Sequences and Series: Master the Concepts with Engaging Quizzes

Question 1

Which of the following sequences is convergent?

Accepted Answer

1, 1/2, 1/4, 1/8, ...

Answer

1, 3, 9, 27, ...

Answer

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

Answer

1, 2, 4, 8, ...

Question 2

What is the definition of the common difference in an arithmetic sequence?

Accepted Answer

The constant value added to each term to get the next term.

Answer

The variable value of each term.

Answer

The random value subtracted from each term to get the next term.

Answer

The initial value of the sequence.

Question 3

Which condition ensures the convergence of an infinite geometric series?

Accepted Answer

Absolute value of the common ratio is less than 1 (|r| < 1)

Answer

Absolute value of the common ratio is greater than 1 (|r| > 1)

Answer

Common ratio is equal to 0 (|r| = 0)

Answer

Common ratio is equal to 1 (|r| = 1)

Question 4

Determine the nth term of a geometric sequence with a = 2 and r = 3.

Accepted Answer

a_n = 2 * 3^(n-1)

Answer

a_n = 2^n * 3

Answer

a_n = 3 * 2^(n-1)

Answer

a_n = 3^n * 2

Question 5

Which formula represents the sum of the first n terms of an arithmetic sequence?

Accepted Answer

S_n = n/2 * (a_1 + a_n)

Answer

S_n = n * (a_1 + a_n)

Answer

S_n = n/2 * (a_1 - a_n)

Answer

S_n = n * (a_1 - a_n)

Question 6

Write the general term of a geometric sequence with a = 4 and r = 1/2.

Accepted Answer

a_n = 4 * (1/2)^(n-1)

Answer

a_n = 2 * 4^(n-1)

Answer

a_n = 2 * (1/4)^(n-1)

Answer

a_n = 4 * 2^(n-1)

Question 7

In the arithmetic sequence 2, 5, 8, 11, ..., what is the constant difference between consecutive terms called?

Accepted Answer

Common difference

Answer

Common ratio

Answer

Nth term

Answer

First term

Question 8

Which of the following is the correct formula for finding the nth term of the geometric sequence 2, 6, 18, 54, ...?

Accepted Answer

a * r^(n-1)

Answer

S = n/2 * (a + l)

Answer

a * n + b

Answer

a + (n-1) * d

Question 9

Given the formula for the sum of the first n terms of an arithmetic series as Sn = 3n^2 - 2n, what is the value of the 5th term?

Accepted Answer

23

Answer

17

Answer

29

Answer

None of the above

Question 10

In the geometric sequence 16, 8, 4, 2, ..., what is the constant multiplier between consecutive terms called?

Accepted Answer

Common ratio

Answer

Nth term

Answer

First term

Answer

Common difference

Question 11

If the first term of a geometric sequence is 4 and the common ratio is 3, what is the 5th term of the sequence?

Accepted Answer

324

Answer

432

Answer

216

Answer

None of the above

Question 12

What is the general term of the arithmetic sequence 3, 7, 11, 15, ...?

Accepted Answer

3 + 4n

Answer

4 + 3n

Answer

2 + 3n

Question 13

Calculate the sum of the first 10 terms of the geometric sequence 2, 6, 18, ...

Accepted Answer

1022

Answer

1012

Answer

1024

Answer

1032

Question 14

Which formula represents the sum of an infinite geometric series?

Accepted Answer

S = a / (1 - r), where |r| < 1

Answer

S = a * (1 - r)

Answer

S = a + ar + ar^2

Answer

S = a / (1 + r)

Question 15

Find the nth term of the sequence defined by a_n = 3n^2 + 2n - 1.

Accepted Answer

3n^2 + 2n - 1

Answer

n^2 - 3n + 2

Answer

2n^2 + 3n + 1

Answer

n^2 + 2n - 3

Question 16

Determine the limit of the sequence a_n = (2n + 3) / (n - 1) as n approaches infinity.

Accepted Answer

2

Answer

1

Answer

0

Answer

Infinity

Question 17

Which statement is NOT a property of geometric sequences?

Accepted Answer

The difference between any two consecutive terms is constant.

Answer

The sequence has a limit if the common ratio is less than 1.

Answer

The product of any two terms is equal to the square of the middle term.

Answer

The ratio of any two consecutive terms is constant.

Question 18

Find the first four terms of the sequence defined recursively by a_1 = 1 and a_n = 2 * a_{n-1} + 1.

Accepted Answer

1, 3, 7, 15

Answer

1, 2, 4, 8

Answer

1, 4, 9, 16

Answer

1, 3, 5, 7

Question 19

Calculate the sum of the first 50 terms of the arithmetic sequence 5, 9, 13, ...

Accepted Answer

6250

Answer

6750

Answer

7250

Answer

5250

Question 20

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

Accepted Answer

1/2

Answer

1/4

Answer

-1/2

Answer

2

Question 21

What is the next number in the arithmetic sequence: 5, 9, 13, 17, ...?

Accepted Answer

21

Answer

23

Answer

19

Answer

25

Question 22

In the arithmetic sequence: -3, 2, 7, 12, ..., what is the common difference?

Accepted Answer

5

Answer

4

Answer

-5

Answer

10

Question 23

What is the 8th term of the geometric sequence: 2, -6, 18, -54, ...?

Accepted Answer

-4374

Answer

1458

Answer

-1458

Answer

4374

Question 24

What is the common ratio in the geometric sequence: 1/4, 1/2, 1, 2, ...?

Accepted Answer

2

Answer

-2

Answer

1/2

Answer

1/4

Question 25

What is the sum of the first 10 terms of the arithmetic series: 1 + 4 + 7 + ...?

Accepted Answer

145

Answer

135

Answer

155

Answer

165

Question 26

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

Accepted Answer

2

Answer

1

Answer

1/2

Answer

Does not exist

Question 27

A sequence is defined recursively by a(1) = 3 and a(n) = a(n-1) + 2. What is the 5th term of this sequence?

Accepted Answer

11

Answer

9

Answer

7

Answer

13

Question 28

Which of the following is a geometric sequence?

Accepted Answer

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

Answer

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

Answer

1, 3, 6, 10, ...

Answer

2, 4, 6, 8, ...

Question 29

The first term of an arithmetic series is 2, and the sum of the first 6 terms is 42. What is the common difference of this series?

Accepted Answer

4

Answer

8

Answer

2

Answer

6

Question 30

A ball is dropped from a height of 16 meters. Each time it bounces, it reaches 3/4 of its previous height. What is the total vertical distance the ball travels before it comes to rest?

Accepted Answer

64 meters

Answer

48 meters

Answer

32 meters

Answer

16 meters

Question 31

What is the common difference in the arithmetic sequence: -3, 2, 7, 12,...?

Accepted Answer

5

Answer

-5

Answer

3

Answer

10

Question 32

Find the 8th term of the geometric sequence: 3, -6, 12, -24,...

Accepted Answer

384

Answer

-384

Answer

-192

Answer

192

Question 33

Which of the following is an arithmetic sequence?

Accepted Answer

1, 4, 7, 10,...

Answer

1, 1, 1, 1,...

Answer

2, 4, 8, 16,...

Answer

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

Question 34

What is the sum of the first 5 terms of the arithmetic series: 2 + 5 + 8 + ... ?

Accepted Answer

40

Answer

29

Answer

17

Answer

50

Question 35

The first term of a geometric series is 2 and the common ratio is 3. What is the sum of the first 4 terms?

Accepted Answer

80

Answer

54

Answer

242

Answer

26

Question 36

An arithmetic sequence has a common difference of -2 and its 5th term is 10. What is its first term?

Accepted Answer

18

Answer

12

Answer

6

Answer

2

Question 37

Which of the following geometric series converges?

Accepted Answer

1 + 1/2 + 1/4 + 1/8 + ...

Answer

-1 + 1 - 1 + 1 - ...

Answer

1 + 2 + 4 + 8 + ...

Question 38

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

Accepted Answer

1

Answer

2

Answer

1/2

Answer

The series diverges

Question 39

A theater has 20 rows of seats. The first row has 10 seats, and each subsequent row has 2 more seats than the row before it. How many seats are in the theater?

Accepted Answer

580

Answer

390

Answer

420

Answer

200

Question 40

A ball is dropped from a height of 16 meters. Each time it bounces, it reaches a height that is 3/4 of its previous height. What is the total vertical distance traveled by the ball before it comes to rest?

Accepted Answer

112 meters

Answer

48 meters

Answer

The distance is infinite

Answer

64 meters

Question 41

Which of the following is an example of an arithmetic sequence?

Accepted Answer

2, 5, 8, 11, 14

Answer

2, 6, 12, 24, 48

Answer

2, 4, 8, 16, 32

Answer

2, 3, 5, 8, 13

Question 42

Find the nth term of the arithmetic sequence 5, 9, 13, 17, ...

Accepted Answer

5 + 4(n - 1)

Answer

9 + 4(n - 1)

Answer

5 + 4n

Answer

9 + 4n

Question 43

Find the sum of the first 10 terms of the geometric sequence 2, 6, 18, 54, ...

Accepted Answer

2046

Answer

1023

Answer

8192

Answer

4092

Question 44

Which of the following is NOT a property of an infinite geometric series?

Accepted Answer

The sum of an infinite geometric series is always positive.

Answer

The sum of an infinite geometric series with |r| > 1 diverges.

Answer

The sum of an infinite geometric series with |r| < 1 is a finite number.

Question 45

Find the sum of the infinite geometric series 1 + 1/3 + 1/9 + 1/27 + ...

Accepted Answer

3/2

Answer

2/3

Answer

1/2

Answer

3

Question 46

Which of the following is an example of an alternating series?

Accepted Answer

1 - 1/2 + 1/4 - 1/8 + ...

Answer

2 - 4 + 8 - 16 + ...

Answer

1 + 1/2 + 1/4 + 1/8 + ...

Question 47

What is the alternating series test for convergence?

Accepted Answer

If the absolute value of the terms of an alternating series decrease and approach zero, then the series converges.

Answer

If the absolute value of the terms of an alternating series increase and approach infinity, then the series converges.

Question 48

Find the sum of the first 10 terms of the alternating series 1 - 1/2 + 1/4 - 1/8 + ...

Accepted Answer

0.9375

Answer

1.375

Answer

0.6875

Answer

2

Question 49

Which of the following sequences converges?

Accepted Answer

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

Answer

1, 1/2, 1/4, 1/8, ...

Answer

1, 2, 4, 8, ...

Answer

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