratio r?

r = (a)

96.

Given a sequence {9, 54, 324, 1944, ...}

Determine the common ratio r?

r = (a)

97.

Given a sequence {7, 56, 448, 3584, ...}

Determine the common ratio r?

r = (a)

98.

Create the explicit formula for the sequence:
5, 9, 13, ...
Do not simplify

a)

a_n=1+(n-1)4

b)

a_n=4+(n-1)5

c)

a_n=5+(n-1)4

d)

a_n=9+(n-1)4

99.

Create the explicit formula for the sequence:
15, 9, 3, ...
Do not simplify

a)

a_n=15+(n-1)6

b)

a_n=21+(n-1)(-6)

c)

a_n=15+(n-1)(-6)

d)

a_n=9+(n-1)6

100.

Create the explicit formula for the sequence:
12, 19, 26, ...
Do not simplify

a)

a_n=5+(n-1)7

b)

a_n=12+(n-1)5

c)

a_n=12+(n-1)7

d)

a_n=5+(n-1)12

101.

Create the explicit formula for the sequence:
7, 9, 11, ...
Do not simplify

a)

a_n=7+(n-1)4

b)

a_n=2+(n-1)7

c)

a_n=7+(n-1)2

d)

a_n=9+(n-1)2

102.

Create the explicit formula for the sequence:
20, 29, 38, ...
Do not simplify

a)

a_n=9+(n-1)11

b)

a_n=11+(n-1)9

c)

a_n=20+(n-1)9

d)

a_n=9+(n-1)20

103.

Create the explicit formula for the sequence:
-3, 8, 19, ...
(Hint: Write your formula and then simplify it.)

a)

a_n=11-3n

b)

a_n=-6+11n

c)

a_n=11n-14

d)

a_n=12-3n

104.

Create the explicit formula for the sequence:
25, 38, 51, ...
(Hint: Write your formula and then simplify it.)

a)

a_n=12+3n

b)

a_n=25+13n

c)

a_n=13n+12

d)

a_n=12-5n

105.

Given the sequence:
25, 18, 11, 4,...
Write the explicit equation that models the sequence. (Hint: Simplify your equation.)

a)

a_n = 7n + 32

b)

a_n = -7n + 25

c)

a_n= -7n + 32

d)

a_n = 7n + 25

106.

Given the sequence:
-25, -20, -15, -10,...
Write the explicit equation that models the sequence. (Hint: Simplify your equation.)

a)

a_n = 5n - 25

b)

a_n = -5n - 25

c)

a_n= 5n -30

d)

a_n = 5n - 25

107.

Find the next three terms:
5, 8, 11, 14...

a)

16, 19, 22

b)

17, 19, 21

c)

17, 20, 23

d)

16, 18, 20

108.

What is the next term in the series? 15, 35, 55...

a)

55

b)

15

c)

32

d)

75

109.

What is the 7th term in the series? 15, 35, 55...

a)

155

b)

135

c)

132

d)

75

110.

What is the common difference of the sequence below?

6, 9, 12, 15, ...

Hint: Common difference means the ADDING pattern

a)

3

b)

6

c)

9

d)

12

111.

Using the formula $a_n=a_1+d\left(n-1\right)$ , where $a_1$ represents the first term and $d$ represents the common difference, write a formula for the sequence 18, 16, 14, 12, 10, 8, ...

a)

$a_n=18+2\left(n-1\right)$

b)

$a_n=18-2\left(n-1\right)$

c)

$a_n=2+18\left(n-1\right)$

d)

$a_n=-2+18\left(n-1\right)$

112.

We have a sequence represented by the formula $a_n=20+5\left(n-1\right)$ . What is the 200th term?

Hint: The variable n represents term number. So here, n = 200.

Second Hint: Put in your calculator 20+5(200-1).

a)

200

b)

450

c)

1,015

d)

2,475

113.

Write an explicit formula for the sequence 45, 40, 35, 30, ...

Hint: The sequence is arithmetic so use this formula: $a_n=a_1+d\left(n-1\right)$ .

a)

$a_n=45+5\left(n-1\right)$

b)

$a_n=45-5\left(n-1\right)$

c)

$a_n=5+45\left(n-1\right)$

d)

$a_n=5-45\left(n-1\right)$

114.

Write an explicit formula for the sequence 1.5, 2.0, 2.5, 3.0, ...

Hint: The sequence is arithmetic so use this formula: $a_n=a_1+d\left(n-1\right)$ .

a)

$a_n=1.5+0.5\left(n-1\right)$

b)

$a_n=1.5-0.5\left(n-1\right)$

c)

$a_n=0.5+1.5\left(n-1\right)$

d)

$a_n=0.5-1.5\left(n-1\right)$

115.

Write an explicit formula for the sequence -9, -7, -5, -3, ...

Hint: The sequence is arithmetic so use this formula: $a_n=a_1+d\left(n-1\right)$ .

a)

$a_n=-9+2\left(n-1\right)$

b)

$a_n=-9-2\left(n-1\right)$

c)

$a_n=2-9\left(n-1\right)$

d)

$a_n=-2-9\left(n-1\right)$

116.

Arithmetic sequences form a linear equation.

Geometric sequences form an exponential equation.

Given the geometric sequence 2, 6, 18, ..., write an explicit formula.

a)

$a_n=6\left(2\right)^{n-1}$

b)

$a_n=2\left(6\right)^{n-1}$

c)

$a_n=3\left(2\right)^{n-1}$

d)

$a_n=2\left(3\right)^{n-1}$

117.

Given the geometric sequence 1, 5, 25, 125, ..., write an explicit formula.

Hint: The formula needed is $a_n=a_1\left(r\right)^{n-1}$ .

a)

$a_n=1\left(5\right)^{n-1}$

b)

$a_n=5\left(5\right)^{n-1}$

c)

$a_n=5\left(1\right)^{n-1}$

d)

$a_n=1\left(1\right)^{n-1}$

118.

Given the geometric sequence 64, 16, 4, 1, ..., write an explicit formula.

Hint: The formula needed is $a_n=a_1\left(r\right)^{n-1}$ .

Second Hint: Similar to arithmetic sequences representing both adding AND subtracting patterns (because subtracting IS adding a negative)... geometric sequences represent both multiplying AND dividing patterns. Dividing is just multiplying by a reciprocal.

a)

$a_n=64\left(4\right)^{n-1}$

b)

$a_n=4\left(64\right)^{n-1}$

c)

$a_n=64\left(\frac{1}{4}\right)^{n-1}$

d)

$a_n=\frac{1}{4}\left(64\right)^{n-1}$

119.

Given the geometric sequence 80, 40, 20, 10, ..., write an explicit formula.

Hint: The formula needed is $a_n=a_1\left(r\right)^{n-1}$ .

a)

$a_n=80\left(\frac{1}{2}\right)^{n-1}$

b)

$a_n=\frac{1}{2}\left(80\right)^{n-1}$

c)

$a_n=80\left(2\right)^{n-1}$

d)

$a_n=2\left(80\right)^{n-1}$

120.

What is the fifth term for the sequence below?

$a_n=5\left(2\right)^{n-1}$

Hint: Use your calculator and replace n with 5.

a)

a₅ = 160

b)

a₅ = 40

c)

a₅ = 10

d)

a₅ = 80

121.

What is the 8th term in the geometric sequence below?

3, 9, 27, 81, ...

a)

19,683

b)

6,561

c)

2,187

d)

729

122.

Which of the following best describes this sequence?

\left\{135,\ 45,\ 15,\ 5,\ ...\right\}

a)

An arithmetic sequence with a common ratio of $\frac{1}{3}$

b)

A geometric sequence with a common difference of 3.

c)

An arithmetic sequence with a common difference of 3.

d)

A geometric sequence with a common ratio of $\frac{1}{3}$

123.

Which of the following best describes this sequence?

\left\{5,\ 8,\ 11,\ 14,\ ...\right\}

a)

An arithmetic sequence with a common ratio of 3.

b)

A geometric sequence with a common difference of 3.

c)

An arithmetic sequence with a common difference of 3.

d)

A geometric sequence with a common ratio of 3.

124.

What do $a_{n-1}$ in subscript notation and $f\left(n-1\right)$ in function notation both mean?

a)

previous term

b)

first term

c)

common difference

d)

the sequence contains only negative numbers

125.

Sometimes sequences are described in function notation.

Given $f\left(1\right)=5.5$ and $f\left(n\right)=f\left(n-1\right)-0.5$ , what are the first 4 terms in the sequence?

a)

5.5, 6, 6.5, 7

b)

5.5, 2.75, 1.375, 0.6875

c)

-0.5, 5, 10.5, 16

d)

5.5, 5, 4.5, 4

126.

Given the sequence -5, -15, -25, -35..., which recursive formula describes it?

a)

$f\left(1\right)=-5$

$f\left(n\right)=f\left(n-1\right)-10$

b)

$f\left(1\right)=-5$

$f\left(n\right)=f\left(n-1\right)+10$

c)

$f\left(-5\right)=1$

$f\left(n\right)=f\left(-5\right)-10$

127.

Given the sequence 11, 15, 19, 23..., which recursive formula describes it?

a)

$f\left(1\right)=11$

$f\left(n\right)=f\left(n-1\right)+5$

b)

$f\left(1\right)=11$

$f\left(n\right)=f\left(n-1\right)+4$

c)

$f\left(11\right)=1$

$f\left(n\right)=f\left(11\right)+4$

128.

Sometimes sequences are described in function notation.

Given $f\left(1\right)=-32$ and $f\left(n\right)=f\left(n-1\right)+4$ , what are the first 4 terms in the sequence?

a)

4, -28, -60, -92

b)

-32, -36, -40, -44

c)

answer not here

d)

-28, -24, -20, -16

129.

Determine if the following sequence is arithmetic or geometric.

6, 30, 150, 750, ...

a)

Arithmetic

b)

Geometric

130.

Identify whether the following sequence is Arithmetic or Geometric and identify the common ratio or difference:
97, 86, 75, 64, ...

a)

Arithmetic
Common Difference: 8

b)

Geometric
Common Ratio: -11

c)

Arithmetic
Common Difference: -11

d)

Geometric
Common Ratio: -8

131.

How is an arithmetic sequence found?

a)

By multiplying the same number to the previous term.

b)

By adding the same number to the previous term.

132.

How is an geometric sequence found?

a)

By adding the same number to the previous term.

b)

By multiplying the previous term by the same number.

Unit 1: Sequences Review

Total questions: 132

Worksheet time: 11hrs 0mins

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