Free Printable Pre-Assessment 1.3 Arithmetic Sequence and Series

1.

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

a)

14

b)

68

c)

63

d)

71

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.

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

4.

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

a)

Yes

b)

No

5.

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

a)

-515

b)

-490

c)

-535

d)

460

6.

Find the sum of the arithmetic series described:

2 + (-2) + (-6) + (-10)..., S₁₀

a)

-160

b)

-328

c)

-320

d)

-336

7.

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

8.

a₁=5, a₂=11, a₁₅=?

a)

95

b)

89

c)

81

d)

159

9.

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

a)

305

b)

503

c)

53

d)

8

10.

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

11.

What is the 7th term in the sequence

7, 11, 15, … ?

a)

30

b)

31

c)

32

d)

33

12.

What is the common difference inthe sequence -7, -5, -3, -1, … ?

a)

1/2

b)

-1/2

c)

2

d)

-2

13.

The 6th term in the arithmetic sequence

18, 11, 4, …

a)

-3

b)

-10

c)

-17

d)

-24

14.

Which of the following is NOT an arithmetic sequence?

a)

48, 24, 12, 6, 3, ...

b)

3, 7, 11, 15, 19, ...

c)

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

d)

1, 0, -1, -2, -3, ...

15.

It is a sequence that has a common difference.

a)

Arithmetic Means

b)

Arithmetic Sequence

c)

Arithmetic Series

d)

Arithmetic Pattern

16.

Insert 5 arithmetic means in the sequence

-3, ___, ___, ___, ___, ___, 12

a)

$-\frac{3}{2},\ 1,\ \frac{7}{2},\ 6,\ \frac{17}{2}\$

b)

$-1,\ 3,\ 6,\ 9,\ 11\$

c)

$0,\ \frac{1}{2},\ 3,\ \frac{5}{2},\ 6,\ \frac{7}{2}\$

d)

$-\frac{1}{2},\ 2,\ \frac{9}{2},\ 7,\ \frac{19}{2}\$

17.

These are terms between any two non-consecutive terms of an arithmetic sequence.

a)

Arithmetic Means

b)

Arithmetic Sequences

c)

Arithmetic Series

d)

Arithmetic Pattern

18.

A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd, and so on, how many seats are there in all? Assume the pattern continues.

a)

2,791 seats

b)

2,803 seats

c)

2,816 seats

d)

2.829 seats

19.

It is the sum of definite number of terms of an arithmetic sequence

a)

Arithmetic Means

b)

Arithmetic Sequence

c)

Arithmetic Series

d)

Arithmetic Patterns

20.

Which of the following is the correct formula for finding the Arithmetic Series?

a)

$S_n=2n\left(a_1\cdot a_n\right)$

b)

$S_n=2n\left(a_1+a_n\right)$

c)

$S_n=\frac{n}{2}\left(a_1\cdot a_n\right)$

d)

$S_n=\frac{n}{2}\left(a_1+a_n\right)$

21.

Is the sequence arithmetic: 86, 81, 76, 70, ...

a)

Yes

b)

No

22.

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

a)

8

b)

11

c)

-11

d)

-8

23.

Create the explicit formula for the sequence:

2, 8, 14, ...

a)

a_n= 2 + 6n

b)

a_n= -6 + 6n

c)

a_n= 6n - 4

d)

a_n= 4 - 6n

24.

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

a)

18

b)

17

c)

15

d)

14

25.

Find S_n for the given series:
a₁=22
d=-8
n=21

a)

1911

b)

-1449

c)

-2436

d)

-1218

26.

Find the sum of the first 100 odd numbers

a)

2500

b)

5000

c)

10000

d)

100000

27.

Find the 35th term in the arithmetic sequence: -10, -14, -18, -22, ...

a)

-216

b)

-148

c)

-146

d)

-150

28.

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

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

29.

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

30.

The first term of an arithmetic sequence is 4 and the common difference is 5. What will be the 12th term?

a)

500

b)

59

c)

54

d)

64

31.

Which sequence(s) represent an arithmetic sequence?

a)

a and e

b)

a, b, and e

c)

b, c, and d

d)

b

32.

An arithmetic sequence is given below.

2, 9, 16, 23, ...

Which is the explicit formula for the n^th term a_n?

a)

a_n= -7n+9

b)

a_n= 7n-5

c)

a_n= 7n-9

d)

a_n= -7n+5

33.

Evaluate the arithmetic series described:
2 + (-2) + (-6) + (-10)..., S₁₀

a)

-160

b)

-328

c)

-320

d)

-336

34.

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

a)

14

b)

20

c)

26

d)

29

35.

You are sitting in row 23 and notice there are 65 seats in your row. The row in front of you has 63 seats and the row behind you has 67 seats. There are 42 rows in the auditorium. How many seats does the auditorium contain? (Hint: Find the number of seats in the first and last rows)

a)

2,604

b)

2,163

c)

2,422

d)

2,803

36.

A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd, and so on, how many seats are there in all? Assume the pattern continues.

(a)

37.

Viola makes gift baskets for Valentine’s Day. She has 13 baskets left over from last year, and she plans to make 12 more each day. If there are 15 work days until the day she begins to sell the baskets, how many baskets will she have to sell? (Sequence or Series)

a)

193 baskets

b)

205 baskets

c)

156 baskets

d)

181 baskets

38.

A large asteroid crashed into a moon of a planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic sequence 26, 44, 62, 80, . . . . Find the total distance that the projectile traveled in seven seconds

(a)

39.

Alyssa earned Php17,000 during the first year of her job at city hall. After each year she received a 4% raise. Find her total earnings during the first five years on the job.

a)

Php 3,541.44

b)

Php 517,077.48

c)

Php 72,189.89

d)

Php 92,077.48

40.

Define arithmetic sequences.

a)

A sequence whose terms change by adding the same number each time.

b)

A sequence whose terms change by multiplying the same number each time.

c)

A sequence whose terms change by dividing the same number each time.

d)

A list of numbers that often (but not always) form a pattern.

41.

For a certain arithmetic sequence, $d=4$ and $a_{30}=57.$ What is a rule for the nth term of the sequence?

a)

$a_n=-63-4n$

b)

$a_n=-59-4n$

c)

$a_n=-63+4n$

d)

$a_n=-59+4n$

42.

Determine the sum of the series written in Sigma Notation.

a)

5400

b)

2692

c)

2700

d)

2704

43.

It is a sequence in which the difference between consecutive terms is the same.

a)

Common Difference

b)

Common Sequence

c)

Arithmetic Sequence

d)

Arithmetic Series

44.

Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...

a)

61, 70, 79

b)

62,73,84

c)

61, 70, 88

d)

60, 79, 88

45.

What are the first 4 terms of an arithmetic sequence with a pattern of -6 if the first term is 76?

a)

76,82,86,90

b)

76,80,86,90

c)

76,70,64,58

d)

76,70,66,50

46.

Find how many terms are in the series below:
7+13+19+25...=1044

a)

16

b)

17

c)

18

d)

19

47.

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

48.

Find the missing terms of the arithmetic sequence:
145, ___, ___, ___, 205

a)

160, 175, 190

b)

165, 185, 195

c)

155, 165, 175

d)

190, 175, 160

49.

a)

A.

b)

B.

c)

C.

d)

D.

50.

a)

A.

b)

B.

c)

C.

d)

D.

51.

a)

A.

b)

B.

c)

C.

d)

D.

52.

Given the first $6$ terms of the arithmetic sequence:

$1,\ 6,\ 11,\ 16,\ 21,\ 26,...$ , find the common difference $d$ and the $7th$ term.

Hint: You can use $a_n=a_{\left(n-1\right)}+d$ or use $a_n=a_1+\left(n-1\right)d$ . To find the common difference $d$ , select a term in the sequence and subtract the preceding term.

a)

$d=-5$

$7th\ term=21$

b)

$d=5$

$7th\ term=36$

c)

$d=5$

$7th\ term=31$

d)

$d=7$

$7th\ term=33$

53.

Viola makes gift baskets for Valentine’s Day. She has 13 baskets left over from last year, and she plans to make 12 more each day. If there are 15 work days until the day she begins to sell the baskets, how many baskets will she have to sell? (Sequence or Series)

a)

193 baskets

b)

205 baskets

c)

156 baskets

d)

181 baskets

Pre-Assessment 1.3 Arithmetic Sequence and Series

Total questions: 53

Worksheet time: 4hrs 25mins

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