Free Printable Sequences and Series

1.

Find the sum of the series.

a)

732

b)

-732

c)

244

d)

-244

2.

How many terms must be added in the summation?

a)

4

b)

5

c)

6

d)

8

3.

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)

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

4.

Find the sum of the first 10 terms for the series: -1 + 2 + 5 + 8 + ...

a)

122

b)

125

c)

128

d)

131

5.

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

a)

14

b)

68

c)

63

d)

71

6.

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

a)

8

b)

11

c)

-11

d)

-8

7.

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

a)

18

b)

17

c)

15

d)

14

8.

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

9.

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

a)

64

b)

32

c)

108

d)

20

10.

Evaluate the series.

a)

36

b)

85

c)

35

d)

86

11.

Find the sum for the following series.

a)

44

b)

-162

c)

-682

d)

324

12.

The arithmetic 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

13.

Find the sum of the series described:

2 + (-2) + (-6) + (-10)..., S₁₀

a)

-160

b)

-328

c)

-320

d)

-336

14.

A sequence is a function whose domain is the set of positive integers. It is also means an ordered list of numbers.

a)

True

b)

False

15.

A sequence is infinite if its domain is the set of positive integers without a last term .

a)

True

b)

False

16.

What is the common difference of an arithmetic sequence whose 6th term is 13 and whose 22th term is 77?

a)

10

b)

8

c)

6

d)

4

17.

What is the next term in the arithmetic sequence 13, 7, 1, -5,...

a)

-1

b)

-6

c)

-11

d)

-13

18.

Which of the following sequence is an arithmetic ?

a)

1,2,4,8,...

b)

4,-5,-14,-25

c)

$1,\ \frac{1}{2},\frac{1}{3},\frac{1}{4}$

d)

6.3, 9.44, 12.58, 15.72

19.

How many multiples of 3 are in between 100 and 400?

a)

99

b)

100

c)

101

d)

102

20.

Find the sum of all multiples of 3 between 100 and 400.

a)

25,150

b)

25,100

c)

25,050

d)

25,000

21.

What is the general term of the sequence whose first term is $\frac{25}{4}$ and a common difference of $\frac{-3}{4}$ ?

a)

$a_n=\frac{-3n}{4}+7$

b)

$a_n=\frac{3n}{4}-7$

c)

$a_n=\frac{25}{4}-3n$

d)

$a_n=\frac{-3n-25}{4}$

22.

Insert three arithmetic means between 10 and 12

a)

$\frac{19}{2},\frac{21}{2},\frac{23}{2}$

b)

$\frac{21}{2},11,\frac{23}{2}$

c)

$\frac{17}{2},\frac{19}{2},\frac{21}{2}$

d)

$\frac{17}{2},\ \frac{18}{2},\frac{19}{2}$

23.

What is the arithmetic mean of 8 and 25?

a)

15.5

b)

16

c)

16.5

d)

17

24.

The 4th term of an arithmetic sequence is 14, and the 20th term is 110, What is the 34th term?

a)

566

b)

490

c)

224

d)

194

25.

Which term of the arithmetic sequence 2,5,8,...,is 110?

a)

39

b)

38

c)

37

d)

36

26.

A theater was designed to have 12 seats in the first row, 15 seats in the second row, 18 seats in the third row and so on. If the theater has seating capacity of 255 seats. How many rows does it have?

a)

17

b)

15

c)

13

d)

10

27.

Find the sum of all the multiples of 6 between 1 to 100.

a)

800

b)

816

c)

832

d)

848

28.

Evaluate the summation $\sum_{n=1}^5\left(3^n-1\right)$ . What is the related series ?

a)

1+3+9+27+81=121

b)

2+4+16+32+64=118

c)

2+5+8+11+14=40

d)

2+8+26+80+242=358

29.

An amphitheater has 25 seats in the first row, 27 seats in the second row, 29 seats in the third row, and so on. If there are 30 rows altogether , what is the seating capacity of the amphitheater?

a)

1500 seats

b)

1185 seats

c)

1620 seats

d)

3240 seats

30.

The arithmetic mean ( average) of a set of numbers $x_1,\ x_2,\ x_3,\ x_4\ ,...x_n$ is given by the formula $\overline{x}=\frac{x_1+_{ }x_2+x_3+x_4+...+x_{n\ }\ }{n}$ = $\frac{\sum_{ }^{ }x}{n}$

a)

True

b)

False

Sequences and Series

Total questions: 30

Worksheet time: 1hrs 27mins

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