Free Printable Arithmetic Sequences

1.

Find the common difference: 29, 21, 13, 5, ...

a)

d = -10

b)

d = -9

c)

d = -8

d)

d = -7

2.

Find the common difference: 1, 201, 401, 601, ...

a)

d = 100

b)

d = 101

c)

d = 200

d)

d = 201

3.

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

a)

-1, 7, 15

b)

-5, 2, 9

c)

3, 12, 21

d)

-65, -73, -81

4.

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

5.

What is a₁ in the following sequence?

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

a)

-6

b)

-14

c)

-22

d)

-30

6.

What is the common difference of the following sequence?

7, 27, 47, 67,...

a)

10

b)

20

c)

3

d)

-20

7.

Is the sequence arithmetic?

17, 9, 1, -7, ...

a)

Yes

b)

No

8.

Is the sequence arithmetic?

78, 785, 7855, 78555, ...

a)

Yes

b)

No

9.

Define arithmetic sequences.

a)

A sequence whose terms change by adding the same number each time.

b)

A sequence whose terms change by multiplying the same number each time.

c)

A sequence whose terms change by dividing the same number each time.

d)

A list of numbers that often (but not always) form a pattern.

10.

Define common difference.

a)

the product between two consecutive terms of a geometric sequence.

b)

the product between two consecutive terms of an arithmetic sequence.

c)

the difference between two consecutive terms of an arithmetic sequence.

d)

the difference between two consecutive terms of a geometric sequence.

11.

A sequence is shown below.

32, 26, 20, 14, ...

Which explicit formula can be used to determine the nth term of the sequence?

a)

a_n = -6n + 38

b)

a_n = 6n + 32

c)

a_n = 6n + 38

d)

a_n = -6n + 32

12.

The 5th, 6th, and 7th terms of an arithmetic sequence are shown below.

-10, -7, -4, ...

Which is an explicit formula for this sequence?

a)

f(n) = -3n - 19

b)

f(n) = -3n - 25

c)

f(n) = 3n - 25

d)

f(n) = 3n - 19

13.

A sequence is shown below.

-20, -17, -14, -11, -8, ...

Which explicit equation can be used to determine the value of the nth term in the sequence?

a)

a_n = n + 3

b)

a_n = 3n + 23

c)

a_n = n - 23

d)

a_n = 3n - 23

14.

An arithmetic sequence has these properties:

a₁ = 2

a_n = a_(n-1) + 5

What are the first four terms of the sequence?

a)

2, 5, 10, 15

b)

2, 5, 7, 12

c)

2, 7, 9, 14

d)

2, 7, 12, 17

15.

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence.

a)

a_n = 25 + 4(n-1)

b)

a_n = 25 + 21(n-1)

c)

a_n= 25 - 4(n-1)

d)

a_n = 13 + 4(n-1)

16.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

17.

Find the first term of the given sequence:
a₁₄=68
d=3

a)

14

b)

20

c)

26

d)

29

18.

Identify the common difference.
3, 7, 11, 15, ...

a)

6

b)

5

c)

4

d)

2

19.

Find the 32nd term of this sequence.
34, 37, 40, 43, ...

a)

32

b)

64

c)

127

d)

356

20.

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence. (Hint: Simplify your equation.)

a)

a_n = 4n + 29

b)

a_n = -4n + 25

c)

a_n= -4n + 29

d)

a_n = 4n + 25

21.

Is the sequence arithmetic: 17, 9, 1, -7, ...

a)

Yes

b)

No

22.

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

a)

-10

b)

-9

c)

-8

d)

-7

23.

Find a₂₀ in the arithmetic sequence: 5, 12, 19, 26...

a)

145

b)

144

c)

142

d)

138

24.

Write the recursive rule for the arithmetic sequence
82, 76, 70, 64, ...

a)

a₁=82; a_n = a_n-1-6

b)

a₁=64; a_n = a_n-1-6

c)

a₁=82; a_n = a_n-1+6

d)

a₁=64; a_n = a_n-1+6

25.

Identify a₁ and d for the sequence
-5, -2, 1, 4, ...

a)

a₁ = 3 and d = -5

b)

a₁= -8 and d = 3

c)

a₁ = -5 and d = 3

d)

a₁ = -5 and d = -3

26.

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

27.

Given the recursive formula below, find the explicit formula.
a₀= 1
a_n = a_n-1 + 5

a)

a_n= 6 + 5n

b)

a_n = 1 + 5n

28.

Given the recursive formula below, find the explicit formula.
a₁= 5
a_n = a_n-1 - 6

a)

a_n = 5 - 6n

b)

a_n = 11 - 6n

29.

Given the explicit equation below, write the linear equation.
u_n = 7 - 3n

a)

y = 7 - 3x

b)

y = 10 - 3x

30.

How does a linear equation relate to the explicit formula?

a)

the slope is the common difference

b)

the y-intercept is the common difference

c)

the two are not related

d)

the slope is u₁

31.

Convert to explicit form.

a_n = a_n-1 + 4; a₁ = 5

a)

f(n) = 4 + 5(n - 1)

b)

f(n) = 5 ⋅ (4)^{n - 1}

c)

f(n) = 5 + 4n

d)

f(n) = 5 + 4(n - 1)

32.

Identify a₁ and d for the sequence
-5, -2, 1, 4, ...

a)

a₁ = 3 and d = -5

b)

a₁= -8 and d = 3

c)

a₁ = -5 and d = 3

d)

a₁ = -5 and d = -3

33.

What does $f\left(n-1\right)$ mean?

a)

previous term

b)

first term

c)

common difference

d)

the sequence contains only negative numbers

34.

What does $f\left(1\right)$ mean?

a)

one

b)

first term

c)

common difference

d)

the sequence starts with the value 1

35.

3, 15, 75, ... is an arithmetic sequence

a)

True

b)

False

36.

Which is a *recursive rule* for the nth term in the sequence 15, 8, 1, ...?

a)

$a_1=15,\ a_n=a_{n-1}-7$

b)

$a_n=15-7\left(n-1\right)$

c)

$a_1=-7,\ a_n=a_{n-1}+15$

d)

$a_n=-7+15\left(n-1\right)$

37.

Write the recursive rule for the arithmetic sequence
82, 76, 70, 64, ...

a)

a₁=82; a_n = a_n-1-6

b)

a₁=64; a_n = a_n-1-6

c)

a₁=82; a_n = a_n-1+6

d)

a₁=64; a_n = a_n-1+6

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.

Create the explicit formula for the sequence:

2, 8, 14, ...

a)

y=2+6x

b)

y=-6+6x

c)

y=6x-4

d)

y=4-6x

40.

Find the common difference: -18, -23, -28, -33, ...

a)

d = -5

b)

d = 5

c)

d = -3

d)

d = 3

41.

Is the sequence arithmetic: 17, 9, 1, -7, ...

a)

Yes

b)

No

42.

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

a)

-1, 7, 15

b)

-5, 2, 9

c)

3, 12, 21

d)

-65, -73, -81

43.

Find a₂₆ in the arithmetic sequence: -15, -35, -55, -75, ...

a)

-515

b)

-490

c)

-535

d)

460

44.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

45.

An arithmetic sequence is given below.

2, 9, 16, 23, ...

Which is the explicit formula for the n^th term a_n?

a)

a_n= -7n+9

b)

a_n= 7n-5

c)

a_n= 7n-9

d)

a_n= -7n+5

46.

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

a)

18

b)

17

c)

15

d)

14

47.

Find the explicit formula:
-23, -16, -9, -2, ...

a)

a_n = -23 + 7(n -1)

b)

a_n = -23 - 7(n -1)

c)

a_n = 7 - 23(n -1)

d)

a_n = 7 + 23(n -1)

48.

Find the explicit formula:
-3, -33, -63, -93, ...

a)

a_n = -3 - 30(n -1)

b)

a_n = -3 + 30(n -1)

c)

a_n = -30 - 3(n -1)

d)

a_n = -30 + 3(n -1)

49.

Which of the following recursive formulas represents the given sequence.

4, 12, 20, 28, 36, ...

a)

$a_1=4$ , $a_n=a_{\left(n-1\right)}\cdot3$

b)

$a_1=4$ , $a_n=a_{\left(n-1\right)}+8$

c)

$a_1=4$ , $a_n=a_{\left(n-1\right)}-8$

d)

undefined , $a_n=a_{\left(n-1\right)}\cdot9$

50.

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

a)

155

b)

135

c)

132

d)

75

Arithmetic Sequences

Total questions: 50

Worksheet time: 4hrs 59mins

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