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creat problem of artimatic and geometric seqiance

Total questions: 80

Worksheet time: 5hrs 1mins

Name
Class
Date
1.

Which of the following is not an Arithmetic Progression?

a)

1, 4, 7, 10, .....

b)

3, 7, 12, 16, ......

c)

-5, -2, 1, 4, .....

d)

11, 14, 17, 20, .....

2.

4, 24, 144, 864, ...

Find the next 3 terms

a)

1024, 4096, 16384

b)

256, −1024, 4096

c)

256, 1024, 4096

d)

5184, 31104, 196624

3.

−4, −12, −36, −108, ...

Find the common ratio

a)

r=−2

b)

r=3

c)

r=−3

d)

r=2

4.

Evaluate the geometric series described.

3+15+75+375+..., n=6

a)

11,718

b)

9,769

c)

10,603

d)

-3/4

5.

Evaluate the geometric series

1-2+4-8..., n=8

a)

1/3

b)

-87

c)

-86

d)

-85

6.

a₁=2, r=−2, Sn = 22

Determine the number of terms n in the series

a)

6

b)

8

c)

7

d)

5

7.

Number lines can be used for

a)

addition

b)

subtraction

c)

addition or subtraction

d)

neither

8.

Pattern is the

a)

rule in a table.

b)

input numbers in a table.

c)

output numbers in a table.

d)

geometric shapes in a picture.

9.

What is the missing term for the arithmetic sequence:

-22, -16, -10, (a)   , 2, 8,...

10.

What is the common difference in the sequence 5, 11, 17, 23, 29,...

a)

-6

b)

6

c)

4

d)

5

11.

Which kind of sequence has a common ratio?

a)

geometric

b)

arithmetic

c)

cannot be determined

12.

Find the next four terms of the arithmetic sequence 16, 24, 32,...

a)

40, 48, 56, 64

b)

36, 40, 44, 48

c)

35, 40, 45, 50

d)

40, 44, 50, 56

13.
What is the common ratio of the geometric sequence below?
5, 25, 125, 625...
a)
25
b)
20
c)
5
d)
4
14.
Which kind of sequence has a common difference?
a)
Arithmetic
b)
Geometric
15.
Is this sequence Arithmetic, Geometric, or Neither?
{14, 22, 30, 38, .. }
a)
Arithmetic
b)
Geometric
c)
Neither
16.
The next two terms of the sequence 12,17,22,27 are
a)
28 and 33
b)
29 and 34
c)
32 and 37
d)
30 and 35
17.
The next term of the sequence 2,4,8,16 are
a)
64
b)
32
c)
108
d)
20
18.

Is the given sequence geometric?

a)

Yes

b)

No

c)

Cannot be determined

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.
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
21.
Find a12 in the sequence -1, -3, -9, -27, ...
a)
-177,147
b)
-19,683
c)
-59,049
d)
118,098
22.
Find the common ratio for the geometric sequence.
a)
10
b)
1/2
c)
2
d)
4
23.

Is the given sequence geometric?

a)

Yes

b)

No

c)

Cannot be determined

24.

What is the fourth term of the sequence defined by

a1 = 3,

an = an-1 – 7

a)

–1

b)

–6

c)

–18

d)

–10

25.
What is the recursive rule for the sequence 
2, 6, 18, 54, ...?
a)
an=2(3)n-1
b)
a1 = 2, an = an-1 + 4
c)
a1 = 2, an = 3an-1
d)
a1 = 3, an = 2an-1
26.
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
27.
What type of series is
32 + 16 + 8 + 4 + 2 + 1
a)
Finite Arithmetic
b)
Finite Geometric
c)
Infinite Arithmetic
d)
Infinite Geometric
28.
Find the common ratio (multiplier):  a1 = 4 and a4 = 256
a)
84
b)
64
c)
4
d)
8
29.
Find the common difference:  a2 = 6 and a6 = -14
a)
-1
b)
-5
c)
-2
d)
2
30.
Find the sum for the following series. 
a)
44
b)
-162
c)
-682
d)
324
31.
Evaluate the series.
a)
36
b)
85
c)
35
d)
86
32.
Find the 22nd term of the following sequence:
5, 8, 11, ...
a)
14
b)
68
c)
63
d)
71
33.

-21, -16, -11, -6, ...

Is this sequence arithmetic, geometric, or neither?

a)

arithmetic (common difference d = 5)

b)

geometric (common ratio r = 5)

c)

neither

34.
What is the common ratio for the sequence:
28, 14, 7, 3.5...
a)
2
b)
1/2
c)
-14
d)
-7
35.
Is the sequence 2, 4, 12, 48,... geometric?
a)
yes
b)
no
36.

The next term of the sequence 2,4,8,16 is

a)

64

b)

32

c)

108

d)

20

37.

Describe the sequence, find the 5th term, and write the rule

-8, -6, -4, -2...

a)

geometric, a5 = 2, an = 2n - 10

b)

geometric, a5 = 0, an = -10n + 2

c)

arithmetic, a5 = 2, an = -10n + 2

d)

arithmetic, a5 = 0, an = 2n - 10

38.

Which of the following represents the sequence 3, 6, 9, 12, ...

a)

1, 3, 5, 7, ...

b)

f(1)=3; f(x)=f(x-1)*2

c)

f(x)=27(1/3)x

d)
e)
39.

Write the first 5 terms represented by the equation f(x)=3x+2

a)

2, 5, 8, 11, 14

b)

5, 8, 11, 14, 17

c)

3, 5, 7, 9, 11

d)

2, 6, 18, 54,162

40.

Which functions describe the sequence -1, -7, -13, -19, . . .? PICK 2

a)

f(1)= -1; f(n)=f(n-1)-6

b)

f(1)= -1; f(n)=f(n-1)+6

c)

f(x)= 6x+5

d)

f(x)= -6x+5

41.

Which EXPLICIT function describes the sequence 500, 250, 125, ... ?

a)

f(1)= 500; f(n)=f(n-1)*1/2

b)

f(x)=1000(1/2)x

c)

f(x)=1000(2)x

d)

f(1)=500; f(n)=f(n-1)*2

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

What does a1 represent?

a)

Any term

b)

First term

c)

Last term

45.

What does r represent?

a)

Radical

b)

Common difference

c)

Common ratio

46.

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5th birthday?

a)

$10

b)

$300

c)

$162

d)

$416

47.

What is the 9th term in a geometric sequence with a common ratio of 2 and a first term of 3?

a)

384

b)

768

c)

1,536

d)

27

48.

A geometric sequence has a common ration(r) of 3 and the 8th term (a8) is 13,122. What is the first term of the sequence (a1)?

a)

3

b)

6

c)

18

d)

2

49.

The rule for finding an of a geometric sequence is

an = 10(2)n-1 What is the common ratio(r) of the sequence?

a)

2

b)

10

c)

20

d)

2n

50.

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

51.
Find a12 in the sequence -1, -3, -9, -27, ...
a)
-177,147
b)
-19,683
c)
-59,049
d)
118,098
52.
What is the 14th term of the geometric sequence?
a)
14,348,907
b)
4,782,969
c)
1,594,323
d)
45
53.
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
54.

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

55.
Is the sequence -432, 72, -12, 2,...geometric?
a)
yes
b)
no
56.

What does a1 represent?

a)

Any term

b)

First term

c)

Last term

57.

What does r represent?

a)

Radical

b)

Common difference

c)

Common ratio

58.
Find the common ratio for the geometric sequence.
a)
2
b)
-2
c)
1/2
d)
-1/2
59.
Identify the common difference.
97, 86, 75, 64, ...
a)
8
b)
11
c)
-11
d)
-8
60.

To find the next term in an arithmetic sequence…

a)

add the common difference d

b)

multiply by the common ratio r

61.

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

62.

-21, -16, -11, -6, ...

Is this sequence arithmetic, geometric, or neither?

a)

arithmetic (common difference d = 5)

b)

geometric (common ratio r = 5)

c)

neither (no common difference OR common ratio) neither (no common difference OR common ratio)

63.

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

64.

256, 128, 64, 32, ...

How do you know what's next?

a)

NEXT = NOW • 2

b)

NEXT = NOW • 1/2

c)

NEXT = NOW + 2

d)

NEXT = NOW ÷ 1/2

65.
Find a12 for the rule an = 6(2)n-1
a)
4096
b)
24,576
c)
2048
d)
12,288
66.
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
67.
Find the first four terms of the sequence given the rule:
a1 = 10: an = an-1(3)
a)
3, 9, 27, 81
b)
10, 30, 90, 270
c)
10, 13, 16, 19
d)
30, 90, 270, 810
68.
Find the eighth term of a geometric sequence for which a3 = 224 and r = -½.
a)
-28
b)
-112
c)
56
d)
-7
69.
Find the next three terms for the geometric sequence:
2, -12, 72, ...
a)
432, 2592, 15,552
b)
-432, 2592, -15,552
c)
3672, 25,272, 154,872
d)
cannot be determined
70.
Find the common ratio for the geometric sequence:
64, 16, 4,...
a)
4
b)
-4
c)
¼
d)
-¼
71.
Find the next three terms for the geometric sequence:
64, 16, 4,...
a)
0, -4, -8
b)
1, ¼, 1/16
c)
1, -3, -7
d)
cannot be determined
72.

In June, Cory begins to save money for a video game and a TV he wants to buy in December. He starts with $20. Each month he plans to save 10% more than the previous month. How much money will he have at the end of December?

a)

$154.31

b)

$228.72

c)

$251.59

d)

$189.74

73.

Justine earned $17,000 during the first year of her job at city hall. After each year she received a 4% raise. Find her total earnings during the first five years on the job.

a)

$3,541.44

b)

$517,077.48

c)

$72,189.89

d)

$92,077.48

74.

A large asteroid crashed into a moon of a planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic sequence 26, 44, 62, 80, . . . . Find the total distance that the projectile traveled in seven seconds

(a)  

75.

Viola makes gift baskets for Valentine’s Day. She has 13 baskets left over from last year, and she plans to make 12 more each day. If there are 15 work days until the day she begins to sell the baskets, how many baskets will she have to sell? (Sequence or Series)

a)

193 baskets

b)

205 baskets

c)

156 baskets

d)

181 baskets

76.

A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd, and so on, how many seats are there in all? Assume the pattern continues.

(a)  

77.
A bouncing ball reaches heights of 16 cm, 12.8 cm, and 10.24 cm on three consecutive bounces. If the ball was originally dropped from 25 cm (a1 = 25), how much total distance in the downward direction has the ball traveled after five bounces? 
a)
25 cm
b)
84.04 cm
c)
53.7956 cm
d)
59.04 cm
78.
The local power company plans to raise rates to cover the increased cost of producing power. They determine the costs will increase by 4.2% per year for the next 10 years. If you paid a total of $1031.60 for power last year, what would you expect to pay for power over the next 10 years? 
(Hint: Find a1, a10, and r)
a)
$13,020.97
b)
$10,316.00
c)
$2,704.97
d)
$12,220.97
79.
a)
17
b)
32
c)
42
d)
52
80.
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

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