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Worksheets

Arithmetic Sequences

Total questions: 81

Worksheet time: 6hrs 26mins

Name
Class
Date
1.

The 6th term of an arithmetic sequence is 6 and the 16th term is 14. What is the 27th term?

(a)  

2.

Find the 10th term of the arithmetic progression 1, 3.5, 6, 8.5,...

(a)  

3.

Do the numbers 2, 6, 10, 12, 16... form an arithmetic progression?


Please, answer yes or no

(a)  

4.

Let an be an arithmetic sequence. If a1 = 4 and a2 = 7, determine a11.


(Note: a1 is the first number in the sequence, so a1 = a)

(a)  

5.

Let an be an arithmetic sequence, for which d = 12 and a3 = 43. Find a1.

(a)  

6.

Let an be an arithmetic sequence, for which a1 = 15 and d = 3. Find the sum of the first 10 numbers in the sequence.

(a)  

7.

Let an be an arithmetic sequence. If a1 = 7 and d = 4, determine the sum of the first 6 numbers in the sequence.

(a)  

8.

Let an be an arithmetic sequence, for which the first term a1 = 1 and common difference d = 1. Find a1083

(a)  

9.

Common difference (d) of an arithmetic progression is 3 and find a20 - a15 = (a)  

10.

The first term of an arithmetic sequence is equal to 6 and the common difference is equal to 3. Find the value of the 50th term

(a)  

11.

An arithmetic sequence has a its 5th term equal to 22 and its 15th term equal to 62. Find its 100th term

(a)  

12.

Find a30 given that the first few terms of an arithmetic sequence are given by 6,12,18, ...

(a)  

13.

Find d given that a1 = 10 and a20 = 466

(a)  

14.

Find a20 given that a3 = 9 and a8 = 24

(a)  

15.

Show that the sequence 7, 11, 15, 19, 23, (a)   is an Arithmetic Sequence. Find its 27th term of the sequence

16.

Cab/Taxi Rental Rates after each km when the fare is $30 for the first km and raise by $12 for each additional km. What will be the charge after traveling of 50 km?

(a)  

17.

Donny put $800 into his son’s kiddy bank when he was one year old and increased the amount by $1000 every year. Find the amount of money in the kiddy bank on his 4th birthday

(a)  

18.

Find the value of n. If a = 10, d = 5, an = 95

(a)  

19.

Find the 20th term for the given Arithmetic Sequence:

3, 5, 7, 9, ….

(a)  

20.

The first term of an Arithmetic Sequence is p and its common difference is q. Find its 10th term of the sequence.

(a)  

21.

Which term of the arithmetic sequence below is equal to zero (0)

21, 18, 15, (a)  

22.

The 6th term of an arithmetic sequence is –10 and 10th term is –26. Determine the 15th term of sequence.

(a)  

23.

an arithmetic sequence consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find the 32nd term.

(a)  

24.

Which term of the sequence below is equal to 109?


4, 9, 14, 19, (a)  

25.

The taxi fare of the first kilometers is £15 and £8 for each additional km. How much cost is needed to pay for 25 km travelling by the taxi?

(a)  

26.
Find the 22nd term of the following sequence:
5, 8, 11, ...
a)
14
b)
68
c)
63
d)
71
27.
Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint:  Write your formula and then simplify it.)
a)
an=2+6n
b)
an=-6+6n
c)
an=6n-4
d)
an=4-6n
28.
Find the first term of the given sequence:
a14=68
d=3
a)
14
b)
20
c)
26
d)
29
29.
Identify the common difference.
97, 86, 75, 64, ...
a)
8
b)
11
c)
-11
d)
-8
30.
Identify the common difference.
3, 7, 11, 15, ...
a)
6
b)
5
c)
4
d)
2
31.
Find the 32nd term of this sequence.
34, 37, 40, 43, ...
a)
32
b)
64
c)
127
d)
356
32.
Find the 32nd term of this sequence.
9, 4, -1, -6, -11, ...
a)
81
b)
-34
c)
-146
d)
-225
33.
Find the 25th term of the sequence if a1 = 5 and d = 0.5
a)
18
b)
17
c)
15
d)
14
34.
Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.  (Hint:  Simplify your equation.)
a)
an = 4n + 29
b)
an = -4n + 25
c)
an = -4n + 29
d)
an = 4n + 25
35.
The next two terms of the sequence 4,7,10,13 are ....
a)
16 and 19
b)
15 and 19
c)
16 and 18
d)
15 and 18
36.
Is the sequence arithmetic: 78, 785, 7855, 78555, ...
a)
Yes
b)
No
37.
Is the sequence arithmetic: 17, 9, 1, -7, ...
a)
Yes
b)
No
38.
Is the sequence arithmetic: -3, 3, -3, 3, ...
a)
Yes
b)
No
39.

Find the pattern: -34, -29, -24, -19, ...

a)

-5

b)

+5

c)

-6

d)

+6

40.

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

a)

-10

b)

-9

c)

-8

d)

-7

41.

Find the pattern: -18, -23, -28, -33, ...

a)

-5

b)

+5

c)

-3

d)

3

42.

Find the pattern: 1, 201, 401, 601, ...

a)

+100

b)

+101

c)

+200

d)

+201

43.
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
44.
Find the next three terms in the arithmetic sequence: -3, -8, -13, -18, ...
a)
-20, -24, -28
b)
-21, -25, -29
c)
-23, -28, -33
d)
-24, -29, -32
45.
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
46.
Find the 35th term in the arithmetic sequence: -10, -14, -18, -22, ...
a)
-216
b)
-148
c)
-146
d)
-150
47.
Find 26th term in the arithmetic sequence: -15, -35, -55, -75, ...
a)
-515
b)
-490
c)
-535
d)
460
48.
Find the 26th term in the arithmetic sequence: 20, 26, 32, 38, ...
a)
182
b)
176
c)
170
d)
-118
49.

Find the 20th term in the arithmetic sequence: 5, 12, 19, 26...

a)

145

b)

144

c)

142

d)

138

50.

Find the 41st term in the arithmetic sequence: 230, 226, 222, 218 ...

a)

80

b)

155

c)

70

d)

125

51.

Find the 25th term of the sequence if the first term is 5 and the sequence is increasing by 12\frac{1}{2} .

a)

18

b)

17

c)

15

d)

14

52.

The pattern followed by the sequence 3, 6, 9, 12 is...

a)

+3

b)

+4

c)

-4

d)

+6

53.

The next term of the series 11, 8, 5, 2 are

a)

-1

b)

-2

c)

1

d)

2

54.
Find the 22nd term of the following sequence:
5, 8, 11, ...
a)
14
b)
68
c)
63
d)
71
55.

What are the first 4 terms of an arithmetic sequence with a pattern of -6 if the first term is 76?

a)

76, 70, 64, 58

b)

76, 82, 88, 94

c)

70, 64, 58, 52

d)

82, 88, 94, 100

56.
Is the sequence arithmetic: -3, 3, -3, 3, ...
a)
Yes
b)
No
57.
Is the sequence arithmetic: 17, 9, 1, -7, ...
a)
Yes
b)
No
58.
Find the common difference: -34, -29, -24, -19, ...
a)
d = -5
b)
d = 5
c)
d = -6
d)
d = 6
59.
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
60.
What is the distance from one number to the next in a sequence of numbers that is represented by a (d) in an arithmetic sequence?
a)
Common denominator
b)
Common opposites
c)
Common domain
d)
Common difference
61.
The next two terms of the sequence 4,7,10,13 are ....
a)
16 and 19
b)
15 and 19
c)
16 and 18
d)
15 and 18
62.
Identify the common difference. 
10, 20, 30, 40, ...
a)
5
b)
10
c)
15
d)
20
63.
Identify the common difference.
3, 7, 11, 15, ...
a)
6
b)
5
c)
4
d)
2
64.
Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.
a)
an = 4n + 29
b)
an = -4n + 25
c)
an = -4n + 29
d)
an = 4n + 25
65.
Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.  (Hint:  Simplify your equation.)
a)
an = 4n + 29
b)
an = -4n + 25
c)
an = -4n + 29
d)
an = 4n + 25
66.
Find the 22nd term of the following sequence:
5, 8, 11, ...
a)
14
b)
68
c)
63
d)
71
67.
Find the 32nd term of this sequence.
9, 4, -1, -6, -11, ...
a)
81
b)
-34
c)
-146
d)
-225
68.
Find the common difference: -34, -29, -24, -19, ...
a)
d = -5
b)
d = 5
c)
d = -6
d)
d = 6
69.
Find the common difference: 29, 21, 13, 5, ...
a)
d = -10
b)
d = -9
c)
d = -8
d)
d = -7
70.
Find the common difference: -18, -23, -28, -33, ...
a)
d = -5
b)
d = 5
c)
d = -3
d)
d = 3
71.
Find a20 in the arithmetic sequence: 5, 12, 19, 26...
a)
145
b)
144
c)
142
d)
138
72.
Identify the common difference.
97, 86, 75, 64, ...
a)
8
b)
11
c)
-11
d)
-8
73.
Is the sequence arithmetic: 37, 31, 25, 19, ...
a)
Yes
b)
No
74.
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
75.
Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.
a)
an = 4n + 29
b)
an = -4n + 25
c)
an = -4n + 29
d)
an = 4n + 25
76.
Given the recursive formula, find the first four terms:
an = an-1 + 5
a1 = -16
a)
-16, -21, -26, -31
b)
5, -11, -27, -43
c)
-16, -80, -500, -200
d)
-16, -11, -6, -1
77.
Find the 22nd term of the following sequence:
5, 8, 11, ...
a)
14
b)
68
c)
63
d)
71
78.
Identify the common difference.
3, 7, 11, 15, ...
a)
6
b)
5
c)
4
d)
2
79.
What is the rule (explicit equation) for the nth term given 
60, 55, 50, 45, ...
a)
an= -5+60n
b)
an= -5n+55
c)
an= -5n+65
d)
an= 5n+55
80.
Write the explicit rule for the arithmetic sequence
12, 10, 8, 6, ...
a)
an = 12n - 14
b)
an = 2n - 14
c)
an = -2n + 14
d)
an = -12n + 14
81.
Find the first term of the given sequence:
a14=68
d=3
a)
14
b)
20
c)
26
d)
29

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