Sequences and Series Quizzes: Master Arithmetic and Geometric Progressions

Question 1

Question: Examine the number sequence: 3, 9, 27, 81, ...
Identify the pattern and determine if it's an arithmetic or geometric sequence.

Accepted Answer

Geometric sequence with a common ratio of 3

Answer

Arithmetic sequence with a common difference of 6

Answer

Arithmetic sequence with a common difference of 3

Answer

Geometric sequence with a common ratio of 6

Question 2

Find the nth term of an arithmetic sequence that starts at 5 and decreases by 3 each time.

Accepted Answer

5 - 3n

Answer

5 + 3n

Answer

3n - 5

Answer

n - 8

Question 3

The nth term of a geometric sequence is given by 2^n. What is the common ratio?

Accepted Answer

2

Answer

1

Answer

4

Answer

8

Question 4

Which option is not a type of sequence?

Accepted Answer

Quadratic

Answer

Arithmetic

Answer

Geometric

Answer

Fibonacci

Question 5

Find the limit of the sequence: 1/2, 1/4, 1/8, ...

Accepted Answer

0

Answer

1/2

Answer

1

Answer

∞

Question 6

Which of the following sequences is convergent?

Accepted Answer

1, 1/2, 1/4, ...

Answer

1, 2, 3, ...

Answer

1, -1, 1, -1, ...

Answer

1, 2, 4, 8, 16, ...

Question 7

Find the explicit formula for the sequence: 1, 4, 9, 16, ...

Accepted Answer

a(n) = 2^n

Answer

a(n) = n^2

Answer

a(n) = n + 1

Answer

a(n) = n^3

Question 8

Identify the type of sequence: 1, 4, 9, 16, ...

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Harmonic

Answer

None of these

Question 9

Which formula can be used to find the nth term of a geometric sequence?

Accepted Answer

an = a1 * r^(n-1)

Answer

an = a1 + (n-1) * d

Answer

an = a1 / r^(n-1)

Answer

an = a1 * (r-1)^(n-1)

Question 10

Which of the following is NOT a characteristic of arithmetic sequences?

Accepted Answer

First term and common difference are not fixed

Answer

Constant difference between terms

Answer

Sum of any two consecutive terms is the same

Answer

Number of terms in a sequence can be finite or infinite

Question 11

Determine the common ratio of the geometric sequence 1, 2, 4, 8, ...

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 12

Find the nth term of the geometric sequence 3, 6, 12, 24, ...

Accepted Answer

3^n

Answer

2n

Answer

3n

Answer

6^n

Question 13

What is the general term of the geometric sequence: 3, 9, 27, 81, ...?

Accepted Answer

3^n

Answer

3(n-1)

Answer

3n

Answer

3n-1

Question 14

Which equation represents the nth term of the arithmetic sequence: 2, 5, 8, ...?

Accepted Answer

an = 2 + 3n

Answer

an = 3 + 2n

Answer

an = 5 + 3n

Answer

an = 3 + 5n

Question 15

What is the sum to infinity of the geometric series: 1 + 1/2 + 1/4 + 1/8 + ...?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 16

What is the next term in the arithmetic sequence 2, 5, 8, 11, ...?

Accepted Answer

14

Answer

15

Answer

16

Answer

17

Question 17

Find the 5th term of the sequence defined by the recurrence relation an = 3an-1 - 1, where a1 = 2.

Accepted Answer

17

Answer

14

Answer

20

Answer

23

Question 18

Which of the following is the characteristic of a convergent sequence?

Accepted Answer

Approaches a finite limit

Answer

Increases without bound

Answer

Oscillates between different values

Answer

Decreases without bound

Question 19

Which of the following gives the general term of an arithmetic sequence with first term 5 and common difference 3?

Accepted Answer

a_n = 5n + 3

Answer

a_n = 3n + 2

Answer

a_n = 3n - 5

Answer

a_n = 5n - 3

Question 20

The formula for the sum of the first n terms of an arithmetic sequence with first term a and common difference d is:

Accepted Answer

S_n = n(a + d) / 2

Answer

S_n = n(2a + d) / 2

Answer

S_n = n(a - d) / 2

Answer

S_n = n(a + 2d) / 2

Question 21

What is the general term of an arithmetic sequence?

Accepted Answer

an = a + (n - 1)d

Answer

an = a + (n + 1)d

Answer

an = a - (n - 1)d

Answer

an = a - (n + 1)d

Question 22

Which of the following sequences is NOT an arithmetic sequence?

Accepted Answer

1, 2, 4, 8, 16, ...

Answer

1, 3, 5, 7, ...

Answer

2, 4, 8, 16, ...

Answer

3, 6, 9, 12, ...

Question 23

Find the common difference of the arithmetic sequence 3, 7, 11, 15, ...

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 24

Find the common difference of the arithmetic sequence: 5, 10, 15, 20, ...

Accepted Answer

2

Answer

5

Answer

10

Answer

15

Question 25

Which of the following is a geometric sequence with a common ratio of 2?

Accepted Answer

2, 4, 8, 16, 32

Answer

1, 3, 9, 27, 81

Answer

1, 2, 4, 8, 16

Answer

2, 3, 6, 12, 24

Question 26

Find the common ratio of the geometric sequence: 2, 6, 18, 54, ...

Accepted Answer

3

Answer

2

Answer

6

Answer

9

Question 27

In a geometric sequence, the first four terms are 5, 15, 45, and 135. What is the common ratio?

Accepted Answer

3

Answer

2

Answer

5

Question 28

Find the sum of the first 10 terms of the arithmetic sequence 3, 7, 11, ...?

Accepted Answer

150

Answer

120

Answer

180

Answer

210

Question 29

What is the pattern rule for the arithmetic sequence 6, 10, 14, 18, ...?

Accepted Answer

a_n = 6 + 4(n - 1)

Answer

a_n = 10 + 4(n - 1)

Answer

a_n = 14 + 4(n - 1)

Answer

a_n = 18 + 4(n - 1)

Question 30

Which of the following is an example of a Fibonacci sequence?

Accepted Answer

1, 1, 2, 3, 5, 8, 13, ...

Answer

1, 3, 5, 7, 9, 11, 13, ...

Answer

2, 4, 6, 8, 10, 12, 14, ...

Answer

1, 2, 4, 8, 16, 32, 64, ...

Question 31

Calculate the sum of the first 10 terms of the geometric series 1 + 1/2 + 1/4 + 1/8 + ...

Accepted Answer

2

Answer

2.5

Answer

1.5

Answer

1

Question 32

Find the nth term of the geometric sequence: 6, 12, 24, 48, ...

Accepted Answer

6 * 2^(n-1)

Answer

6 * 2^n

Answer

12 * 2^(n-1)

Question 33

The first term of an arithmetic sequence is 5 and the common difference is 3. What is the 10th term?

Accepted Answer

32

Answer

29

Answer

35

Answer

26

Question 34

What is the sum of the first 5 terms of the geometric sequence 2, 6, 18, ... ?

Accepted Answer

242

Answer

122

Answer

362

Answer

482

Question 35

The 3rd term of an arithmetic sequence is 11 and the 7th term is 23. What is the common difference?

Accepted Answer

3

Answer

5

Answer

2

Answer

4

Question 36

Which of the following sequences is geometric?

Accepted Answer

2, 4, 8, 16, ...

Answer

2, 5, 8, 11, ...

Answer

1, 4, 9, 16, ...

Answer

1, 3, 5, 7, ...

Question 37

The first term of a geometric sequence is 3 and the common ratio is 2. What is the 6th term?

Accepted Answer

96

Answer

48

Answer

64

Answer

192

Question 38

Find the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ...

Accepted Answer

2

Answer

3

Answer

1

Question 39

The sum of the first n terms of an arithmetic series is given by Sn = 3n^2 + 2n. What is the 5th term of the series?

Accepted Answer

32

Answer

36

Answer

28

Question 40

A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 3/4 of its previous height. What is the total distance traveled by the ball before it comes to rest?

Accepted Answer

40 meters

Answer

50 meters

Answer

30 meters

Answer

20 meters

Question 41

The first term of an arithmetic sequence is 2 and the 5th term is 14. What is the common difference?

Accepted Answer

3

Answer

2

Answer

4

Answer

1

Question 42

The sum of the first 10 terms of a geometric sequence is 1023. If the first term is 1, what is the common ratio?

Accepted Answer

2

Answer

3

Answer

4

Answer

1

Question 43

The first three terms of an arithmetic sequence are 5, 8, and 11. What is the 10th term of this sequence?

Accepted Answer

32

Answer

35

Answer

29

Answer

26

Question 44

The sum of the first five terms of a geometric sequence is 124. If the first term is 4, what is the common ratio?

Accepted Answer

2

Answer

3

Answer

1.5

Question 45

Which of the following sequences is NOT an arithmetic sequence?

Accepted Answer

2, 4, 8, 16, ...

Answer

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

Answer

1, 4, 7, 10, ...

Answer

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

Question 46

The sum of the first 'n' terms of an arithmetic series is given by Sn = 3n² + 2n. What is the 10th term of this series?

Accepted Answer

62

Answer

58

Answer

68

Answer

52

Question 47

A ball is dropped from a height of 10 meters. Each time it bounces, it reaches a height that is 80% of its previous height. What is the total distance travelled by the ball after three bounces?

Accepted Answer

29.6 meters

Answer

30.6 meters

Answer

25.6 meters

Answer

33.6 meters

Question 48

The first term of a geometric sequence is 2 and the common ratio is 3. What is the sum of the first 5 terms of this sequence?

Accepted Answer

242

Answer

363

Answer

484

Answer

121

Question 49

The sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ... is:

Accepted Answer

2

Answer

1

Answer

1.5

Answer

3

Question 50

The 5th term of an arithmetic sequence is 17 and the 10th term is 32. What is the common difference of this sequence?

Accepted Answer

3

Answer

5

Answer

2

Answer

4

Question 51

The sum of the first 10 terms of a geometric sequence is 1023. If the common ratio is 2, what is the first term of this sequence?

Accepted Answer

1

Answer

3

Answer

4

Answer

2

Question 52

A sequence is defined by the recursive formula: a1 = 2, an = an-1 + 3. What is the 6th term of this sequence?

Accepted Answer

17

Answer

20

Answer

14