Free Printable Sequence and Series Unit Review Algebra 2B Riley

1.

This summation is the same as which series?

a)

1 + 2 + 3 + 4 + 5 + 6

b)

(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2) + (5 - 2) + (6 - 2)

c)

(1 - 2) + (6 - 2)

d)

(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2)

2.

This summation is the same as which series?

a)

1 + 2 + 3 + 4 + 5 + 6

b)

(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2) + (5 - 2) + (6 - 2)

c)

(1 - 2) + (6 - 2)

d)

(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2)

3.

Evaluate.

a)

290

b)

278

c)

250

d)

295

4.

Evaluate.

a)

2445

b)

3360

c)

2500

d)

3500

5.

Evaluate.

a)

539

b)

364

c)

346

d)

361

6.

Evaluate.

a)

20

b)

28

c)

18

d)

21

7.

Evaluate.

a)

112

b)

99

c)

140

d)

-8

8.

Evaluate.

a)

1260

b)

1109

c)

1400

d)

1339

9.

Evaluate.

a)

1260

b)

1200

c)

945

d)

1145

10.

Evaluate.

a)

1445

b)

2009

c)

1745

d)

1709

11.

Evaluate the series below.
$\sum_{k=0}^{\infty}\frac{2}{3}\left(\frac{1}{\left(8\right)}\right)^k$

a)

$\frac{3}{8}$

b)

$\frac{8}{3}$

c)

$\frac{16}{21}$

d)

$\frac{21}{16}$

12.

Is this summation finite or infinite?

a)

Finite, because there are only 6 terms to add up.

b)

Infinite, because there are an infinite number of terms to add up.

13.

Evaluate.

a)

225

b)

140

c)

784

d)

153

14.

The summation is the same as which series?

a)

(4+10) + (4+20) + (4+30) + (4+40) + (4+50) + (4+60) + (4+70) + (4+80) + (4+90) + (4+100) + (4+110)

b)

1+2+3+4+5+6+7+8+9+10+11

c)

4 + 110

d)

4 + 10

15.

Calculate the sum.

a)

66

b)

14

c)

704

d)

114

16.

Evaluate.

a)

290

b)

278

c)

250

d)

295

17.

Evaluate.

a)

225

b)

140

c)

784

d)

153

18.

Evaluate the arithmetic series described.

a)

481

b)

489

c)

444

d)

888

19.

Evaluate the series.

a)

36

b)

85

c)

35

d)

86

20.

What is the proper expansion for the following series?
$\sum_{k=0}^33\left(-2\right)^k$

a)

3 + (-6) + 18

b)

3 + (-6) +12

c)

3 + (-6) + 12 + (-24)

d)

-6 + 12 + (-24) + 48

21.

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

a)

305

b)

503

c)

53

d)

8

22.

Determine the sum of the series written in Sigma Notation.

a)

-1

b)

255

c)

295

d)

350

23.

Write the explicit formula for the sequence.

9, 5, 1, -3, ...

a)

$a_n=9+5\left(n-1\right)$

b)

$a_n=9-4\left(n-1\right)$

c)

$a_n=4+9\left(n-1\right)$

d)

$a_n=9\cdot4^{\left(n-1\right)}$

24.

Write the explicit formula for the sequence.

216, 72, 24, 8, ...

a)

$a_n=216\cdot\left(\frac{1}{3}\right)^{\left(n-1\right)}$

b)

$a_n=8\cdot3^{\left(n-1\right)}$

c)

$a_n=216-144\left(n-1\right)$

d)

$a_n=216\cdot3^{\left(n-1\right)}$

25.

Write the explicit formula for the sequence.

15, 22, 29, 36, 43, ...

a)

$a_n=15+22\left(n-1\right)$

b)

$a_n=15\cdot7^{\left(n-1\right)}$

c)

$a_n=15+7\left(n-1\right)$

d)

$a_n=29-14^{\left(n-1\right)}$

26.

Write the explicit formula for the sequence.

7, 28, 112, 448, ...

a)

$a_n=7+4\left(n-1\right)$

b)

$a_n=7\cdot4^{\left(n-1\right)}$

c)

$a_n=\frac{448}{4n}$

d)

$a_n=28+84\left(n-1\right)$

27.

Write the explicit formula for the sequence.

10, -2, -14, -26, ...

a)

$a_n=10\cdot\left(-\frac{1}{5}\right)^{\left(n-1\right)}$

b)

$a_n=-2\cdot7^{\left(n-1\right)}$

c)

$a_n=10-8\left(n-1\right)$

d)

$a_n=10-12\left(n-1\right)$

28.

Determine if the following sequence is arithmetic or geometric.

6, 30, 150, 750, ...

a)

Arithmetic

b)

Geometric

29.

Determine if the following sequence is arithmetic or geometric.

2, 5, 8, 11, 14, ...

a)

Arithmetic

b)

Geometric

30.

Determine if the following sequence is arithmetic or geometric.

80, 20, 5, 1.25, ...

a)

Arithmetic

b)

Geometric

31.

Determine if the following sequence is arithmetic or geometric.

-3, -6, -12, -24, ...

a)

Arithmetic

b)

Geometric

32.

Determine if the following sequence is arithmetic or geometric.

1, 7, 13, 19, ...

a)

Arithmetic

b)

Geometric

33.

Use the explicit formula to find the first four terms of the sequence.
$a_n=3+5\left(n-1\right)$

a)

3, 15, 75, 375

b)

3, 8, 13, 18

c)

5, 8, 11, 14

d)

5, 15, 45, 135

34.

Use the explicit formula to find the first four terms of the sequence.
$a_n=9\cdot4^{\left(n-1\right)}$

a)

4, 36, 324, 2916

b)

9, 36, 144, 576

c)

9, 13, 17, 21

d)

4, -5, -14, -23

35.

Use the explicit formula to find the 7th term of the sequence.
$a_n=22-3\left(n-1\right)$

a)

4

b)

1

c)

18

d)

114

36.

Use the explicit formula to find the 5th term of the sequence.
$a_n=3\cdot2^{\left(n-1\right)}$

a)

24

b)

7,776

c)

48

d)

96

37.

Use the explicit formula to find the 3rd term of the sequence.
$a_n=128\cdot\left(\frac{1}{2}\right)^{\left(n-1\right)}$

a)

64

b)

32

c)

16

d)

8

38.

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint: Write your formula and then simplify it.)

a)

a_n=2+6n

b)

a_n=-6+6n

c)

a_n=6n-4

d)

a_n=4-6n

39.

Find the explicit formula:
-3, -33, -63, -93, ...

a)

a_n = -3 - 30(n -1)

b)

a_n = -3 + 30(n -1)

c)

a_n = -30 - 3(n -1)

d)

a_n = -30 + 3(n -1)

40.

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

a)

14

b)

68

c)

63

d)

71

41.

Find the 32nd term of this sequence.
34, 37, 40, 43, ...

a)

32

b)

64

c)

127

d)

356

42.

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence. (Hint: Simplify your equation.)

a)

a_n = 4n + 29

b)

a_n = -4n + 25

c)

a_n= -4n + 29

d)

a_n = 4n + 25

43.

What is the 15th term of the sequence an = -3n+50

a)

95

b)

-5

c)

5

d)

-95

44.

Find the explicit formula:
-23, -16, -9, -2, ...

a)

a_n = -23 + 7(n -1)

b)

a_n = -23 - 7(n -1)

c)

a_n = 7 - 23(n -1)

d)

a_n = 7 + 23(n -1)

45.

What is the explicit formula for the sequence?

4, -20, 100, -500, ...

a)

$a_n=4\left(2\right)^{n-1}$

b)

$a_n=4\left(-5\right)^{n-1}$

c)

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

d)

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

46.

What is the explicit formula for the sequence?

-1, 2, -4, 8, ...

a)

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

b)

$a_n=-\frac{1}{4}\left(2\right)^{n-1}$

c)

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

d)

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

47.

What is the explicit formula for the sequence?

2, 6, 18, 54, ...

a)

$a_n=-9\left(-5\right)^{n-1}$

b)

$a_n=-10\left(-5\right)^{n-1}$

c)

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

d)

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

48.

What is the explicit formula for the sequence?

-4, -8, -16, -32,...

a)

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

b)

$a_n=-4\left(2\right)^{n-1}$

c)

$a_n=-2^{n-1}$

d)

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

49.

What is the explicit formula for the sequence?

-3, 6, -12, 24,...

a)

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

b)

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

c)

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

d)

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

50.

What is the explicit formula for the sequence?

192, 48, 12, 3, ...

a)

$a_n=3\left(\frac{1}{4}\right)^{n-1}$

b)

$a_n=3\left(4\right)^{n-1}$

c)

$a_n=192\left(\frac{1}{4}\right)^{n-1}$

d)

$a_n=192\left(4\right)^{n-1}$

51.

What is the explicit formula for the sequence?

-2, -4, -8, -16,...

a)

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

b)

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

c)

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

d)

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

52.

What is the explicit formula for the sequence?

3, 15, 75, 375, ...

a)

$a_n=-4^{n-1}$

b)

$a_n=-4\left(4\right)^{n-1}$

c)

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

d)

$a_n=4\left(-5\right)^{n-1}$

53.

What is the explicit formula for the sequence?

-4, 24, -144, 864, ..

a)

$a_n=-4\left(-6\right)^{n-1}$

b)

$a_n=-5\left(-6\right)^{n-1}$

c)

$a_n=\frac{2}{3}\left(-6\right)^{n-1}$

d)

$a_n=\frac{5}{3}\left(-6\right)^{n-1}$

54.

What is the explicit formula for the sequence?

3, 15, 75, 375, ..

a)

$a_n=12\left(4\right)^{n-1}$

b)

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

c)

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

d)

$a_n=3\left(4\right)^{n-1}$

55.

Find the next three terms:
5, 8, 11, 14...

a)

16, 19, 22

b)

17, 19, 21

c)

17, 20, 23

d)

16, 18, 20

56.

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

a)

u₁ = 15
u_n = u_n-1 + 3

b)

u₀ = 15
u_n = u_n-1 + 3

c)

u₁ = 15
u_n = u_n-1 - 3

d)

u₀ = 15
u_n = u_n-1 - 3

57.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n=a_n-1+11
a₁=6

b)

a_n=a_n-1-4
a₁=6

c)

a_n=a_n-1+9
a₁=6

d)

a_n=a_n-1+6
a₁=6

58.

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

a)

-16, -21, -26, -31

b)

5, -11, -27, -43

c)

-16, -80, -500, -200

d)

-16, -11, -6, -1

59.

The next two terms of the sequence 2,-4, 8,-16 are

a)

32, 64

b)

32, -64

c)

-64, 108

d)

32, 20

60.

Determine the first 3 terms of the following sequence.
t1= -3
tn=3tn-1

a)

-3, 9, 27

b)

-3, -9, -27

c)

-3, -6, -9

d)

-3, 6,9

61.

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1- 1

a)

14

b)

13

c)

17

d)

16

62.

Write a recursive formula for the following sequence:

16,8, 4, 2,...

a)

a₁=16

a_n=2a_n-1

b)

a₁=16

a_n=.5a_n-1

c)

a₁=16

a_n=a_n-1 + .5

d)

a₁=16

a_n=a_n-1+ 2

63.

Given the recursive formula below, find the first five terms.

u₁ = 3

u_n = u_n-1 + 2

a)

3, 5, 7, 9, 11

b)

5, 7, 9, 11, 13

c)

2, 4, 6, 8, 10

d)

1, 3, 5, 7, 9

64.

Given the recursive formula below, write the first three terms.

a₁ = 4

a_n= 2a_n-1 + 5

a)

7, 19, 43

b)

4, 9, 14

c)

4, 13, 31

d)

1, 7, 19

65.

Determine if the following sequence is arithmetic or geometric.

4, 9, 14, 19, 24, ...

a)

Arithmetic

b)

Geometric

66.

Determine if the following sequence is arithmetic or geometric.

6, 12, 24, 48, 96, ...

a)

Arithmetic

b)

Geometric

67.

Identify the common difference of the given arithmetic sequence.

5, 1, -3, -7, ...

a)

d = -4

b)

d = -5

c)

d = 5

d)

d = 7

68.

Identify the common ratio for the given geometric sequence.

2, 6, 18, 54, 162, ...

a)

r = 4

b)

r = 3

c)

r = $\frac{1}{4}$

d)

r = 12

69.

Which of the following recursive formulas represents the given sequence.

4, 12, 20, 28, 36, ...

a)

$a_1=4$ , $a_n=a_{\left(n-1\right)}\cdot3$

b)

$a_1=4$ , $a_n=a_{\left(n-1\right)}+8$

c)

$a_1=4$ , $a_n=a_{\left(n-1\right)}-8$

d)

$a_1=4$ , $a_n=a_{\left(n-1\right)}\cdot9$

70.

Which of the following recursive formulas represents the given sequence.

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

a)

$a_1=7$ , $a_n=a_{\left(n-1\right)}+7$

b)

$a_1=7$ , $a_n=a_{\left(n-1\right)}\cdot7$

c)

$a_1=7$ , $a_n=a_{\left(n-1\right)}\cdot2$

d)

$a_1=7$ , $a_n=a_{\left(n-1\right)}+14$

71.

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

a₁ = 10: a_n = 3a_n-1

a)

3, 9, 27, 81

b)

10, 30, 90, 270

c)

10, 13, 16, 19

d)

30, 90, 270, 810

72.

Find the 4th term for the sequence defined by a₁=9; a_n=a_n-1+8

a)

35

b)

17

c)

41

d)

33

73.

Find the 4th term for the sequence f(1)=3, f(n)=f(n-1)+5

a)

3

b)

8

c)

15

d)

18

74.

Each individual number in a sequence of numbers is called what?

a)

Common difference

b)

Successive term

c)

Term

d)

Geometric term

75.

What does a₁ represent?

a)

Any term

b)

First term

c)

Last term

76.

Identify the rule as recursive or explicit, then find the first 4 terms of the sequence.
a₁ = 100; a_n = a_n-1 - 8

a)

Explicit; 100, 92, 84, 76

b)

Recursive; 100, 92, 84, 76

c)

Explicit; 100, 108, 116, 124

d)

Recursive; 100, 108, 116, 124

77.

What is the recursive rule for the sequence:

2, 6, 18, 54...

a)

f(1)=3, f(n)=2f(n-1)

b)

f(1)=2, f(n)=4f(n-1)

c)

f(1)=3, f(n)=2f(n-1)

d)

f(1)=2, f(n)=3f(n-1)

78.

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

a)

324, 972, 2916

b)

972, 2916, 8748

c)

405, 1215, 3645

79.

Find the 3rd term for the sequence f(1)=3, f(n)=-4*f(n-1)

a)

3

b)

-12

c)

-48

d)

48

80.

What would be the next term?

4, 8, 12, 16, ...

a)

20

b)

24

c)

0

d)

32

81.

What would be the next term?

1, 3, 9, 27,...

a)

81

b)

45

c)

243

d)

30

82.

What is the next number in the sequence?

10, 20, 30, 40.....

a)

60

b)

50

c)

65

d)

55

83.

What is the next number in the sequence?

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

a)

6

b)

10

c)

9

d)

16

84.

What is the next number in the sequence?

3, 6, 9, 12...

a)

9

b)

13

c)

15

d)

16

85.

What is the next number in the sequence?

15, 30, 45, ...

a)

60

b)

50

c)

65

d)

55

86.

What is the next number in the sequence?

100, 95, 90, 85......

a)

84

b)

90

c)

75

d)

80

87.

What is the next number in the sequence?

1, 10, 100....

a)

10000

b)

1000

c)

10,000

d)

110

Sequence and Series Unit Review Algebra 2B Riley

Total questions: 87

Worksheet time: 7hrs 15mins

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