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Worksheets

Alg1 Arithmetic and Geometric Sequences

Total questions: 145

Worksheet time: 13hrs 34mins

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 the first term a1 = 1 and common difference d = 1. Find a1083

(a)  

7.

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

8.

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)  

9.

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

(a)  

10.

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

(a)  

11.

Find d given that a1 = 10 and a20 = 466

(a)  

12.

Find a20 given that a3 = 9 and a8 = 24

(a)  

13.

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

14.

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)  

15.

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)  

16.

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

(a)  

17.

Find the 20th term for the given Arithmetic Sequence:

3, 5, 7, 9, ….

(a)  

18.

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

(a)  

19.

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

21, 18, 15, (a)  

20.

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

(a)  

21.

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

(a)  

22.

Which term of the sequence below is equal to 109?


4, 9, 14, 19, (a)  

23.

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)  

24.
Find the 22nd term of the following sequence:
5, 8, 11, ...
a)
14
b)
68
c)
63
d)
71
25.
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
26.
Find the first term of the given sequence:
a14=68
d=3
a)
14
b)
20
c)
26
d)
29
27.
Identify the common difference.
97, 86, 75, 64, ...
a)
8
b)
11
c)
-11
d)
-8
28.
Identify the common difference.
3, 7, 11, 15, ...
a)
6
b)
5
c)
4
d)
2
29.
Find the 32nd term of this sequence.
34, 37, 40, 43, ...
a)
32
b)
64
c)
127
d)
356
30.
Find the 32nd term of this sequence.
9, 4, -1, -6, -11, ...
a)
81
b)
-34
c)
-146
d)
-225
31.
Find the 25th term of the sequence if a1 = 5 and d = 0.5
a)
18
b)
17
c)
15
d)
14
32.
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
33.
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
34.
Is the sequence arithmetic: 78, 785, 7855, 78555, ...
a)
Yes
b)
No
35.
Is the sequence arithmetic: 17, 9, 1, -7, ...
a)
Yes
b)
No
36.
Is the sequence arithmetic: -3, 3, -3, 3, ...
a)
Yes
b)
No
37.

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

a)

-5

b)

+5

c)

-6

d)

+6

38.

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

a)

-10

b)

-9

c)

-8

d)

-7

39.

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

a)

-5

b)

+5

c)

-3

d)

3

40.

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

a)

+100

b)

+101

c)

+200

d)

+201

41.
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
42.
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
43.
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
44.
Find the 35th term in the arithmetic sequence: -10, -14, -18, -22, ...
a)
-216
b)
-148
c)
-146
d)
-150
45.
Find 26th term in the arithmetic sequence: -15, -35, -55, -75, ...
a)
-515
b)
-490
c)
-535
d)
460
46.
Find the 26th term in the arithmetic sequence: 20, 26, 32, 38, ...
a)
182
b)
176
c)
170
d)
-118
47.

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

a)

145

b)

144

c)

142

d)

138

48.

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

a)

80

b)

155

c)

70

d)

125

49.

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

50.

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

a)

+3

b)

+4

c)

-4

d)

+6

51.

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

a)

-1

b)

-2

c)

1

d)

2

52.
Find the 22nd term of the following sequence:
5, 8, 11, ...
a)
14
b)
68
c)
63
d)
71
53.

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

54.
Is the sequence arithmetic: -3, 3, -3, 3, ...
a)
Yes
b)
No
55.
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
56.
Identify the common difference. 
10, 20, 30, 40, ...
a)
5
b)
10
c)
15
d)
20
57.
Identify the common difference.
3, 7, 11, 15, ...
a)
6
b)
5
c)
4
d)
2
58.
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
59.
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
60.

Which of the following is an example of an arithmetic sequence?

a)

4, 8, 16, 32, 64

b)

1, 2, 4, 7, 11

c)

15, 13, 11, 9, 7

d)

3, 6, 12, 24, 48

61.

Which sequence is NOT an arithmetic sequence?

a)

-7, -13, -19, -25,...

b)

-10, -6, -2, 2,..

c)

6, 8, 10, 12,...

d)

3, 15, 75, 375,...

62.

The difference between two terms in an arithmetic sequence is called ___________________.

a)

Formula

b)

Common Ratio

c)

Common Difference

d)

Common Factor

63.

Which of the following is the correct formula in finding the nth term of an arithmetic sequence?

a)

an = a1 + (n - 1)d

b)

an = a1 + (n + 1)d

c)

an = a1 - (n - 1)d

d)

an = a1 +- (n + 1)d

64.
Given the first five terms, write the recursive formula.
15, 12, 9, 6, 3 ....
a)

a1 = 15
an = an-1 + 3

b)

a0 = 15
an = an-1 + 3

c)

a1 = 15
an = an-1 - 3 

d)

a0 = 15
an = an-1 - 3

65.
Given the recursive formula below, find the explicit formula.  
a0 = 1
an = an-1 + 5
a)
an = 6 + 5n
b)
an = 1 + 5n
c)

an = 6- 5n

d)

an = 5+n

66.
Given the sequence below, write the explicit formula.
3, 8, 13, 18 ... 
a)

an = 3 + 5n

b)

an = -2 + 5n

c)

an = -8 + 5n

d)

an = n+ 5

67.

Write a recursive formula for the following sequence:

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

a)

a1= 10

an= an-1 - 5

b)

a1= 10

an= an-1 + 5

c)

a1= 10

an= an (5)

d)

a1= 10

an= an-1 (5)

68.

Which of the following recursive formulas represents the given sequence?


7, 14, 28, 56, 112, ...

a)

a1=7a_1=7 , an=a(n−1)+7a_n=a_{\left(n-1\right)}+7

b)

a1=7a_1=7 , an=a(n−1)⋅7a_n=a_{\left(n-1\right)}\cdot7

c)

a1=7a_1=7 , an=a(n−1)⋅2a_n=a_{\left(n-1\right)}\cdot2

d)

a1=7a_1=7 , an=a(n−1)+14a_n=a_{\left(n-1\right)}+14

69.

Find the recursive formula for the sequence. 1, 3, 9, 27,...1,\ 3,\ 9,\ 27,...  

a)

f(1)=1, f(n)=f(n−1)⋅3f\left(1\right)=1,\ f\left(n\right)=f\left(n-1\right)\cdot3  

b)

f(1)=1, f(n)=f(n−1)⋅1+3f\left(1\right)=1,\ f\left(n\right)=f\left(n-1\right)\cdot1+3  

c)

f(1)=1, f(n)=1⋅3n−1f\left(1\right)=1,\ f\left(n\right)=1\cdot3^{n-1}  

d)

f(1)=1, f(n)=3⋅1n−1f\left(1\right)=1,\ f\left(n\right)=3\cdot1^{n-1}  

70.

What does a1 represent?

a)

Any term

b)

First term

c)

Last term

d)

The nth term

71.
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
72.

If an+1 represents the third term, which term does an represent?

a)

Fourth Term

b)

Second Term

c)

First Term

d)

Fifth Term

73.

Given the following sequence and an = 7, what is an+1?

2, 7, 12, 17,...

a)

2

b)

12

c)

17

d)

22

74.

Find the first four terms of the sequence.

an= a(n-1) - 18 where a1=10

a)

18, 8, -2, -12

b)

28, 46, 64, 82

c)

-8, -26, -44, -60

d)

10, -8, -26, -44

75.

What does r represent?

a)

Radical

b)

Common difference

c)

Common ratio

76.
Find the common ratio for the geometric sequence.
a)
10
b)
1/2
c)
2
d)
4
77.
Is the sequence -432, 72, -12, 2,...geometric?
a)
yes
b)
no
78.

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

79.
Write the explicit formula for the geometric sequence.
a)
an = 4(3)n-1
b)
an = 3(4)n-1
c)
an = -4(3)n-1
d)
an = 3(-4)n-1
80.
This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?
a)
4
b)
3
c)
2
d)
6
81.
Find the first four terms of the sequence given the rule:
an = 4(5)n-1
a)
20, 100, 500, 2500
b)
5, 20, 80, 320
c)
4, 20, 100, 500
d)
4, 9, 14, 19
82.
What is the 14th term of the geometric sequence?
a)
14,348,907
b)
4,782,969
c)
1,594,323
d)
45
83.

Given the sequence:

125, 25, 5, ....

Write the rule an using the geometric sequence formula:

a)

an = (125)(1/5)(n-1)

b)

an = 625(1/5)(n-1)

c)

an = 625(5)(n-1)

d)

an = 125 + 5n

84.
Find a12 in the sequence -1, -3, -9, -27, ...
a)
-177,147
b)
-19,683
c)
-59,049
d)
118,098
85.

Write the fifth term of each geometric sequence

8, 24, 72, 216, (a)  

86.

Write the fifth term of each geometric sequence

3, 12, 48, 192, (a)  

87.

Write the fifth term of each geometric sequence

5, -10, 20, -40, (a)  

88.

Write the fifth term of each geometric sequence

-4, 12, -36, 108, (a)  

89.

Write the fifth term of each geometric sequence

10, 5, 2.5, 1.25, (a)  

90.

The 3rd term of the geometric sequence is 27 and the 5th term is 243. What is the common ratio of the sequence?

a)

4

b)

6

c)

3

d)

8

91.

If the second term of a geometric sequence is 5/2 and the fifth term is 20, what is the 10th term?

a)

80

b)

320

c)

160

d)

640

92.

{6, 18, 54, ___...}

a)

164

b)

162

c)

156

d)

154

93.

{x2 ,x5 ,x8 , _...}

a)

x⁹

b)

x¹⁰

c)

x¹¹

d)

x¹²

94.

A $100,000 machine is depreciated 20% each year. The depreciated values form this geometric sequence;

$100,000, $80,000, $64000, $51200, $40960,...

What is the depreciated value of the machine after 5 years if its value after 1 year is $80,000?

a)

32,678

b)

33,789

c)

32,768

d)

33,789

95.
Is the sequence 2, 4, 12, 48,... geometric?
a)
yes
b)
no
96.
What is the common ratio for the sequence:
28, 14, 7, 3.5...
a)
2
b)
1/2
c)
-14
d)
-7
97.
Find the common ratio: 4, -16, 64, -256, ...
a)
r = -4
b)
r = 2
c)
r = -2
d)
r = 4
98.
Find the common ratio: 64, -16, 4, -1, ...
a)
r = -8
b)
r = -1/4
c)
r = -4
d)
r = 4
99.
Find the next three terms: 4, 12, 36, 108, ...
a)
324, 972, 2916
b)
972, 2916, 8748
c)
405, 1215, 3645
100.
Find the next three terms: -4, -12, -36, -108, ...
a)
36, -108, 324
b)
-324, -972, -2916
c)
324, -972, 2916
d)
-108, 324, -972
101.
Which formula is used to find the explicit equation for geometric sequences?
a)
an = an-1 + d
b)
an = an-1 * r
c)
an = a1 + d(n-1)
d)
an = a1 * rn-1
102.
Find the general rule for: 64, -32, 16, -8, …  
a)
64(1/2)n-1
b)
(-32)n-1
c)
64(-1/2)n-1
d)
(32)n-1
103.
Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ?
a)
an = an-1 x 3
b)
an = 5(3)n-1
c)
an = 3(5)n-1
d)
an = 5 + (n-1)3
104.
Find the 11th term for:  64, -32, 16, -8, …  
a)
-.0625
b)
.0625
c)
-.03125
d)
.03125
105.
You have $10 in you bank account.  It doubles every month.  How much money will you have after 5 months?
a)
$50
b)
$35
c)
$320
d)
$250
106.

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

107.
What kind of sequence is illustrated below?
 400, 200, 100, 50, 25, ...
a)
Arithmetic
b)
Geometric
c)
Neither
108.
What is the 8th term in the sequence below?
3, 9, 27, 81, ...
a)
19,683
b)
6,561
c)
2,187
d)
729
109.

What is the 6th term of the geometric sequence

2/25, 2/5, 2, 10, ...?

a)

25

b)

250

c)

1 250

d)

2 500

110.

Which of the following is NOT a geometric sequence?

a)

-2, -4, -8, -16, …

b)

3, -6, 9, -12, …

c)

1/5, 1/10, 1/20, 1/40, ...

d)

3, 1, 1/3, 1/9, ...

111.

What is the common ratio of the sequence 54, 18, 6, 2…?

a)

3

b)

-3

c)

1/3

d)

-1/3

112.

a1=4a_1=4  

r=−2r=-2  

Find the 5th term of the geometric sequence.

a)

32

b)

-32

c)

64

d)

-64

113.

The next term of the geometric sequence

4, 16, 64, ... is

a)

256

b)

132

c)

120

d)

150

114.

What is the common ratio for the following sequence:

3, 15, 75, 375, ...

a)

12

b)

1/5

c)

5

d)

3

115.
What is the common ratio for the sequence:
28, 14, 7, 3.5...
a)
2
b)
1/2
c)
-14
d)
-7
116.

Find the first four terms of the sequence given the rule:

an = 4(5)n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

117.

What is a5 in the sequence defined as follows?

an = 5 ⋅ 2(n-1)

a)

a5 = 160

b)

a5 = 40

c)

a5 = 10

d)

a5 = 80

118.

To find the next term in a geometric sequence…

a)

add the common difference d

b)

multiply by the common ratio r

119.

A sequence can be generated by using the given sequence where a1=3a_1=3  .
What are the first three terms in the sequence?

a)

3, 15, 453,\ 15,\ 45

b)

5, 8, 115,\ 8,\ 11

c)

5, 15, 455,\ 15,\ 45  

d)

3, 15, 753,\ 15,\ 75  

120.

A sequence follows the given recursive rule where  a1=17a_1=17  . Find the 6th term.

a)

272272  

b)

−544-544  

c)

77  

d)

−34-34  

121.

Find the 5th term of the geometric sequence:

a)

10

b)

19

c)

1701

d)

567

122.

an=a1rn−1a_n=a_1r^{n-1}  

Given the formula for a geometric sequence,  ana_n   stands for

a)

common difference

b)

wanted term

c)

common ratio

d)

first term

123.
What is the common ration of 9,-36, and144
a)
-47
b)
4
c)
-4
d)
27
124.
The next term of sequence 2,4,8,16 is
a)
64
b)
108
c)
32
d)
20
125.
The next term in the series is 4,16,32,
a)
256
b)
120
c)
132
d)
150
126.

The 1st term of a geometric sequence is 3 and the eighth term is 384. Find the common ratio of the sequence

(a)  

127.

Write down the 8th term in the Geometric Sequence

1, 3, 9, ...

(a)  

128.

Find the number of terms (n) in the geometric sequence

6, 12, 24, ..., 1536.

(a)  

129.

Find the 9th term of 3, 12, 48, 192, ...

(a)  

130.

What is the eleventh term of the geometric sequence 3, 6, 12, 24, ... ?

(a)  

131.

The first term of a geometric sequence is 5 and the sixth term is 160.

What is the common ratio?

(a)  

132.

The fourth term of a geometric sequence is 27 and the seventh term is 1. What is the first term?

(a)  

133.

is the sequence 2, 4, 8,16,,,, a geometric sequence?

(a)  

134.

What is the common ratio of the geometric sequence

3, -6, 12, -24, 48...?

(a)  

135.

Find the fourth term of a geometric progression, whose first term is 2 and the common ratio is 3.

(a)  

136.

Given the number of bacteria in a Petri dish is 10 and they double themselves every minute, does the number of bacteria in the Petri dish after n minutes form a geometric sequence?


please answer yes or no.

(a)  

137.

Given the number of bacteria in a Petri dish is 10 and they double themselves every minute, how many bacteria will be in dish after 6 minutes?

(a)  

138.

True or False

Given "a" the first term is negative and "r" the common ratio is positive then all the terms in the geometric sequence will be negative.

(a)  

139.

Given a is the first term of a geometric sequence and 2 is the common ratio, what is the 5th term in terms of a?

(a)  

140.

The seventh term of a geometric sequence is 1458 and the fourth term is 54. What are the possible values for a and r respectively?

(a)  

141.

Find the sum of the first 8 terms of the geometric sequence 3, 6, 12, (a)  

142.

In 2013, the number of students in a small school is 284. It is estimated that the student population will increase by 4% each year.


Estimate the student population in 2020.

(a)  

143.

The initial population of chicken on a farm was 40. The population increased by 5% each week.


How many chickens were present after 20 weeks?

(a)  

144.

The initial population of chicken on a farm was 40. The population increased by 5% each week.


How long would it take for the population to reach 240 chickens?

(a)  

145.

What is the common ratio for the sequence:

28, 14, 7, 3.5...

(a)  

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