Sequences and Series: Master Arithmetic and Geometric Progressions

Question 1

Which formula is used to find the nth term (an) of an arithmetic sequence?

Accepted Answer

an = a + (n-1)d

Answer

an = a + nd

Answer

an = a + dn

Answer

an = nd + a

Question 2

A bacteria population doubles every day. If there are initially 500 bacteria, how many bacteria will there be after 5 days?

Accepted Answer

16,000

Answer

8,000

Answer

4,000

Answer

2,000

Question 3

What is the common difference of the arithmetic sequence 7, 11, 15, ...?

Accepted Answer

2

Answer

4

Answer

6

Answer

8

Question 4

Which of the following sequences is a geometric sequence?

Accepted Answer

3, 9, 27, 81, ...

Answer

2, 4, 6, 8, ...

Answer

5, 10, 20, 40, ...

Answer

1, 3, 5, 7, ...

Question 5

Find the sum of the first 10 terms of the geometric sequence: 3, 6, 12, 24, ...

Accepted Answer

3072

Answer

1536

Answer

768

Answer

384

Question 6

Find the sum of the first 12 terms of the geometric sequence: 5, 10, 20, 40, ...

Accepted Answer

3840

Answer

1920

Answer

960

Answer

480

Question 7

Find the common ratio of the geometric sequence: 3, 9, 27, 81, ...

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 8

Identify the characteristic NOT applicable to geometric sequences:

Accepted Answer

First term is always 1

Answer

Constant ratio between consecutive terms

Answer

Exponential growth or decay of terms

Answer

Sum of any two terms equals the third term

Question 9

Identify the common difference of the arithmetic sequence whose nth term is given by Un = 5n - 2

Accepted Answer

5

Answer

2

Answer

7

Answer

10

Question 10

Determine the formula to find the nth term of an arithmetic sequence.

Accepted Answer

an = a1 + (n - 1) * d

Answer

an = a1 * (n - 1) * d

Answer

an = a1 + (n + 1) * d

Answer

an = a1 * (n + 1) * d

Question 11

Identify the formula to find the nth term of a geometric sequence.

Accepted Answer

an = a1 * r^n

Answer

an = a1 * (n - 1) * r

Answer

an = a1 + (n + 1) * r

Answer

an = a1 * (n + 1) * r

Question 12

What is the formula for the nth term of the geometric sequence: 2, 6, 18, ... ?

Accepted Answer

2(3^(n-1))

Answer

2n

Answer

3n

Answer

6n

Question 13

A geometric sequence starts with 3 and has a common ratio of *r*.  The 6th term is 486. What is the value of *r*?

Accepted Answer

r = 2

Answer

r = -2

Answer

r = 3

Answer

r = -3

Question 14

Determine whether the geometric series 2 + 6 + 18 + 54 + ... converges or diverges. Provide a brief explanation for your answer.

Accepted Answer

Diverges because the common ratio is less than 1.

Answer

Converges because the common ratio is greater than 1.

Answer

Converges because the common ratio is positive.

Answer

Diverges because the common ratio is negative.

Question 15

Calculate the sum of the first 10 terms of the geometric sequence 2, 4, 8, 16, ...

Accepted Answer

1023

Answer

1022

Answer

1024

Answer

1025

Question 16

What is the necessary condition for a geometric series to converge?

Accepted Answer

|r| < 1

Answer

|r| > 1

Answer

|r| = 1

Answer

|r| = 0

Question 17

The population of rabbits on an island increases by 20% each month. If the initial population is 100, what is the population after n months?

Accepted Answer

100(1.2)^n

Answer

100(0.8)^n

Answer

120(1.2)^n

Answer

100(1.2)^(n+1)

Question 18

The nth term of an arithmetic sequence with first term 5 and common difference 3 is:

Accepted Answer

5 + 3n

Answer

3 + 5n

Answer

5n + 3

Answer

3n + 5

Question 19

Which sequence is not geometric?

Accepted Answer

4, 6, 8, 10, ...

Answer

1, 2, 4, 8, ...

Answer

2, 4, 8, 16, ...

Answer

3, 9, 27, 81, ...

Question 20

The common ratio of the geometric sequence 1, 1/2, 1/4, ... is:

Accepted Answer

1/2

Answer

1/4

Answer

2

Answer

4

Question 21

The nth term (general term) of a geometric sequence with first term 'a' and common ratio 'r' is:

Accepted Answer

ar^(n-1)

Answer

nr

Answer

a + (n-1)r

Answer

r^n

Question 22

Find the first term of the geometric sequence whose nth term is 2^(n-1)

Accepted Answer

1

Answer

3

Answer

2

Answer

4

Question 23

What is the 10th term of the arithmetic sequence 2, 5, 8, 11...?

Accepted Answer

29

Answer

35

Answer

26

Answer

32

Question 24

The sum of the first 'n' terms of an arithmetic series is found using the formula: Sn = n/2[2a + (n-1)d]. What does 'd' represent in this formula?

Accepted Answer

Common difference

Answer

First term

Answer

Sum of the series

Answer

Number of terms

Question 25

A ball is dropped from 10 meters high. Each bounce reaches 3/4 of the previous height.  What is the total distance travelled by the ball before it stops bouncing?

Accepted Answer

70 meters

Answer

60 meters

Answer

80 meters

Answer

40 meters

Question 26

An arithmetic sequence starts with 5 and has a common difference of 3. What is the value of the 10th term?

Accepted Answer

32

Answer

26

Answer

35

Answer

29

Question 27

Calculate the sum of the first 5 terms in the geometric sequence: 2, 6, 18...

Accepted Answer

242

Answer

122

Answer

362

Answer

182

Question 28

The first three terms of an arithmetic sequence are: 2x, x + 5, and 3x - 1.  What is the value of x?

Accepted Answer

3

Answer

1

Answer

4

Answer

2

Question 29

The sum of the first 10 terms in an arithmetic series is 155. The first term is 3.  What is the common difference?

Accepted Answer

2

Answer

1

Answer

4

Answer

3

Question 30

A geometric sequence has a first term of 4 and a common ratio of 1/2. What is the 5th term?

Accepted Answer

1/2

Answer

1/4

Answer

1

Answer

2

Question 31

An infinite geometric series has a sum of 10 and its first term is 2.  What is the common ratio?

Accepted Answer

0.8

Answer

0.6

Answer

0.9

Answer

0.7

Question 32

A ball is dropped from a height of 16 meters. On each bounce, it rebounds to 3/4 of its previous height. Calculate the total distance the ball travels before coming to rest.

Accepted Answer

64 meters

Answer

80 meters

Answer

96 meters

Answer

48 meters

Question 33

The 5th term of an arithmetic sequence is 17, and the 10th term is 32. What is the first term of the sequence?

Accepted Answer

3

Answer

5

Answer

2

Answer

4

Question 34

Find the sum of the series: 1 + 2 + 4 + 8 + ... + 128

Accepted Answer

255

Answer

256

Answer

254

Question 35

A loan of £5000 is taken out at an annual interest rate of 5%, compounded annually. How much will the loan amount to after 3 years?

Accepted Answer

£5788.13

Answer

£6000

Answer

£5637.50

Answer

£5500

Question 36

What is the next term in the arithmetic sequence: 5, 8, 11, 14, ...?

Accepted Answer

17

Answer

18

Answer

19

Answer

16

Question 37

An arithmetic sequence has a first term of 2 and a common difference of 3. What is the 10th term?

Accepted Answer

29

Answer

35

Answer

32

Answer

27

Question 38

Find the sum of the first 5 terms of the arithmetic series: 4 + 7 + 10 + ...

Accepted Answer

55

Answer

50

Answer

35

Answer

40

Question 39

A sequence is defined by the rule: u_n = 2n - 5. What is the 5th term of this sequence?

Accepted Answer

5

Answer

-1

Answer

7

Answer

3

Question 40

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

Accepted Answer

-3

Answer

-2

Answer

2

Answer

3

Question 41

A geometric sequence has a first term of 5 and a common ratio of 2. What is the 6th term?

Accepted Answer

160

Answer

80

Answer

640

Answer

320

Question 42

Find the sum of the first 4 terms of the geometric series: 1 + 3 + 9 + ...

Accepted Answer

40

Answer

27

Answer

81

Answer

13

Question 43

A geometric series has first term 10 and common ratio 0.5.  What is the sum to infinity of this series?

Accepted Answer

20

Answer

Infinity

Answer

10

Answer

5

Question 44

The first three terms of a sequence are: 2x, x + 6, 3x - 2.  If this is an arithmetic sequence, what is the value of x?

Accepted Answer

4

Answer

6

Answer

2

Answer

8

Question 45

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 traveled by the ball before it comes to rest?

Accepted Answer

64 meters

Answer

Infinite

Answer

48 meters

Answer

80 meters

Question 46

Which of the following is the nth term of the arithmetic sequence 2, 5, 8, 11, ...?

Accepted Answer

3n - 1

Answer

n + 1

Answer

4n - 2

Answer

2n + 3

Question 47

Find the sum of the first 10 terms of the geometric series 1, 2, 4, 8, ...

Accepted Answer

1023

Answer

2047

Answer

511

Answer

1024

Question 48

Which of the following is the common difference of the arithmetic sequence -3, 0, 3, 6, ...?

Accepted Answer

3

Answer

6

Answer

-3

Answer

2

Question 49

Find the first term of the geometric series 4, 8, 16, 32, ...

Accepted Answer

2

Answer

4

Answer

1

Answer

8

Question 50

Which of the following is the nth term of the arithmetic sequence 10, 15, 20, 25, ...?

Accepted Answer

5n + 5

Answer

10n + 5

Answer

15n - 5

Answer

5n - 5

Question 51

Find the sum of the first 15 terms of the geometric series 2, 4, 8, 16, ...

Accepted Answer

32766

Answer

32767

Answer

65532

Answer

16383

Question 52

Which of the following is the common difference of the arithmetic sequence 7, 11, 15, 19, ...?

Accepted Answer

4

Answer

-4

Answer

3

Answer

8

Question 53

Find the first term of the geometric series 6, 12, 24, 48, ...

Accepted Answer

3

Answer

12

Answer

2

Answer

6

Question 54

Which of the following is the nth term of the arithmetic sequence 1, 4, 7, 10, ...?

Accepted Answer

3n - 2

Answer

4n - 2

Answer

2n + 1

Answer

3n + 2

Question 55

Find the sum of the first 20 terms of the geometric series 5, 10, 20, 40, ...

Accepted Answer

2097151

Answer

1048575

Answer

4194303

Answer

2097152