Free Printable FA in Geometric Sequence and Series

1.

Find the common ratio of the geometric sequence:
$2,\ \frac{1}{2},\ \frac{1}{8},\ \frac{1}{32},\ ...$

a)

$\frac{1}{3}$

b)

$\frac{1}{12}$

c)

$\frac{1}{16}$

d)

$\frac{1}{4}$

2.

Evaluate the geometric series described below.
$a_1=-1,\ r\ =\ 4,\ n\ =\ 8$

a)

-585

b)

585

c)

-21,845

d)

21,845

3.

What is the sum of the first ten terms of the sequence 4, -12, 36, -144 . . . ?

a)

59,050

b)

-59,048

c)

-78,732

d)

118,096

4.

Evaluate $\sum_{k\ =\ 1}^7\left(-2\right)^{k\ -1\ }$

a)

44

b)

$\frac{1}{3}$

c)

43

d)

49

5.

Find the sum of the infinite geometric series:

200 - 100 + 50 - 25 + ...

a)

525 / 2

b)

400 / 3

c)

3 / 400

d)

2 / 525

6.

Is the sequence -432, 72, -12, 2,...geometric?

a)

yes

b)

no

7.

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

8.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

9.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

10.

Find a₁₂ in the sequence -1, -3, -9, -27, ...

a)

-177,147

b)

-19,683

c)

-59,049

d)

118,098

11.

Is the sequence 2, 4, 12, 48,... geometric?

a)

yes

b)

no

12.

Find the next three terms: 3, -18, 108, -648

a)

-6480, -3880, -233280

b)

6480, -38880, 233280

c)

5184, -31104, 186624

d)

3888, -23328, 139968

13.

What is the explicit rule for the sequence:
11, 22, 44, 88...

a)

_gn = 2(11)^n-1

b)

_gn = 11x2

c)

_gn = 11(2)^n-1

d)

g_n = 11+(2)^n-1

14.

The n^th term of a geometric sequence is given by ...

a)

b)

c)

d)

15.

The sum of an infinite Geometric series is given by:

a)

b)

c)

d)

16.

An infinite series exists for which of the following situations?

a)

An arithmetic series

b)

A geometric series

c)

A geometric series with | r | > 1

d)

A geometric series with | r | < 1

17.

The sum of an finite Geometric series is given by:

a)

b)

c)

d)

18.

Find the common ratio: 16, 8, 4, 2, ...

a)

r = 2

b)

r = 8

c)

r = 1/4

d)

r = 1/2

19.

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

20.

What would be the missing terms of the series

-1 ,- 5, - 25 , ... ,- 78125

a)

125 , 625 , - 3125 , 15625

b)

125 , - 625 , - 15625

c)

-125 , - 625 , - 3125 , - 15625

d)

625 , - 3125 , - 15625

21.

Find the 13th term:
2, 6, 18, 54, ….

a)

1,000,000

b)

1,062,882

c)

123,587

d)

5 bazillion

22.

What is the twelfth term in the sequence 3, -6, 12, . . . ?

a)

-2,048

b)

6,144

c)

-6,144

d)

-531,441

23.

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

24.

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

25.

Find the sum of the infinite geometric series, if it exists:

-3 + -3/2 + -3/4 + -3/8...

a)

-6

b)

-8

c)

no sum

d)

-4

26.

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

27.

What is the twelfth term in the sequence 3, -6, 12, . . . ?

a)

-2,048

b)

6,144

c)

-6,144

d)

-531,441

28.

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

29.

For n = 1,2,3 . . .the explicit formula,
a_n = (-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. . .}

30.

a)

149

b)

11,200

c)

5,600

d)

140

31.

The next two terms of the sequence 8,4,2,1, 1/2 are

a)

1/3 and 1/4

b)

1/4 and 1/8

c)

1/8 and 1/6

d)

1/5 and 1/7

32.

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

33.

What is the explicit rule for the sequence:
11, 22, 44, 88...

a)

_gn = 2(11)^n-1

b)

_gn = 11x2

c)

_gn = 11(2)^n-1

d)

g_n = 11+(2)^n-1

34.

Find the 13th term:
2, 6, 18, 54, ….

a)

1,000,000

b)

1,062,882

c)

123,587

d)

5 bazillion

35.

Find the next three terms: 3, -18, 108, -648

a)

-6480, -3880, -233280

b)

6480, -38880, 233280

c)

5184, -31104, 186624

d)

3888, -23328, 139968

36.

Find the 32nd term of this sequence.
9, 4, -1, -6, -11, ...

a)

81

b)

-34

c)

-146

d)

-225

37.

In an arithmetic sequence if a₁₅ =108 and d=7, find a₁.

a)

14

b)

101

c)

206

d)

10

38.

a)

A.

b)

B.

c)

C.

d)

D.

39.

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

a)

a_n = 4n + 29

b)

a_n = -4n + 25

c)

a_n= -4n + 29

d)

a_n = 4n + 25

40.

Find the geometric sum

a)

-1456

b)

-4095

c)

1456

d)

4095

41.

Find the sum of the first 9 terms: -2 + -6 + -18 + ...

a)

-59,048

b)

-39,366

c)

-19,682

d)

-4,374

42.

Find the sum of a geometric series where g₁=4, r = -2 and g_n = 16,384

a)

-10,921.3333333

b)

10,922

c)

10,924

d)

-10,924

43.

Solving for the nth term of geometric sequence, given thata₁ = 4 and r= 6, what is the value of the 4th term?

a)

144

b)

864

c)

124

d)

764

44.

Determine whether the sequence is arithmetic, geometric, or neither.

a)

arithmetic

b)

geometric

c)

neither

45.

Determine whether the sequence is arithmetic, geometric, or neither.

a)

arithmetic

b)

geometric

c)

neither

46.

Determine whether the sequence is arithmetic, geometric, or neither.

a)

arithmetic

b)

geometric

c)

neither

47.

Find the common ratio for the geometric sequence.

a)

10

b)

1/2

c)

2

d)

4

48.

Write the explicit formula for the geometric sequence.

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

49.

Find the common ratio for the geometric sequence.

a)

1

b)

-1

c)

7

d)

-7

50.

Write the explicit formula for the geometric sequence.

a)

a_n = 7(1)ⁿ

b)

a_n = 7(-1)ⁿ

c)

a_n = 7(-1)^n-1

d)

a_n = -1(7)^n-1

51.

Find the common ratio for the geometric sequence.

a)

-4

b)

4

c)

1/4

d)

-1/4

52.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

53.

Find the common ratio for the geometric sequence.

a)

2/3

b)

3/2

c)

-2/3

d)

-3/2

54.

Write the explicit formula for the geometric sequence.

a)

a_n = 162(2/3)^n-1

b)

a_n = (2/3)(162)^n-1

c)

a_n = 162(3/2)^n-1

d)

a_n = 162 + (n-1)(-54)

55.

Find the common ratio for the geometric sequence.

a)

2

b)

-2

c)

1/2

d)

-1/2

56.

Write the explicit formula for the geometric sequence.

a)

a_n = 2(100)^n-1

b)

a_n = 100(2)^n-1

c)

a_n = 100(1/2)^n-1

d)

a_n = (1/2)(100)^n-1

57.

What is the 14th term of the geometric sequence?

a)

14,348,907

b)

4,782,969

c)

1,594,323

d)

45

58.

What is the 11th term of the geometric sequence?

a)

-5120

b)

97,656,250

c)

19,531,250

d)

-19,531,250

59.

What does r represent?

a)

Radical

b)

Common difference

c)

Common ratio

60.

What does a₁ represent?

a)

Any term

b)

First term

c)

Last term

61.

Find the common ratio for the geometric sequence.

a)

10

b)

1/2

c)

2

d)

4

62.

Is the sequence -432, 72, -12, 2,...geometric?

a)

yes

b)

no

63.

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

64.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

65.

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

66.

Given the sequence:

125, 25, 5, ....

Write the rule a_n using the geometric sequence formula:

a)

a_n = (125)(1/5)^(n-1)

b)

a_n = 625(1/5)^(n-1)

c)

a_n = 625(5)^(n-1)

d)

a_n = 125 + 5n

67.

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

a)

$10

b)

$300

c)

$162

d)

$416

68.

What is the common ratio of this sequence ? 5, 25, 125, ...

a)

4

b)

2

c)

5

d)

6

69.

What is the 5th term of the sequence 7, 14, 28, ...?

a)

72

b)

48

c)

56

d)

112

70.

Which of the following is a geometric sequence?

a)

2, 4, 5, . . .

b)

2, 6, 18, . . .

c)

2, 4, 6, . . .

d)

10, 20, 200, . . .

71.

Solving for the nth term of geometric sequence, given thata₁ = 1 and r= 2, what is the value of the 4th term?

a)

2

b)

8

c)

4

d)

16

72.

Find the sum of the first four terms of the geometric sequence that begins with 1 with a common ratio of 3.

a)

25

b)

37

c)

40

d)

80

73.

Evaluate the sum of the geometric sequence 1 + 2 + 4 + 8..., n = 6

a)

63

b)

60

c)

46

d)

56

74.

Find the common ratio for the geometric sequence.

a)

1

b)

-1

c)

7

d)

-7

75.

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

76.

What is the sum of the first three terms of the sequence 3, 15, 75,375...?

a)

15

b)

67

c)

93

d)

125

77.

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

a)

$10

b)

$300

c)

$162

d)

$416

78.

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

79.

What is the nth term of a geometric sequence where $a_3=\frac{50}{9}$ and $a_5=\frac{6250}{243}$ ?

a)

$a_n=\left(\frac{5}{3}\right)^{n-1}$

b)

$a_n=2\left(\frac{5}{3}\right)^{n-1}$

c)

$a_n=-2\left(\frac{5}{3}\right)^{n-1}$

d)

$a_n=\frac{1}{2}\left(\frac{5}{3}\right)^{n-1}$

80.

A sequence can be generated by using $a_n=4\ a_{\left(n-1\right)},$ where $a_1=6$ and n is a whole number greater than 1. What are the first four terms in the sequence?

a)

6, 24, 96, 384

b)

6, 10, 14, 18

c)

6, 20, 100, 500

d)

6, 20, 76, 300

81.

A culture initially contains 200 bacteria. If the number of bacteria doubles every 2 hours, how many bacteria will be in the culture at the end of 12 hours?

a)

819200

b)

409600

c)

6400

d)

12800

FA in Geometric Sequence and Series

Total questions: 81

Worksheet time: 3hrs 42mins

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