Sequences and Series: Master the Concepts with Engaging Quizzes

Question 1

Which of the following is not a type of sequence?

Accepted Answer

Quadratic

Answer

Arithmetic

Answer

Geometric

Answer

Harmonic

Question 2

Find the nth term of the harmonic sequence: 1/2, 1/3, 1/4, 1/5, ...

Accepted Answer

1/(n+1)

Answer

1/n

Answer

1/(n+2)

Answer

1/(n-1)

Question 3

Determine the general term of the Fibonacci sequence.

Accepted Answer

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

Answer

F(n) = 2F(n-1) - F(n-2)

Answer

F(n) = F(n-1) * F(n-2)

Answer

F(n) = F(n-1) / F(n-2)

Question 4

Find the nth term of the sequence defined by the recurrence relation: t(n) = 2t(n-1) - 1, t(1) = 2

Accepted Answer

2^n - 1

Answer

2^(n-1)

Answer

2^n + 1

Answer

2^(n-1) + 1

Question 5

The formula for the nth term of the Fibonacci sequence is:

Accepted Answer

Fn = (1 + √5)^n / √5^n

Answer

Fn = (1 - √5)^n / √5^n

Answer

Fn = (1 + √5)^n

Answer

Fn = (1 - √5)^n

Question 6

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

Accepted Answer

The ratio of consecutive terms is constant.

Answer

The difference between consecutive terms is constant.

Answer

The sum of consecutive terms is constant.

Answer

The product of consecutive terms is constant.

Question 7

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

Accepted Answer

4n - 1

Answer

4n + 1

Answer

4n - 3

Answer

4n + 3

Question 8

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

Accepted Answer

1022

Answer

1018

Answer

1024

Answer

1016

Question 9

Determine the type of the following sequence: 2, 4, 8, 16, ...

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Neither

Question 10

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

Accepted Answer

6 * 2^(n-1)

Answer

12 * 2^(n-1)

Answer

24 * 2^(n-1)

Answer

48 * 2^(n-1)

Question 11

The nth term of an arithmetic sequence is given by the formula:

Accepted Answer

a_n = a_1 + (n - 1) * d

Answer

a_n = a_1 - (n - 1) * d

Answer

a_n = a_1 * (n - 1) * d

Answer

a_n = a_1 / (n - 1) * d

Question 12

Which of the following infinite series converges?

Accepted Answer

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

Answer

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

Answer

1 + 2 + 4 + 8 + ...

Answer

1 - 2 + 4 - 8 + ...

Question 13

The sum of the first 5 terms of the geometric sequence 2, 6, 18, 54, ... is:

Accepted Answer

126

Answer

62

Answer

252

Answer

504

Question 14

Find the common difference of the arithmetic sequence: 10, 15, 20, 25, ...

Accepted Answer

5

Answer

10

Answer

15

Answer

20

Question 15

Find the sum to infinity of the geometric series 0.1 + 0.01 + 0.001 + ...

Accepted Answer

1/9

Answer

1/10

Answer

1/11

Answer

1/12

Question 16

What is the nth term of the geometric sequence with an initial term of 2 and a common ratio of 3?

Accepted Answer

3 * 2n-1

Answer

2n

Answer

3n

Answer

2 * 3n-1

Question 17

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

Accepted Answer

The sequence is bounded.

Answer

The difference between any two consecutive terms is constant.

Answer

The sum of any two terms is equal to the sum of the first and last terms.

Answer

The sequence can be represented by a linear equation.

Question 18

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

Accepted Answer

Sum of terms

Answer

Common ratio

Answer

First term

Answer

Nth term

Question 19

A series is given by 1 + 2x + 4x^2 + 8x^3 + ... What is the sum of the first 3 terms?

Accepted Answer

1 + 2x + 4x^2

Answer

1 + 2 + 4 + 8

Answer

1 + 3x + 6x^2 + 12x^3

Answer

1 + 2x + 4x^2 + 8x^3

Question 20

Which of the following formulas gives the nth partial sum of a geometric sequence?

Accepted Answer

Sn = n(a1 + an)/2

Answer

Sn = n(2a1 + an-1)/2

Answer

Sn = n(a1 - an)/2

Answer

Sn = n(a1 + an)/4

Question 21

A geometric series has a first term of 1 and a common ratio of 2. What is the sum of the first 4 terms?

Accepted Answer

16

Answer

15

Answer

17

Answer

18

Question 22

Find the explicit formula for the arithmetic sequence with first term 3 and common difference 4.

Accepted Answer

a_n = 3 + 4(n - 1)

Answer

a_n = 3(n - 1) + 4

Answer

a_n = 4 + 3(n - 1)

Answer

a_n = 4(n - 1) + 3

Question 23

Identify the correct general term of the arithmetic sequence 2, 5, 8, 11, ...

Accepted Answer

a_n = 2 + 3(n - 1)

Answer

a_n = 1 + 2(n - 1)

Answer

a_n = 3 + 5(n - 1)

Answer

a_n = 5 + 2(n - 1)

Question 24

Which of the following is an example of a convergent series?

Accepted Answer

∑(1/2^n)

Answer

∑(ln(n))

Answer

∑(n!)

Answer

∑(cos(n))

Question 25

What is the common difference of the arithmetic sequence 10, 15, 20, 25, ...?

Accepted Answer

5

Answer

10

Answer

20

Answer

15

Question 26

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

Accepted Answer

a_n = n^2 - 3n + 1

Answer

a_n = n^3 - 3n^2 + 1

Answer

a_n = n^2 + 3n - 1

Question 27

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

Accepted Answer

3

Answer

2

Answer

6

Answer

9

Question 28

Determine the convergence or divergence of the geometric series: 1 + 2 + 4 + 8 + ...

Accepted Answer

Diverges

Answer

Converges to infinity

Answer

Converges to 20

Answer

Converges to 10

Question 29

Which condition is necessary for a geometric series to be convergent?

Accepted Answer

|r| < 1

Answer

r = 1

Answer

r = 0

Answer

|r| > 1

Question 30

What is the limit of the sequence 1, 1/2, 1/4, 1/8, ...?

Accepted Answer

0

Answer

1/2

Answer

∞

Answer

1

Question 31

Which of the following sequences is NOT an arithmetic sequence?

Accepted Answer

Fibonacci sequence

Answer

-3, -3, -3, -3, ...

Answer

2, 5, 8, 11, ...

Answer

10, 7, 4, 1, ...

Question 32

What is the recursive formula for the Fibonacci sequence?

Accepted Answer

F(n) = F(n-1) + F(n-2), where F(1) = 1 and F(2) = 1

Answer

F(n) = F(n-1) + 1

Answer

F(n) = F(n-1) - F(n-2)

Answer

F(n) = 2F(n-1)

Question 33

The second term of a geometric sequence is 12 and the fourth term is 48. What is the first term of the sequence?

Accepted Answer

3

Answer

12

Answer

9

Answer

6

Question 34

What is the common difference of the arithmetic sequence 1/2, 1, 3/2, 2, ...?

Accepted Answer

1/2

Answer

3/2

Answer

2

Answer

1

Question 35

A company offers a starting salary of $30,000 for the first year with a 5% annual raise for the next five years. What is the total salary earned over the six years?

Accepted Answer

$195,769.38

Answer

$210,000

Answer

$225,000

Answer

$180,000