Free Printable Sequence and series- arithmetic and geometric progressions

1.

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

a)

14

b)

101

c)

206

d)

10

2.

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

3.

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

a)

-2,048

b)

6,144

c)

-6,144

d)

-531,441

4.

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

5.

a)

149

b)

11,200

c)

5,600

d)

140

6.

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

7.

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

8.

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

9.

Find the 13th term:
2, 6, 18, 54, ….

a)

1,000,000

b)

1,062,882

c)

123,587

d)

5 bazillion

10.

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

11.

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

a)

81

b)

-34

c)

-146

d)

-225

12.

Find the geometric sum

a)

-1456

b)

-4095

c)

1456

d)

4095

13.

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

a)

-59,048

b)

-39,366

c)

-19,682

d)

-4,374

14.

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

15.

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

16.

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. . .}

17.

Find the 12th term of the arithmetic sequences 5, 11, 17, 23,..

a)

70

b)

71

c)

-71

d)

-70

18.

Find the 15th term of the arithmetic sequences -3, -8, -13,..

a)

-70

b)

-73

c)

70

d)

73

19.

Find the 7th term of the arithmetic progressions $\frac{2}{3},\frac{6}{5},\frac{26}{15},...$

a)

-58/15

b)

-50/15

c)

58/15

d)

50/15

20.

Find the sum of the first 9 terms of arithmetic progressions 21, 15, 9,...

a)

-27

b)

27

c)

-20

d)

20

21.

Find the sum of the first 18 terms of arithmetic progressions -8, 0, 8,...

a)

-1080

b)

-1800

c)

1800

d)

1080

22.

Find the sum of the arithmetic progressions 7, 9, 11,...,79. (Hint: find Tn first)

a)

1591

b)

-1591

c)

-1590

d)

1590

23.

Find the sum of the arithmetic progressions 0.05, 0.15, 0.25, ..., 4.05. (Hint: find Tn first)

a)

-84

b)

84

c)

-84.05

d)

84.05

24.

In an arithmetic sequence, the fifth term is 34 and the tenth term is 43. Find the sum of the first 20 terms of the sequence.

a)

878

b)

-878

c)

787

d)

-787

25.

The first three terms of an arithmetic sequence are m, 2m+n, 3m+2n,... Find the tenth term in terms of m and n.

a)

10m-9n

b)

-10m-9n

c)

10m+9n

d)

-10m+9n

26.

The third term of an arithmetic sequence is 12 and the sum of the first eight terms is 168. Find the 14th term.

a)

78

b)

-78

c)

-70

d)

70

27.

Find the 10th term of the geometric sequences $\frac{1}{2},1,2,4,...$

a)

-256

b)

256

c)

265

d)

-265

28.

Find the 8th term of the geometric progression -16, 8, -4, 2,...

a)

-1/18

b)

-1/8

c)

1/8

d)

1/18

29.

Find the 9th term of the geometric sequences 0.1, 0.01, 0.001,...

a)

$1\times10^{-9}$

b)

$-1\times10^{-9}$

c)

$1\times10^9$

d)

$-1\times10^9$

30.

Find the sum of the first 8 terms of geometric progressions 3, 6, 12, 24,...

a)

765

b)

-765

c)

756

d)

-756

31.

Find the sum of the first 20 terms of geometric progressions 81, 27, 9, 3,...

a)

120.5

b)

121.5

c)

-120.5

d)

-121.5

32.

Find the sum of the first 10 terms of geometric sequences -240, 48, -9.6, 1.92,...

a)

-100

b)

100

c)

200

d)

-200

33.

The third term of a geometric progression is 128 and the seventh term is 40.5. Find the fifth term and the sum to infinity.

a)

$T_5=-72;\ S_{\infty}=910.22$

b)

$T_5=72;\ S_{\infty}=910.22$

c)

$T_5=72;\ S_{\infty}=-910.22$

d)

$T_5=-72;\ S_{\infty}=-910.22$

34.

For what values of x does the sequence

$3,\ 6x,\ 12x^2,...$ have a sum to infinity? ()Hin

a)

$-\frac{1}{2}<x<\frac{1}{2}$

b)

$-\frac{1}{2}>x>\frac{1}{2}$

c)

$-1<x<1$

d)

$-1>x>1$

35.

Find the fifth term of the geometric sequence with a first term of 8 and a sum to infinity of 12.

a)

$T_5=\frac{8}{80}$

b)

$T_5=\frac{8}{81}$

c)

$T_5=-\frac{8}{81}$

d)

$T_5=-\frac{8}{80}$

36.

The first three terms of a geometric sequence are $\sqrt{2},2,\sqrt{8}$ . Find the common ratio, r, and the sixth term of the sequence.

a)

$r=-\sqrt{2};\ T_6=8$

b)

$r=\sqrt{2};\ T_6=-8$

c)

$r=\sqrt{2};\ T_6=8$

d)

$r=-\sqrt{2};\ T_6=-8$

37.

What is the common ratio in this geometric sequence?

{96, 48, 24, 12, ... }

a)

1/2

b)

2

c)

12

d)

24

38.

Which functions describe the sequence -5, 0, 5, 10, . . .? PICK 2

a)

f(1)=-10; f(n)=f(n-1)+5

b)

f(1)=-5; f(n)=f(n-1)+5

c)

f(x)=5x-10

d)

f(x)=5x-5

39.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

40.

Identify the common difference.
97, 86, 75, 64, ...

a)

8

b)

11

c)

-11

d)

-8

41.

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

a)

18

b)

17

c)

15

d)

14

42.

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

43.

Is the sequence arithmetic: 17, 9, 1, -7, ...

a)

Yes

b)

No

44.

Find a₂₆ in the arithmetic sequence: -15, -35, -55, -75, ...

a)

-515

b)

-490

c)

-535

d)

460

45.

a₁=5, a₂=11, a₁₅=?

a)

95

b)

89

c)

81

d)

159

46.

Find the sum of the arithmetic series described:

2 + (-2) + (-6) + (-10)..., S₁₀

a)

-160

b)

-328

c)

-320

d)

-336

47.

The sequence 28, 34, 40, 46, 52, ..., 88 has 11 terms. Find the sum of the 11 terms.

a)

550

b)

638

c)

610

d)

288

48.

Evaluate: $\sum_{x=2}^{11}\left(5x-2\right)$

a)

305

b)

503

c)

53

d)

8

49.

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

50.

Expand: $\sum_{k=3}^6\left(2k-1\right)$

a)

4, 6, 8, 10

b)

4, 6, 8

c)

5, 7, 9, 11

d)

5, 7, 9

51.

The explicit formula is used to find a specific term in a sequence.

a)

True

b)

False

52.

The recursive formula can only be used if you know the previuos term

a)

True

b)

False

53.

What are the next 3 terms in this sequence of terms? 3, 7, 11, 15

a)

18, 22, 26

b)

19, 21, 23

c)

19, 23, 27

d)

18, 21, 24

54.

Find the EXPLICIT arithmetic sequence formula for the following data set: 2, 4, 6, 8...

a)

2n

b)

2n - 2

c)

2n + 4

d)

4n

55.

When the terms of a sequence differ by the same non zero number it is called what kind of sequence?

a)

Algebraic

b)

Neither

c)

Geometric

d)

Arithmetic

56.

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

57.

What is the previous term for:
-6, 1, 8, 15...

a)

-13

b)

13

c)

1

d)

-12

58.

Find the 22nd term. a₁=10, d=5

a)

115

b)

200

c)

10

d)

220

59.

What is the common ratio for the sequence:
28, 14, 7, 3.5...

a)

2

b)

1/2

c)

-14

d)

-7

60.

Find the common ratio: 64, -16, 4, -1, ...

a)

r = -8

b)

r = -1/4

c)

r = -4

d)

r = 4

61.

Find the next three terms: 4, 12, 36, 108, ...

a)

324, 972, 2916

b)

972, 2916, 8748

c)

405, 1215, 3645

62.

Given the sequence:
125, 25, 5, ....
Write the explicit rule:

a)

y = (125)(5)^(x)

b)

y = 125(1/5)^(x)

c)

y = 625(5)^(x)

d)

y = 125 + 5x

63.

Is this sequence arithmetic, geometric, or neither?
1,2,4,7,11,16,22,...

a)

arithmetic

b)

geometric

c)

neither

d)

none of the above

64.

What is the explicit rule for the sequence:
4, 12, 36, ...

a)

a_n = 4/3(3)ⁿ

b)

a_n = 4x3

c)

a_n = 2(3)ⁿ

65.

a)

196

b)

392

c)

49

d)

254

66.

Calculate the final sum/total of the series.

a)

6

b)

21

c)

9

d)

2

67.

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

68.

a)

149

b)

11,200

c)

5,600

d)

140

69.

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

70.

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

71.

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

72.

To find the next term in an arithmetic sequence…

a)

add the common difference d

b)

multiply by the common ratio r

73.

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

a)

6

b)

7

c)

3

d)

2

74.

Evaluate S_n:

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

(Hint: is this arithmetic or geometric?)

a)

2384

b)

595

c)

1192

d)

1190

75.

Evaluate S₈:

2 + 6 + 10 + 14 + ...

a)

128

b)

494

c)

256

d)

255

76.

Evaluate the sum of the geometric series:

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

a)

65104

b)

56732

c)

-1/6

d)

65816

77.

Evaluate sum S₈:

a₁=?, a₈=839,808, r= -6

a)

717456

b)

719835

c)

665624

d)

668938

78.

Evaluate S₁₂ for the arithmetic series where:

a₁=?, a₁₂=48, and d=4

a)

310

b)

312

c)

620

d)

624

79.

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

a)

9

b)

10

c)

11

d)

12

80.

Find the sum of a geometric series where

a₁=4, r = -2 , a_n = 16,384

a)

-10,921.3333333

b)

10,922

c)

10,924

d)

-10,924

81.

Find the common ratio in the geometric sequence

1, -3, 9, -27

a)

-3

b)

3

c)

4

d)

20

82.

Determine whether the sequence is arithmetic or geometric and find the next term.

45, 90, 180, 360, ____

a)

geometric 720

b)

arithmetic 720

c)

geometric 540

d)

arithmetic 540

83.

Determine whether the sequence is arithmetic or geometric and find the next term.

25, 50, 75, 100, ____

a)

arithmetic 125

b)

geometric 125

c)

arithmetic 200

d)

geometric 200

84.

What is the common difference in this arithmetic sequence? 7, 10, 13, 16, ...

a)

3

b)

4

c)

0

d)

1/3

85.

Find the missing term in the arithmetic sequence

84, _____, 110

a)

95

b)

97

c)

90

d)

100

86.

What is the common difference in this arithmetic sequence? 2, 11, 20, 29, ...

a)

10

b)

9

c)

11

d)

12

87.

What is the common difference in this arithmetic sequence? 23, 19, 15, 11, 7, ...

a)

-3

b)

-4

c)

0

d)

3

88.

What is the formula for an arithmetic sequence?

a)

an = a * (r)^n-1

b)

an = a * r

c)

an = a + (r-1)^d

d)

an = a + (n-1)(d)

89.

What is the formula for a geometric sequence?

a)

an = a * (r)^n-1

b)

an = a * r

c)

an = a + (r-1)^d

d)

an = a + (n-1)(d)

90.

A arithmetic sequence is a sequence who's pattern involves

a)

adding or subtracting

b)

multiplying or dividing

c)

addition and dividing

d)

nothing

91.

A geometric sequence is a sequence who's pattern involves

a)

adding or subtracting

b)

multiplying or dividing

c)

addition and dividing

d)

nothing

92.

Is the sequence arithmetic: 78, 785, 7855, 78555, ...

a)

Yes

b)

No

93.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

94.

If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be

a)

7

b)

11

c)

18

d)

0

95.

Find the 26th term in the arithmetic sequence: 20, 26, 32, 38, ...

a)

182

b)

176

c)

170

d)

-118

96.

The following are Arithmetic Progressions, except

a)

12, 6, 3, ...

b)

4, 2, 0, ...

c)

x, x+2, x+4, ...

d)

$\frac{1}{2},\ 0,\ -\frac{1}{2},\ ...$

97.

$10^{th}$ term of the AP y, y + 2, y + 4 , ... is 16, find the value of y.

a)

-4

b)

-2

c)

0

d)

2

98.

The 7^th term of an AP is 3 times the 2^nd term, find a relation between a and d.

a)

$a=\frac{3}{2}d$

b)

$a=\frac{2}{3}d$

c)

$a=\frac{1}{2}d$

d)

$a=3d$

99.

How many terms of the AP 2, 7, 12, ... will add up to 156?

a)

7

b)

8

c)

9

d)

10

100.

The sum of the first 11^th term of an AP is 120, and the sum of the first 12^th term is 132. Find the value of the 12^th term.

a)

12

b)

-12

c)

32

d)

-32

101.

The first three terms of an AP are -2, -4, -6, .... Find the sum of the 25 terms after the 3^rd term.

a)

-812

b)

-800

c)

-788

d)

-650

102.

The next term of an AP $\sqrt{7}$ , $\sqrt{28}$ , $\sqrt{63}$ ,......is

a)

$\sqrt{70}$

b)

$\sqrt{84}$

c)

$\sqrt{98}$

d)

$\sqrt{112}$

103.

If 4, x₁,x₂,x₃,28 are in AP then x₃ is ______

a)

19

b)

23

c)

22

d)

cannot be determined.

104.

The sum of first 'n' terms of an AP is (3n²+6n). The common difference of the AP is ______

a)

6

b)

9

c)

15

d)

-3

105.

The 5^th term of an AP is -3 and its common difference is -4. The sum of its first 10 terms is_________

a)

50

b)

-50

c)

30

d)

-30

106.

The 13^th term of an AP is 4 times its 3^rd term. If its 5^th term is 16 then the sum of its first ten terms is _______

a)

150

b)

175

c)

160

d)

135

107.

Which term of an AP 72, 63, 54, ...... is 0 ?

a)

8^th

b)

9^th

c)

10^th

d)

11^th

108.

Formula to find sum of n terms in an AP is ________

a)

sn = a+ (n - 1)d

b)

$s_n$ = $\frac{n}{2}$ (a +(n-1)d)

c)

undefined= undefined (2a +(n-1)d)

d)

undefined= undefined (2a +(n+1)d)

109.

What is the common difference of an AP in which a₁₈ - a₁₄ = 32?

a)

8

b)

-8

c)

4

d)

-4

110.

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

111.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

112.

Find the first term of the given sequence:
a₁₄=68
d=3

a)

14

b)

20

c)

26

d)

29

113.

What is the a₁₂ term in the following sequence? 2, 4, 6, 8, 10, 12, ………..

a)

46

b)

34

c)

24

d)

88

114.

Is this sequence Arithmetic, Geometric, or Neither?
{2, 9, 7, 14, 12, 19, ... }

a)

Arithmetic

b)

Geometric

c)

Neither

115.

What is the 38th term of this sequence?
{26, 22, 18, 14, ... }

a)

-4

b)

10

c)

-122

d)

174

116.

What is the common ratio of this sequence?
{2, 10, 50, 250, ... }

a)

1,250

b)

5

c)

10

d)

50

117.

What is the common difference in this sequence?
{48, 32, 16, 0, ... }

a)

1/2

b)

2

c)

-8

d)

-16

118.

Find the 10th term of this sequence:
{96, 48, 24, 12, ... }

a)

3/16

b)

1/2

c)

6

d)

3

119.

These are the first three terms of an arithmetic sequence:
{½, ¾, 1, ... }
What are the fourth and fifth terms of the sequence?

a)

5/4, 7/4

b)

5/4, 3/2

c)

3/2, 5/2

d)

3/2, 2

120.

What are the first three terms of the sequence defined by the following equation?
a_n = 7 + (n - 1)5

a)

7, 35, 175

b)

7, 2, -3

c)

12, 17, 22

d)

7, 12, 17

121.

Is this sequence arithmetic, geometric, or neither?
{26, 22, 18, 14, ...}

a)

Arithmetic

b)

Geometric

c)

Neither

122.

What kind of sequence is illustrated below?
400, 200, 100, 50, 25, ...

a)

Arithmetic

b)

Geometric

c)

Neither

123.

Which kind of sequence has a common difference?

a)

Arithmetic

b)

Geometric

124.

The individual numbers in a sequences are called...

a)

Common difference

b)

Successive term

c)

Term

d)

Geometric term

125.

What is the common ratio of the geometric sequence below?
5, 25, 125, 625...

a)

25

b)

20

c)

5

d)

4

126.

What is the common difference of the arithmetic sequence below?
-6, -1, 4, 9...

a)

5

b)

-5

c)

-6

d)

1/5

127.

What is the 8th term in the sequence below?
3, 9, 27, 81, ...

a)

19,683

b)

6,561

c)

2,187

d)

729

128.

The next term of the series 11,8,5,2 is...

a)

-1

b)

-2

c)

1

d)

2

129.

What are the first 4 terms of an arithmetic sequence with a common difference 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

130.

What are the first 4 terms of an arithmetic sequence with a common difference 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

Sequence and series- arithmetic and geometric progressions

Total questions: 130

Worksheet time: 4hrs 20mins

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