Sequences and Series: Interactive Learning Quizzes for High School Freshmen

Question 1

Which of the following is NOT a property of a geometric sequence?

Accepted Answer

Common difference is constant

Answer

Constant ratio between consecutive terms

Answer

First term is non-zero

Answer

Sum of any two terms is another term in the sequence

Question 2

What is the sum of the first 8 terms of the geometric sequence 2, 6, 18, ...?

Accepted Answer

510

Answer

382

Answer

638

Answer

766

Question 3

Identify the arithmetic sequence among the given options.

Accepted Answer

1, 3, 5, 7, ...

Answer

1, 4, 9, 16, ...

Answer

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

Answer

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

Question 4

Which formula represents the nth term (an) of an arithmetic sequence, given its first term (a1) and common difference (d)?

Accepted Answer

an = a1 + (n - 1)d

Answer

an = a1 - (n - 1)d

Answer

an = a1n + d

Answer

an = a1d + n

Question 5

Which formula represents the sum of the first n terms (Sn) of a geometric sequence, given its first term (a1) and common ratio (r)?

Accepted Answer

Sn = a1(1 - r^n) / (1 - r)

Answer

Sn = a1(1 + r^n) / (1 + r)

Answer

Sn = a1(1 - r) / (1 + r)

Answer

Sn = a1(1 + r) / (1 - r)

Question 6

Which formula represents the sum to infinity of a geometric series, given its first term (a1) and common ratio (r)?

Accepted Answer

S = a1 / (1 - r)

Answer

S = a1 / (1 + r)

Answer

S = a1(1 - r) / (1 - r^2)

Answer

S = a1(1 + r) / (1 + r^2)

Question 7

Identify the common ratio of the geometric sequence 2, 6, 18, ...

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 8

A farmer plants 1000 corn seeds in a field. The number of seeds doubles each year. How many seeds will be in the field after 5 years?

Accepted Answer

64000

Answer

32000

Answer

16000

Answer

128000

Question 9

In an arithmetic sequence, the first term is 5, and the common difference is 3. What is the formula for the nth term?

Accepted Answer

a_n = 5 + 3(n-1)

Answer

a_n = 3 + 5(n-1)

Answer

a_n = 5 - 3(n-1)

Answer

a_n = 3 - 5(n-1)

Question 10

Which of the following is NOT a property of an arithmetic sequence?

Accepted Answer

Constant second difference between consecutive terms

Answer

Constant difference between consecutive terms

Answer

Terms can be positive or negative

Answer

Can be represented by a linear function

Question 11

In a geometric sequence, the third term is 24 and the fifth term is 96. Determine the first term and common ratio.

Accepted Answer

First term = 6, Common ratio = 3

Answer

First term = 3, Common ratio = 2

Answer

First term = 12, Common ratio = 4

Answer

First term = 4, Common ratio = 3

Question 12

Which of the following is unique to arithmetic sequences?

Accepted Answer

Constant common difference

Answer

Constant second difference

Answer

First term

Answer

Number of terms

Question 13

Which of the following is a necessary condition for a geometric sequence to be convergent?

Accepted Answer

Common ratio between -1 and 1

Answer

Common ratio greater than 1

Answer

Common ratio less than -1

Answer

Common ratio equal to 1

Question 14

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the fifth term?

Accepted Answer

32

Answer

16

Answer

64

Answer

128

Question 15

Which of the following is NOT a characteristic of an arithmetic sequence?

Accepted Answer

The sequence has a finite number of terms.

Answer

The difference between any two consecutive terms is constant.

Answer

The first term must be non-zero.

Answer

The sequence can be increasing or decreasing.

Question 16

Which of the following is the infinite sum of the geometric sequence 1 + 1/2 + 1/4 + 1/8 + ...?

Accepted Answer

2

Answer

1

Answer

4

Answer

8

Question 17

What is the difference between an arithmetic sequence and a geometric sequence?

Accepted Answer

Arithmetic sequences have a constant difference between terms, while geometric sequences have a constant ratio between terms.

Answer

Geometric sequences have a constant difference between terms, while arithmetic sequences have a constant ratio between terms.

Answer

Arithmetic sequences have a constant first term, while geometric sequences have a constant last term.

Answer

Geometric sequences have a constant first term, while arithmetic sequences have a constant last term.

Question 18

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

Accepted Answer

a_n = 5 + 3n

Answer

a_n = 3 + 5n

Answer

a_n = 5 - 3n

Answer

a_n = 3 - 5n

Question 19

Find the 10th term of the arithmetic sequence 12, 18, 24, 30, ...

Accepted Answer

78

Answer

84

Answer

90

Answer

96

Question 20

Which of the following is the general term for a geometric sequence with a first term of 10 and a common ratio of 0.5?

Accepted Answer

a_n = 10 * 0.5^n

Answer

a_n = 10 + 0.5n

Answer

a_n = 10 / 0.5^n

Answer

a_n = 10 - 0.5n

Question 21

Which of the following is NOT a property of geometric sequences?

Accepted Answer

The terms are all positive.

Answer

The common ratio is constant.

Answer

The sequence can be finite or infinite.

Answer

The sequence is increasing or decreasing.

Question 22

Find the common ratio of the geometric sequence 1, 3, 9, 27, ...

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 23

Which of the following is NOT a type of mathematical sequence?

Accepted Answer

Cubic

Answer

Arithmetic

Answer

Geometric

Answer

Harmonic

Question 24

What is the next term in the geometric sequence: 2, 6, 18, 54, ...?

Accepted Answer

162

Answer

324

Answer

648

Answer

1296

Question 25

Which of the following is the formula for the nth term of an arithmetic sequence, where a1 is the first term and d is the common difference?

Accepted Answer

an = a1 + (n-1)d

Answer

an = a1 + (n-1)r

Answer

an = a1 * (n-1)d

Answer

an = a1 * (n-1)r

Question 26

What is the sum of the first 10 terms of the geometric sequence 2, 4, 8, 16, ...?

Accepted Answer

1020

Answer

510

Answer

2040

Answer

4080

Question 27

In a geometric sequence, the first term is 'a' and the common ratio is 'r'. Which of the following formulas represents the nth term of this sequence?

Accepted Answer

an = a * r^(n-1)

Answer

an = a * r^n

Answer

an = a + (n-1) * r

Answer

an = a + n * r

Question 28

Consider the geometric series: 1 + 1/2 + 1/4 + 1/8 + .... What is the limit of this series?

Accepted Answer

1

Answer

0

Answer

2

Answer

Infinity

Question 29

Find the common ratio of the geometric sequence: 4, 12, 36, 108, ...

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 30

The Fibonacci sequence is a special type of sequence where each term is the sum of the two preceding ones. Which of the following is an example of a Fibonacci sequence?

Accepted Answer

0, 1, 1, 2, 3, 5, 8, ...

Answer

1, 2, 3, 4, 5, 6, 7, ...

Answer

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

Answer

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

Question 31

Which of the following is the definition of the common difference of an arithmetic sequence?

Accepted Answer

The difference between any two consecutive terms

Answer

The difference between the first term and the second term

Answer

The difference between the last term and the first term

Answer

The sum of the first and last terms

Question 32

What is the formula for the sum of the first 'n' terms of an arithmetic sequence?

Accepted Answer

S = n * (a1 + an) / 2

Answer

S = n * (a1 - an) / 2

Answer

S = n * (an - a1) / 2

Answer

S = n * (a1 + an)

Question 33

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

Accepted Answer

a(n) = a(n-1) + 2

Answer

a(n) = 2n + 1

Answer

a(n) = 3

Answer

a(n) = n^2

Question 34

If a series converges to 10, what is its limit?

Accepted Answer

10

Answer

0

Answer

1

Answer

Infinity

Question 35

If a series is geometric, what is the ratio of the nth term to the (n+1)th term?

Accepted Answer

r

Answer

1/r

Answer

r^2

Answer

1/r^2

Question 36

Which of the following is **not** a type of sequence?

Accepted Answer

Polynomial

Answer

Arithmetic

Answer

Geometric

Answer

Harmonic

Question 37

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

Accepted Answer

2

Answer

4

Answer

6

Answer

8

Question 38

Which of the following is the formula for the sum of the first n terms of a geometric series?

Accepted Answer

S = a_1(1 - r^n) / (1-r)

Answer

S = n(a_1 + a_n) / (r-1)

Answer

S = a_n(1 - r) / (1-r^n)

Answer

S = (a_1 - a_n) / (r-1)

Question 39

Find the tenth term of the sequence defined by a_n = 3n - 2.

Accepted Answer

27

Answer

25

Answer

29

Answer

31

Question 40

Which of the following sequences is **recursively** defined?

Accepted Answer

a_n = a_{n-1} + 3

Answer

a_n = 2n + 1

Answer

a_n = 5^n

Answer

a_n = n!

Question 41

In the geometric sequence 3, 9, 27, 81, ... what is the common ratio?

Accepted Answer

3

Answer

12

Answer

9

Answer

6

Question 42

What is the sum of the first 10 terms of the geometric sequence: 2, 6, 18, 54, ...?

Accepted Answer

59048

Answer

2360

Answer

1770

Answer

590

Question 43

Which of the following is NOT a property of a geometric sequence?

Accepted Answer

All terms are equal.

Answer

The ratio of consecutive terms is constant.

Answer

The first term is non-zero.

Answer

The sequence can be extended indefinitely.

Question 44

What type of sequence is: 2, 4, 8, 16, 32, ...?

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Fibonacci

Answer

Harmonic

Question 45

Which of the following sequences converges (approaches a specific value)?

Accepted Answer

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

Answer

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

Answer

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

Answer

1, 2, 4, 8, ...

Question 46

Which of the following is a real-world application of geometric sequences?

Accepted Answer

Calculating compound interest

Answer

Finding the area of a triangle

Answer

Solving quadratic equations

Answer

Determining the probability of an event

Question 47

Which of the following is the common difference in the arithmetic sequence 2, 5, 8, 11, ...?

Accepted Answer

3

Answer

2

Answer

5

Answer

4

Question 48

What is the 10th term of the geometric sequence 1, 2, 4, 8, ...?

Accepted Answer

1024

Answer

4096

Answer

512

Answer

2048

Question 49

Which of the following is the sum of the first 10 terms of the arithmetic sequence 3, 7, 11, 15, ...?

Accepted Answer

220

Answer

330

Answer

440

Answer

110

Question 50

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

Accepted Answer

2

Answer

1

Answer

8

Answer

4

Question 51

Which of the following sequences is an arithmetic sequence?

Accepted Answer

1, 3, 5, 7, ...

Answer

1, 1, 2, 3, ...

Answer

1, 4, 9, 16, ...

Answer

1, 2, 4, 8, ...

Question 52

What is the common ratio of the geometric sequence 2, 6, 18, 54, ...?

Accepted Answer

3

Answer

4

Answer

6

Answer

2

Question 53

What is the nth term of the arithmetic sequence whose first term is 5 and common difference is 3?

Accepted Answer

5 + 3(n-1)

Answer

3 + 5(n-1)

Answer

3n + 5

Answer

5n + 3

Question 54

Which of the following is the formula for the sum of the first n terms of a geometric series with first term a and common ratio r?

Accepted Answer

a(1 - r^n) / (1 - r)

Answer

a(1 - r) / (1 + r^n)

Answer

a(1 + r^n) / (1 + r)

Answer

a(r^n - 1) / (r - 1)

Question 55

What is the difference between the 10th and 5th terms of the arithmetic sequence 4, 7, 10, 13, ...?

Accepted Answer

6

Answer

3

Answer

9

Answer

12