Free Printable Sequences and Series + Fun

1.

Which term is 12,288 in the sequence given by: 3, 6, 12, 24, ...

a)

11

b)

12

c)

13

d)

14

2.

Which of the following expresses 1+3+5+...+39

a)

$\sum_{k=1}^{20}2k-1$

b)

$\sum_{k=2}^{40}k-1$

c)

$\sum_{k=-1}^{37}k+2$

d)

$\sum_{k=1}^{39}2k-1$

3.

Evaluate the arithmetic series described. (Find the sum):

a₁=0, a_n = 28, n = 8

a)

112

b)

252

c)

125

d)

119

4.

Evaluate: $\sum_{n=1}^{25}9n-19$

a)

2450

b)

4888

c)

2444

d)

4900

5.

Evaluate: $\sum_{n=1}^{15}2m+4$

a)

296

b)

299

c)

300

d)

309

6.

Evaluate the arithmetic series described. (Find the sum):

a₁= 14, a_n = 54, n = 11

a)

748

b)

374

c)

1504

d)

752

7.

15, -85, -185, -285, ...

Find a₃₄

a)

-3285

b)

-3585

c)

-3185

d)

-3385

8.

-20, -24, -28, -32, ...

Find a₂₄

a)

-116

b)

-120

c)

-118

d)

-112

9.

Find the rule or formula:

-15, -6, 3, 12, ...

a)

a_n = -15 + 9n

b)

a_n = -24 + 9n

c)

a_n = -7 + 9n

d)

a_n = -6 + 9n

10.

Find the rule or formula:

-3, 197, 397, 597, ...

a)

a_n = -203 + 200n

b)

a_n = -202 + 199n

c)

a_n = -200 + 203n

d)

a_n = -204 + 200n

11.

Find the three terms in the sequence after the last one given.

-16, -23, -30, -37, ...

a)

-61, -70, -79

b)

-52, -61, -70

c)

-44, -51, -58

d)

-42, -49, -56

12.

Find the three terms in the sequence after the last one given...

-13, 87, 187, 287, ...

a)

488, 588, 688

b)

387, 487, 587

c)

487, 587, 687

d)

391, 492, 593

13.

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

a)

14

b)

68

c)

63

d)

71

14.

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

a)

Yes

b)

No

15.

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

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

16.

a1 = 3, a2 = 6

Is it possible to tell if this sequence is arithmetic or geometric?

a)

Yes, it is arithmetic with common difference 3

b)

Yes, it is geometric with common ratio 2

c)

No, there is not enough information

17.

What is the recursive rule for the sequence:
-2, 12, -72, 432, ...

a)

a_n = -2(-6)^n-1a₁=-2

b)

a_n =a_n-1+ 10
a₁=-2

c)

a_n = -6⋅a_n-1a₁=-2

d)

a_n = a_(n-1) - 6 a₁=-2

18.

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

19.

What is the 5th term in the given sequence?
$a_n=5n-4$

a)

21

b)

16

c)

11

d)

6

20.

Write the first five terms of sequence, $a_n=4n-1$

a)

-1, 3, 7, 11, 15

b)

-5, -1, 3, 7, 11

c)

3, 7, 11, 15, 19

d)

4, 8, 12, 16, 20

21.

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

a)

8

b)

11

c)

-11

d)

-8

22.

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

23.

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

24.

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

a)

-515

b)

-490

c)

-535

d)

460

25.

An arithmetic sequence is represented by the following: $t_{n_{ }}=2n-11$ . Determine the sum of the from the 1st the 80th term.

a)

149

b)

11,200

c)

5,600

d)

140

26.

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

27.

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

28.

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

29.

The sum of an infinite Geometric series is given by:

a)

b)

c)

d)

30.

Evaluate.

a)

5461

b)

800

c)

4095

d)

6241

31.

Find the sum.

24+48+72+...+480

*Hint: Find out what term number 480 is first. Then find the sum.*

a)

5280

b)

9576

c)

10080

d)

5040

32.

What type of series is
32 + 16 + 8 + 4 + 2 + 1

a)

Finite Arithmetic

b)

Finite Geometric

c)

Infinite Arithmetic

d)

Infinite Geometric

33.

Find the common ratio: 4, -16, 64, -256, ...

a)

r = -4

b)

r = 2

c)

r = -2

d)

r = 4

34.

Find the sum: 11 + 15 + 19 + .......+ 83

a)

19

b)

83

c)

893

d)

624

35.

-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

36.

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

a)

yes

b)

no

37.

Find the sum for the following series.

a)

44

b)

-162

c)

-682

d)

324

38.

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

39.

A Greek theater has 30 seats in the first row of the center section. Each row behind the first row gains two additional seats. How many seats are in the 25^throw in the center section?

a)

66

b)

78

c)

100

d)

84

40.

Write the explicit formula for the geometric sequence: 3, -12, 48, -192,…

a)

a_n=4(3)^n-1

b)

a_n=-4(3)^n-1

c)

a_n=3(-4)^n-1

d)

a_n=3(4)^n-1

41.

Mr. Carlson suffers from allergies. When allergy season arrives, his doctor recommends that he take 300 mg of his medication the first day, and decrease the dosage by one half each day for one week. Which "rule" represents his medication doses for the week?

a)

f(n)=(1/2)n

b)

f(n)=300(1/2)^n-1

c)

f(n)=(1/2)^n-1

d)

f(n)=300+(1/2)n

42.

What is the 11th term of the geometric sequence?

-2, 10, -50, 250, …

a)

-14, 348, 907

b)

-19,531,250

c)

1,596,323

d)

45

43.

Alex earns $20,000 salary in the first year of his career. Each year, he gets a $1200 raise. How much does Alex earn in the first four years of his career?

a)

$69,200

b)

$24,800

c)

$87,200

d)

$23,600

44.

Calculate the sum of the following arithmetic series.

a)

1,435

b)

92

c)

46

d)

1,610

45.

In what type of sequence do you ADD a constant value to the previous term?

a)

Arithmetic

b)

Geometric

46.

In what type of sequence do you MULTIPLY a nonzero constant to the previous term?

a)

Arithmetic

b)

Geometric

47.

Find the indicated sum:

a)

12,720

b)

8

c)

1,272

d)

572

48.

Find the sum of the infinite geometric series, if it exists. $\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$

a)

8

b)

8/5

c)

10

d)

Does not exist

49.

Evaluate the infinite geometric series:

1 + 1/5 + 1/25 + ...

a)

5/4

b)

9/5

c)

5/6

d)

65/27

50.

Determine whether the sequence converges or diverges. If it converges, give the limit.

a)

Diverges

b)

Converges to 1

c)

Converges to 1000

51.

Evaluate the infinite series described:

a)

No Sum

b)

0

c)

-1/9

d)

-4/25

52.

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

a)

44

b)

$\frac{1}{3}$

c)

43

d)

49

53.

$-3,\ \ 6,\ -12,\ \ 24,\ ....$ Find the common ratio

a)

3

b)

-2

c)

2

d)

$\frac{1}{2}$

54.

$-4,\ -12,\ -36,\ -108,\ ...$ Find the common ratio

a)

$r=-2$

b)

$r=-3$

c)

$r=3$

d)

$r=2$

55.

$1,\ -2,\ 4,\ -8,\ ...\ \ Find\ a_{11}$

a)

$-512$

b)

$-1024$

c)

$1024$

d)

$512$

56.

$2,\ 10,\ 50,\ 250,\ ...$ Find the explicit formula

a)

$a_n=10\cdot4^{\left(n-1\right)}$

b)

$a_n=2\cdot5^{\left(n-1\right)}$

c)

$a_n=10\cdot5^{\left(n-1\right)}$

d)

$a_n=5\cdot2^{\left(n-1\right)}$

57.

$-2,\ -4,\ -8,\ -16,\ ...$ Find the explicit formula

a)

$a_n=2\cdot5^{\left(n-1\right)}$

b)

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

c)

$a_n=-2\cdot2^{\left(n-1\right)}$

d)

$a_n=2\cdot2^{\left(n-1\right)}$

58.

The first three terms of an arithmetic sequence are as follows

13, 19, 25

What are the next two terms of the sequence?

a)

31 and 37

b)

31 and 36

c)

30 and 37

d)

30 and 36

59.

Which sequence is NOT an arithmetic sequence?

a)

-7, -13, -19, -25,...

b)

-10, -6, -2, 2,..

c)

6, 8, 10, 12,...

d)

3, 15, 75, 375,...

60.

Given the recursive formula, find the explicit form
a_n = a_n-1 - 5
a₁ = 22

a)

a_n = 22 + (n-1)(-5)

b)

a_n = 22 + (n-1)(5)

c)

a_n = -5 + (n-1)(22)

d)

a_n = -16 + (n-1)(-5)

61.

Write a recursive rule for the sequence a_n = 17 + (n-1)(-16)

a)

a₁ = 17
a_n = a_n-1 + 16

b)

a₁ = 17
a_n = a_n-1 - 17

c)

a₁ = 17
a_n = a_n-1 - 15

d)

a₁ = 17
a_n = a_n-1 - 16

62.

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

a)

Explicit Formula

b)

Recursive Formula

c)

Arithmetic Formula

d)

Geometric Formula

63.

Write a recursive formula for the following sequence:

10, 5, 0, -5,...

a)

a₁= 10

a_n= a_n-1 - 5

b)

a₁= 10

a_n= a_n-1 + 5

c)

a₁= 10

a_n= a_n (5)

d)

a₁= 10

a_n= a_n-1 (5)

64.

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)

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

65.

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

66.

Find the first five terms.

a)

$-18,-11,-4,\ 3,\ 10$

b)

$-24,-18,-12,-6,\ 0$

c)

$-20,-13,-6,\ 1,\ 8$

d)

$-18,-12,-6,\ 0,\ 6$

67.

"If you can make it through the night there's a brighter day."

a)

Tupac

b)

Shakespeare

68.

"Some are born great, some achieve greatness, and some have greatness thrust upon them."

a)

Tupac

b)

Shakespeare

69.

"We know what we are, but know not what we may be."

a)

Tupac

b)

Shakespeare

70.

"I exist in the depths of solitude pondering my true goal"

a)

Tupac

b)

Shakespeare

71.

"If music be the food of love, play on."

a)

Tupac

b)

Shakespeare

72.

Cowards die many times before their deaths."

a)

Tupac

b)

Shakespeare

73.

"Fear is stronger than love."

a)

Tupac

b)

Shakespeare

74.

"Love is too young to know what conscience is."

a)

Tupac

b)

Shakespeare

75.

"You cannot escape fate. Just as you rose you shall fall, by my hands."

a)

Tupac

b)

Shakespeare

76.

"Ambition should be made of sterner stuff."

a)

Tupac

b)

Shakespeare

77.

"Everybody's at war with different things. I'm at war with my own heart sometimes."

a)

Tupac

b)

Shakespeare

78.

"A coward dies a thousand times. A soldier dies but once."

a)

Tupac

b)

Shakespeare

79.

"We must remember that tomorrow comes after the dark."

a)

Tupac

b)

Shakespeare

Sequences and Series + Fun

Total questions: 79

Worksheet time: 4hrs 48mins

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