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Arithmetic and Geometric Sequences and Series

Total questions: 120

Worksheet time: 11hrs 21mins

Name
Class
Date
1.

What is the 7th term in the sequence

7, 11, 15, … ?

a)

30

b)

31

c)

32

d)

33

2.

The 6th term in the arithmetic sequence

18, 11, 4, …

a)

-3

b)

-10

c)

-17

d)

-24

3.

Which of the following is NOT an arithmetic sequence?

a)

48, 24, 12, 6, 3, ...

b)

3, 7, 11, 15, 19, ...

c)

1,  12\frac{1}{2}  , 0,  −12-\frac{1}{2} , ...

d)

1, 0, -1, -2, -3, ...

4.

It is a sequence that has a common difference.

a)

Arithmetic Means

b)

Arithmetic Sequence

c)

Arithmetic Series

d)

Arithmetic Pattern

5.

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

(a)  

6.

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

(a)  

7.

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


Please, answer yes or no

(a)  

8.

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)  

9.

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

(a)  

10.

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)  

11.

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

(a)  

12.

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

13.

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)  

14.

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

(a)  

15.

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

(a)  

16.

Find d given that a1 = 10 and a20 = 466

(a)  

17.

Find a20 given that a3 = 9 and a8 = 24

(a)  

18.

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)  

19.

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)  

20.

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)  

21.

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

(a)  

22.

Find the 20th term for the given Arithmetic Sequence:

3, 5, 7, 9, ….

(a)  

23.

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

(a)  

24.

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

21, 18, 15, (a)  

25.

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

(a)  

26.

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

(a)  

27.

Which term of the sequence below is equal to 109?


4, 9, 14, 19, (a)  

28.

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)  

29.
Write the recursive formula for 6, 17, 28, 39, 50....
a)
an=an-1+11
a1=6
b)
an=an-1-4
a1=6
c)
an=an-1+9
a1=6
d)
an=an-1+6
a1=6
30.

A formula that requires the computation of all previous terms to find the value of an.

a)

Explicit Formula

b)

Recursive Formula

c)

Arithmetic Formula

d)

Geometric Formula

31.

Identify the common difference.

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

a)

4

b)

3

c)

-4

d)

-3

32.

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)

33.
Which of the following equations is explicit?
a)
f(n) = 4n + 5
b)
f(n) = f(n-1) x 5
34.
Which of the following equations is recursive?
a)
f(n) = f(n-1) +4
b)
f(n) = 2n - 5
35.

What does a1 represent?

a)

Any term

b)

First term

c)

Last term

36.

an=a1+(n−1)da_n=a_1+\left(n-1\right)d  , where n is the position in the sequence and d is the difference between terms.

a)

Sequence

b)

Recursive Formula

c)

Explicit Formula for an Arithmetic Sequence

d)

Explicit Formula for a Geometric Sequence

37.

Write a sequence to represent the number of smiley faces in each group. Select all that apply.

a)

 an=4+(n−1)2a_n=4+\left(n-1\right)2

b)

f(n)=2+4(n−1)f\left(n\right)=2+4\left(n-1\right)

c)

f(n)=4+2(n−1)f\left(n\right)=4+2\left(n-1\right)

d)

an=an−1+2a_n=a_{n-1}+2

e)

an=an−1−2a_n=a_{n-1}-2

38.

This is an arithmetic sequence. How many dots would be in the next figure?

a)

4

b)

13

c)

14

d)

15

39.
What is the common ratio for the sequence:
28, 14, 7, 3.5...
a)
2
b)
1/2
c)
-14
d)
-7
40.
What is the recursive rule for the sequence:
11, 22, 44, 88...
a)
an = 2(11)n-1
b)
an = 11x 2
c)
an = 11(2)n-1
d)
an = 2an-1
41.

What does r represent?

a)

Radical

b)

Common difference

c)

Common ratio

42.
Find the common ratio for the geometric sequence.
a)
10
b)
1/2
c)
2
d)
4
43.
Is the sequence -432, 72, -12, 2,...geometric?
a)
yes
b)
no
44.

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

45.
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
46.
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
47.
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
48.
What is the 14th term of the geometric sequence?
a)
14,348,907
b)
4,782,969
c)
1,594,323
d)
45
49.

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

50.
Find a12 in the sequence -1, -3, -9, -27, ...
a)
-177,147
b)
-19,683
c)
-59,049
d)
118,098
51.
Find the common ratio: 4, -16, 64, -256, ...
a)
r = -4
b)
r = 2
c)
r = -2
d)
r = 4
52.
Find the common ratio: 64, -16, 4, -1, ...
a)
r = -8
b)
r = -1/4
c)
r = -4
d)
r = 4
53.
Find the next three terms: 4, 12, 36, 108, ...
a)
324, 972, 2916
b)
972, 2916, 8748
c)
405, 1215, 3645
54.
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
55.
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
56.
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
57.
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
58.
Find the 11th term for:  64, -32, 16, -8, …  
a)
-.0625
b)
.0625
c)
-.03125
d)
.03125
59.
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
60.

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

61.
What is the 8th term in the sequence below?
3, 9, 27, 81, ...
a)
19,683
b)
6,561
c)
2,187
d)
729
62.

The sum of an finite Geometric series is given by:

a)
b)
c)
d)
63.

List the first five terms of the geometric sequence. Assume that the sequence begins at n = 1.

a)

1 , 3 , 6 , 9 , 12

b)

3 , 9 , 27 , 81 , 243

c)

0 , 1 , 3 , 9 , 27

d)

1 , 3 , 9 , 27 , 81

64.

a1=4a_1=4  

r=−2r=-2  

Find the 5th term of the geometric sequence.

a)

32

b)

-32

c)

64

d)

-64

65.

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

a)

3

b)

-3

c)

1/3

d)

-1/3

66.

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, ...

67.

The geometric mean of two numbers is 27. If one of the numbers is 81, what is the other number?

a)

3

b)

6

c)

9

d)

12

68.

What is the next term of the geometric sequence 200, 100, 50, 25?

a)

5

b)

1

c)

1/5

d)

25/2

69.

What is the sum of the first six terms of the sequence with 2 as the first term and 3 as the common ratio?

a)

728

b)

738

c)

748

d)

758

70.

What is the sum of the first 10 terms of the sequence -5, 5, -5, …?

a)

-50

b)

50

c)

0

d)

5

71.

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

72.

Which of the following is the sum of all multiples of 3 from 15 to 48?

a)

315

b)

360

c)

378

d)

396

73.
The sequence 28, 34, 40, 46, 52, ..., 88 has 11 terms. Evaluate the related series. 
a)
550
b)
638
c)
610
d)
288
74.
Find Sn for the given series:
a1=22
d=-8
n=21
a)
1911
b)
-1449
c)
-2436
d)
-1218
75.
Evaluate the arithmetic series described:
2 + (-2) + (-6) + (-10)..., S10
a)
-160
b)
-328
c)
-320
d)
-336
76.
Evaluate the arithmetic series described:
11 + 18 + 25 + 32..., S7
a)
225
b)
450
c)
384
d)
224
77.
Evaluate the arithmetic series described:
28 + 38 + 48 + 58..., S7
a)
1644
b)
812
c)
406
d)
3290
78.
Evaluate the arithmetic series described:
14 + 23 + 32 + 41..., S11
a)
1296
b)
1298
c)
2604
d)
649
79.
Evaluate the arithmetic series described:
0 - 7 - 14 - 21..., S17
a)
-959
b)
-1904
c)
-952
d)
-1918
80.
What is the value of r for the following sequence.
1/2+1/4+1/8+1/16+...
a)
2
b)
-2
c)
1/2
d)
-1/2
81.
What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47 + ...?
a)
1,600
b)
18,235
c)
18,475
d)
19,125
82.
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
83.
Find the indicated sum for the arithmetic series:
S20 for 4 + 7 + 10 + 13 + ...
a)
S20 = 650
b)
S20 = -606
c)
S20 = 600
84.
Identify the common difference.
3, 7, 11, 15, ...
a)
6
b)
5
c)
4
d)
2
85.
Create the formula for the sequence:
2, 8, 14, ...
a)
an=2+6n
b)
an=-6+6n
c)
an=6n-4
d)
an=4-6n
86.

Find the sum the series.

a)

20

b)

-25

c)

25

d)

28

87.

Find the sum of the series.

a)

28

b)

-29

c)

30

d)

27

88.

Find the sum of the series

a)

-220

b)

-230

c)

-225

d)

-227

89.
What is the sum of the first ten terms of the sequence 4, -12, 36, -108 . . . ?
a)
59,050
b)
-59,048
c)
-78,732
d)
118,096
90.
What is the twelfth term in the sequence 3, -6, 12, . . . ?
a)
-2,048
b)
6,144
c)
-6,144
d)
-531,441
91.
What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47 + ...?
a)
1,600
b)
18,235
c)
18,475
d)
19,125
92.
For n = 1,2,3 . . .the explicit formula,
 an = (-3)n  + 4, will produce the sequence:
a)
{1, 13, -23, 85. . .}
b)
{1, -5, -23, -77. . .}
c)
{1, -2, -5, -8...}
d)
{1, 10,-5, 85. . .}
93.
a)
149
b)
11,200
c)
5,600
d)
140
94.
Evaluate the arithmetic series described:
2 + (-2) + (-6) + (-10)..., S10
a)
-160
b)
-328
c)
-320
d)
-336
95.
Evaluate the arithmetic series described:
11 + 18 + 25 + 32..., S7
a)
225
b)
450
c)
384
d)
224
96.
Evaluate the arithmetic series described:
28 + 38 + 48 + 58..., S7
a)
1644
b)
812
c)
406
d)
3290
97.
Evaluate the arithmetic series described:
14 + 23 + 32 + 41..., S11
a)
1296
b)
1298
c)
2604
d)
649
98.
Evaluate the arithmetic series described:
0 - 7 - 14 - 21..., S17
a)
-959
b)
-1904
c)
-952
d)
-1918
99.
Evaluate the arithmetic series described:
1 + 3 + 5 + 7..., S8
a)
116
b)
58
c)
64
d)
128
100.
Evaluate the arithmetic series described:
a1 = 12, an = 64, Find S14
a)
1082
b)
532
c)
541
d)
1064
101.
Evaluate the arithmetic series described:
a1 = 5, an = 145, Find S15
a)
1125
b)
2255
c)
2250
d)
2258
102.
You are sitting in row 23 and notice there are 65 seats in your row. The row in front of you has 63 seats and the row behind you has 67 seats. There are 42 rows in the auditorium. How many seats does the auditorium contain? (Hint: Find the number of seats in the first and last rows)
a)
2,604
b)
2,163
c)
2,422
d)
2,803
103.
Find S14 
7, 2, -3, ...
a)
-812
b)
119
c)
-945
d)
-357
104.

To find the next term in an arithmetic sequence…

a)

add the common difference d

b)

multiply by the common ratio r

105.

To find the next term in a geometric sequence…

a)

add the common difference d

b)

multiply by the common ratio r multiply by the common ratio r

106.

∑x=39(2x+2)\sum_{x=3}^9\left(2x+2\right)  How many terms are in the sequence?

a)

6

b)

7

c)

3

d)

2

107.
Calculate the final sum/total of the series.
a)
6
b)
21
c)
9
d)
2
108.
a)
196
b)
392
c)
49
d)
254
109.
a)
149
b)
11,200
c)
5,600
d)
140
110.

Evaluate Sn:

28 + 35 + 42 + 49 + ..., n = 10

(Hint: is this arithmetic or geometric?)

a)

2384

b)

595

c)

1192

d)

1190

111.

Evaluate S8:

2 + 6 + 10 + 14 + ...

a)

128

b)

494

c)

256

d)

255

112.
What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47 + ...?
a)
1,600
b)
18,235
c)
18,475
d)
19,125
113.

Evaluate S12 for the arithmetic series where:

a1=?, a12=48, and d=4

a)

310

b)

312

c)

620

d)

624

114.

The sum of this arithmetic series is 595. a1=28, and an=91. How many terms are there (what is n)?

a)

9

b)

10

c)

11

d)

12

115.
What is the sum of the first 10 terms for the following geometric series:
1+1/2+1/4+1/8+1/16+...
a)
0.999
b)
0.002
c)
9.8
d)
1.998
116.
Find the indicated sum for the geometric series.
S6 for (-4/5) + 8 + (-80) + 800 + ....
a)
S6 = 21,845
b)
S6 = 72,000
c)
S6 = 72,727.2
d)
S6 = -128,840.8
117.

Find the sum of a geometric series where


a1=4, r = -2 , an = 16,384

a)

-10,921.3333333

b)

10,922

c)

10,924

d)

-10,924

118.

Evaluate the sum of the geometric series:

-1 + 5 - 25 + 125 + ... + 78,125

a)

65104

b)

56732

c)

-1/6

d)

65816

119.

Evaluate sum S8:

a1=?, a8=839,808, r= -6

a)

717456

b)

719835

c)

665624

d)

668938

120.
Evaluate the geometric series below:
4 + 20 + 100 + 500...,  S7
a)
88419
b)
78124
c)
91846
d)
92234

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