1. What is a sequence in mathematics?

A. A random collection of objects
B. A collection of ordered numbers following a specific pattern
C. A set of unordered natural numbers
D. A random list of objects or numbers

Answer: B. A collection of ordered numbers following a specific pattern

2. What is the general term of an arithmetic progression (A.P.)?

A. $a_n = a + (n - 1)d$
B. $a_n = ar^{n-1}$
C. $a_n = \frac{a}{n}$
D. $a_n = a + d^n$

Answer: A. $a_n = a + (n - 1)d$

3. Which of the following is true about geometric progression (G.P.)?

A. Each term is equal to the previous term.
B. Each term is a constant multiple of the previous term.
C. The difference between consecutive terms is constant.
D. There is no pattern in G.P.

Answer: B. Each term is a constant multiple of the previous term.

4. In a G.P., the first term $a = 3$ and the common ratio $r = 2$ . What is the 5th term?

A. 48
B. 24
C. 96
D. 15

Answer: A. 48

Explanation: $a_5 = ar^{4} = 3 \times 2^4 = 48$ .

5. If the nth term of a sequence is given by $a_n = 2n - 1$ , what is the 10th term?

A. 19
B. 20
C. 21
D. 22

Answer: C. 21

Explanation: $a_{10} = 2(10) - 1 = 21$ .

6. What is the sum of the first n terms of a G.P. if the first term is $a$ , the common ratio is $r$ , and $r \neq 1$ ?

A. $S_n = \frac{a(1 - r^n)}{1 - r}$
B. $S_n = \frac{a(1 + r^n)}{1 - r}$
C. $S_n = a + r^n$
D. $S_n = a \times n$

Answer: A. $S_n = \frac{a(1 - r^n)}{1 - r}$

7. In a Fibonacci sequence, the third term is the sum of:

A. First and second terms
B. Second and fourth terms
C. First and fourth terms
D. Third and fourth terms

Answer: A. First and second terms

Explanation: $a_3 = a_1 + a_2$ .

8. What is a geometric mean (G.M.) of two positive numbers $a$ and $b$ ?

A. $\frac{a + b}{2}$
B. $\sqrt{ab}$
C. $\frac{a}{b}$
D. $\frac{a - b}{2}$

Answer: B. $\sqrt{ab}$

9. In a sequence of numbers, if the ratio of each term to the previous term is constant, it is called a:

A. Arithmetic progression
B. Geometric progression
C. Fibonacci sequence
D. Harmonic progression

Answer: B. Geometric progression

10. Which of the following sequences is an example of an arithmetic progression (A.P.)?

A. 1, 3, 5, 7, 9, ...
B. 2, 4, 8, 16, 32, ...
C. 1, 2, 3, 5, 8, ...
D. 1, 1, 2, 3, 5, ...

Answer: A. 1, 3, 5, 7, 9, ...

11. In an arithmetic progression, the 7th term is 20 and the 12th term is 40. What is the common difference $d$ ?

A. 2
B. 4
C. 5
D. 6

Answer: B. 4

Explanation: Using $a_n = a + (n-1)d$ , find $d$ by solving the system of equations.

12. The nth term of a sequence is $a_n = 5n - 2$ . What is the 8th term of the sequence?

A. 38
B. 38.5
C. 40
D. 42

Answer: A. 38

Explanation: $a_8 = 5(8) - 2 = 38$

13. In a geometric progression, the first term is 3 and the common ratio is $\frac{1}{3}$ . What is the 4th term?

A. $\frac{1}{27}$
B. $\frac{1}{81}$
C. 9
D. 27

Answer: B. $\frac{1}{81}$

Explanation: $a_4 = 3 \times \left(\frac{1}{3}\right)^3 = \frac{1}{81}$

14. What is the 10th term of the sequence defined by $a_n = 3n + 2$ ?

A. 32
B. 33
C. 34
D. 35

Answer: B. 33

Explanation: $a_{10} = 3(10) + 2 = 33$

15. The sum of the first five terms of a G.P. is 121, and the first term is 3. What is the common ratio $r$ ?

A. 2
B. 3
C. 4
D. 5

Answer: A. 2

Explanation: Use the sum formula for G.P. $S_n = a \frac{1 - r^n}{1 - r}$ and solve for $r$ .

16. If the 5th term of a G.P. is 48 and the common ratio is 2, what is the first term?

A. 3
B. 6
C. 12
D. 24

Answer: B. 6

Explanation: Use the formula for the nth term of a G.P. $a_n = a r^{n-1}$ and solve for $a$ .

17. The first three terms of a G.P. are 4, 12, and 36. What is the common ratio?

A. 2
B. 3
C. 4
D. 6

Answer: B. 3

Explanation: Common ratio $r = \frac{12}{4} = 3$ .

18. If the sum of the first three terms of a G.P. is 39 and their product is 1, what are the terms?

A. 1, 3, 9
B. 3, 9, 27
C. 5, 5, 5
D. 2, 4, 8

Answer: A. 1, 3, 9

19. What is the 7th term of the sequence defined by $a_n = 2^n$ ?

A. 128
B. 64
C. 32
D. 16

Answer: A. 128

Explanation: $a_7 = 2^7 = 128$

20. In a Fibonacci sequence, the 5th term is 5, what is the 6th term?

A. 8
B. 10
C. 13
D. 21

Answer: C. 13

21. The sum of the first 5 terms of an arithmetic progression is 50, and the first term is 10. What is the common difference $d$ ?

A. 5
B. 6
C. 8
D. 10

Answer: B. 6

22. What is the general formula for the nth term of a geometric progression (G.P.)?

A. $a_n = a + (n-1)d$
B. $a_n = ar^{n-1}$
C. $a_n = a(1 + r)^{n-1}$
D. $a_n = a(1 - r)^{n-1}$

Answer: B. $a_n = ar^{n-1}$

23. If the nth term of an arithmetic progression is $a_n = 3n - 1$ , what is the 6th term?

A. 17
B. 18
C. 19
D. 20

Answer: C. 19

24. What is the 4th term of the arithmetic sequence 2, 5, 8, 11, ...?

A. 8
B. 9
C. 10
D. 11

Answer: C. 10

25. In a G.P. with first term 5 and common ratio 3, what is the sum of the first 3 terms?

A. 35
B. 45
C. 55
D. 65

Answer: B. 45

26. The sum of the first 4 terms of a geometric sequence is 120, and the first term is 5. What is the common ratio?

A. 2
B. 3
C. 4
D. 5

Answer: A. 2

27. What is the sum of the first 5 terms of the geometric progression 1, 3, 9, 27, ...?

A. 90
B. 121
C. 121
D. 40

Answer: B. 121

28. In a G.P., the first term is 3, the second term is 6. What is the common ratio?

A. 1
B. 2
C. 3
D. 4

Answer: B. 2

29. If the nth term of a sequence is given by $a_n = 3n + 1$ , what is the 5th term?

A. 14
B. 16
C. 17
D. 18

Answer: A. 14

30. If the first three terms of an arithmetic progression are 1, 5, and 9, what is the common difference?

A. 3
B. 4
C. 5
D. 6

Answer: A. 3

31. In an arithmetic sequence, the sum of the first 10 terms is 150, and the first term is 5. What is the common difference?

A. 10
B. 12
C. 15
D. 16

Answer: B. 12

32. In a Fibonacci sequence, the first two terms are 1 and 1. What is the 6th term?

A. 5
B. 8
C. 13
D. 21

Answer: C. 13

33. What is the sum of the first 4 terms of the G.P. 2, 6, 18, 54?

A. 80
B. 81
C. 82
D. 83

Answer: B. 81

34. The nth term of a sequence is $a_n = 2n^2 + 1$ . What is the 4th term of the sequence?

A. 33
B. 34
C. 35
D. 36

Answer: A. 33

35. The common ratio of a G.P. is 3, and the first term is 4. What is the 5th term?

A. 324
B. 242
C. 108
D. 81

Answer: C. 108

36. In a G.P., the first term is 1, and the common ratio is $\frac{1}{3}$ . What is the sum of the first 5 terms?

A. $\frac{121}{81}$
B. $\frac{121}{243}$
C. $\frac{121}{243}$
D. $100$

Answer: A. $\frac{121}{81}$

37. Which of the following sequences is an example of a Fibonacci sequence?

A. 1, 2, 3, 5, 8, 13
B. 2, 4, 8, 16
C. 1, 2, 4, 8, 16
D. 1, 1, 2, 3, 5

Answer: A. 1, 2, 3, 5, 8, 13

38. Which of the following is true for a G.P.?

A. The terms are equally spaced.
B. The terms have a constant ratio between them.
C. The terms increase by the same number.
D. The terms decrease by the same ratio.

Answer: B. The terms have a constant ratio between them.

39. What is the sum of the first 5 terms of the G.P. 2, 6, 18, 54, 162?

A. 242
B. 243
C. 245
D. 247

Answer: B. 243

40. In a Fibonacci sequence, what is the 10th term if the first two terms are both 1?

A. 34
B. 55
C. 65
D. 89

Answer: B. 55

41. What is the sum of the series 2 + 4 + 6 + 8 + ... + 20?

A. 110
B. 110
C. 120
D. 124

Answer: A. 110

42. What is the 7th term of the sequence defined by $a_n = 4n - 3$ ?

A. 23
B. 24
C. 25
D. 26

Answer: B. 24

43. If $a_3 = 27$ in a geometric progression, and the first term is 3, what is the common ratio?

A. 3
B. 4
C. 5
D. 6

Answer: B. 4

44. In an arithmetic progression, the sum of the first 15 terms is 105, and the first term is 2. What is the common difference?

A. 5
B. 6
C. 7
D. 8

Answer: B. 6

45. The first term of a geometric progression is 8, and the 8th term is 512. What is the common ratio?

A. 2
B. 4
C. 5
D. 8

Answer: B. 4

46. If $a_n = 2n - 1$ , what is the 15th term?

A. 29
B. 31
C. 35
D. 37

Answer: B. 31

47. A sequence is defined by $a_n = n^2$ . What is the 6th term?

A. 36
B. 45
C. 48
D. 49

Answer: B. 45

48. The 3rd term of an arithmetic sequence is 9, and the 8th term is 24. What is the common difference?

A. 2
B. 3
C. 4
D. 5

Answer: C. 4

49. The sum of the first $n$ terms of a geometric progression is given by $S_n = 5 \times (1 - 3^n)$ . What is the first term if $r = 3$ ?

A. 1
B. 2
C. 5
D. 7

Answer: B. 2

50. The sum of the first 8 terms of a geometric series is 15, and the first term is 1. What is the common ratio?

A. $\frac{1}{3}$
B. $\frac{1}{2}$
C. 2
D. 3

Answer: C. 2

51. If the sum of the first $n$ terms of a sequence is given by $S_n = n^2 + n$ , what is the sum of the first 4 terms?

A. 16
B. 20
C. 24
D. 30

Answer: B. 20

52. The first four terms of an arithmetic progression are 7, 12, 17, 22. What is the common difference?

A. 3
B. 4
C. 5
D. 6

Answer: B. 5

53. A geometric progression starts with 5, and the 4th term is 80. What is the common ratio?

A. 3
B. 4
C. 5
D. 6

Answer: B. 4

54. If $a_1 = 2$ , $a_2 = 4$ , $a_3 = 8$ , then what is $a_5$ in the geometric progression?

A. 12
B. 16
C. 20
D. 24

Answer: B. 16

55. If the sum of the first $n$ terms of an arithmetic sequence is $3n + 2$ , what is the first term if $n = 5$ ?

A. 7
B. 9
C. 11
D. 13

Answer: B. 9

56. In an arithmetic progression, the 5th term is 20, and the 15th term is 50. What is the common difference?

A. 2
B. 4
C. 6
D. 8

Answer: C. 6

57. If the 6th term of a geometric progression is 54 and the first term is 3, what is the common ratio?

A. 2
B. 3
C. 4
D. 5

Answer: B. 3

58. What is the sum of the first 10 terms of the sequence $5, 10, 15, 20, \ldots$ ?

A. 50
B. 150
C. 250
D. 500

Answer: C. 250

59. The sum of an arithmetic series with first term $a_1 = 5$ , last term $a_n = 50$ , and 20 terms is calculated to be 525. What is the common difference?

A. 1
B. 2
C. 3
D. 4

Answer: B. 2

60. A sequence is defined by $a_n = 2^n$ . What is the sum of the first 4 terms?

A. 30
B. 31
C. 32
D. 34

Answer: B. 31

61. In an arithmetic progression, the 4th term is 10, and the 8th term is 22. What is the common difference?

A. 3
B. 4
C. 5
D. 6

Answer: B. 4

Explanation: Using the formula $a_n = a_1 + (n-1)d$ , you can find the common difference.

62. The first term of a geometric progression is 3, and the common ratio is 2. What is the 5th term?

A. 24
B. 48
C. 72
D. 96

Answer: B. 48

Explanation: $a_5 = 3 \times 2^{4} = 48$

63. What is the 10th term of the sequence $a_n = 3n - 1$ ?

A. 29
B. 30
C. 31
D. 32

Answer: B. 30

Explanation: $a_{10} = 3(10) - 1 = 30$

64. The first term of an arithmetic progression is 7, and the common difference is 5. What is the 12th term?

A. 55
B. 60
C. 65
D. 70

Answer: B. 60

Explanation: Use $a_n = a_1 + (n-1)d$ to find the 12th term.

65. In a geometric progression, the first term is 2 and the common ratio is $\frac{1}{2}$ . What is the 6th term?

A. $\frac{1}{32}$
B. $\frac{1}{16}$
C. $\frac{1}{8}$
D. $\frac{1}{4}$

Answer: B. $\frac{1}{16}$

Explanation: $a_6 = 2 \times \left( \frac{1}{2} \right)^5 = \frac{1}{16}$

66. The sum of the first 4 terms of an arithmetic progression is 40, and the first term is 6. What is the common difference?

A. 8
B. 10
C. 12
D. 14

Answer: B. 10

Explanation: Use the sum formula for an arithmetic series and solve for $d$ .

67. In a geometric progression, the first term is 4, and the common ratio is $\frac{1}{4}$ . What is the sum of the first 6 terms?

A. $\frac{256}{81}$
B. $\frac{255}{81}$
C. $\frac{255}{80}$
D. $\frac{256}{80}$

Answer: A. $\frac{256}{81}$

68. The first three terms of a geometric progression are 1, 2, 4. What is the 7th term?

A. 32
B. 64
C. 128
D. 256

Answer: B. 64

Explanation: The common ratio is 2. $a_7 = 1 \times 2^{6} = 64$

69. The sum of the first 6 terms of a sequence is 72, and the first term is 6. What is the common ratio?

A. 3
B. 4
C. 5
D. 6

Answer: A. 3

Explanation: Use the sum formula for a geometric progression and solve for $r$ .

70. In a Fibonacci sequence, the first two terms are 1 and 1. What is the 7th term?

A. 13
B. 21
C. 34
D. 55

Answer: C. 34

71. What is the common ratio of the geometric progression 3, 9, 27, 81, ...?

A. 2
B. 3
C. 4
D. 5

Answer: B. 3

72. The 4th term of an arithmetic progression is 14, and the common difference is 2. What is the first term?

A. 8
B. 10
C. 12
D. 16

Answer: B. 10

73. If the sum of the first 5 terms of a geometric progression is 121 and the first term is 3, what is the common ratio?

A. 2
B. 3
C. 4
D. 5

Answer: A. 2

74. The nth term of a geometric progression is given by $a_n = 3 \times 2^{n-1}$ . What is the 6th term?

A. 96
B. 48
C. 24
D. 12

Answer: A. 96

75. The first term of a sequence is 10, and the 5th term is 22. What is the common difference of the arithmetic progression?

A. 3
B. 4
C. 5
D. 6

Answer: B. 4

Explanation: Use $a_5 = a_1 + (5-1)d$ , solve for $d$ .

76. If the first term of a geometric progression is 5 and the 6th term is 125, what is the common ratio?

A. 2
B. 3
C. 4
D. 5

Answer: B. 3

77. In an arithmetic progression, the 2nd term is 5 and the 6th term is 15. What is the common difference?

A. 3
B. 4
C. 5
D. 6

Answer: A. 3

78. If the first two terms of a sequence are 1 and 4, and the common difference is 3, what is the 10th term?

A. 28
B. 29
C. 30
D. 31

Answer: C. 30

79. The sum of the first 6 terms of a geometric progression is 63, and the first term is 3. What is the common ratio?

A. 2
B. 3
C. 4
D. 5

Answer: A. 2

80. If the sum of the first $n$ terms of an arithmetic progression is given by $S_n = 4n + 3$ , what is the 10th term?

A. 43
B. 44
C. 45
D. 46

Answer: B. 44

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Friday, November 22, 2024

MCQ Mathematics Chapter 8: SEQUENCES AND SERIES, HS 1st year

1. What is a sequence in mathematics?

2. What is the general term of an arithmetic progression (A.P.)?

3. Which of the following is true about geometric progression (G.P.)?

4. In a G.P., the first term a=3a = 3a=3 and the common ratio r=2r = 2r=2. What is the 5th term?

5. If the nth term of a sequence is given by an=2n−1a_n = 2n - 1an​=2n−1, what is the 10th term?

6. What is the sum of the first n terms of a G.P. if the first term is aaa, the common ratio is rrr, and r≠1r \neq 1r=1?

7. In a Fibonacci sequence, the third term is the sum of:

8. What is a geometric mean (G.M.) of two positive numbers aaa and bbb?

9. In a sequence of numbers, if the ratio of each term to the previous term is constant, it is called a:

10. Which of the following sequences is an example of an arithmetic progression (A.P.)?

11. In an arithmetic progression, the 7th term is 20 and the 12th term is 40. What is the common difference ddd?

12. The nth term of a sequence is an=5n−2a_n = 5n - 2an​=5n−2. What is the 8th term of the sequence?

13. In a geometric progression, the first term is 3 and the common ratio is 13\frac{1}{3}31​. What is the 4th term?

14. What is the 10th term of the sequence defined by an=3n+2a_n = 3n + 2an​=3n+2?

15. The sum of the first five terms of a G.P. is 121, and the first term is 3. What is the common ratio rrr?

16. If the 5th term of a G.P. is 48 and the common ratio is 2, what is the first term?

17. The first three terms of a G.P. are 4, 12, and 36. What is the common ratio?

18. If the sum of the first three terms of a G.P. is 39 and their product is 1, what are the terms?

19. What is the 7th term of the sequence defined by an=2na_n = 2^nan​=2n?

20. In a Fibonacci sequence, the 5th term is 5, what is the 6th term?

21. The sum of the first 5 terms of an arithmetic progression is 50, and the first term is 10. What is the common difference ddd?

22. What is the general formula for the nth term of a geometric progression (G.P.)?

23. If the nth term of an arithmetic progression is an=3n−1a_n = 3n - 1an​=3n−1, what is the 6th term?

24. What is the 4th term of the arithmetic sequence 2, 5, 8, 11, ...?

25. In a G.P. with first term 5 and common ratio 3, what is the sum of the first 3 terms?

26. The sum of the first 4 terms of a geometric sequence is 120, and the first term is 5. What is the common ratio?

27. What is the sum of the first 5 terms of the geometric progression 1, 3, 9, 27, ...?

28. In a G.P., the first term is 3, the second term is 6. What is the common ratio?

29. If the nth term of a sequence is given by an=3n+1a_n = 3n + 1an​=3n+1, what is the 5th term?

30. If the first three terms of an arithmetic progression are 1, 5, and 9, what is the common difference?

31. In an arithmetic sequence, the sum of the first 10 terms is 150, and the first term is 5. What is the common difference?

32. In a Fibonacci sequence, the first two terms are 1 and 1. What is the 6th term?

33. What is the sum of the first 4 terms of the G.P. 2, 6, 18, 54?

34. The nth term of a sequence is an=2n2+1a_n = 2n^2 + 1an​=2n2+1. What is the 4th term of the sequence?

35. The common ratio of a G.P. is 3, and the first term is 4. What is the 5th term?

36. In a G.P., the first term is 1, and the common ratio is 13\frac{1}{3}31​. What is the sum of the first 5 terms?

37. Which of the following sequences is an example of a Fibonacci sequence?

38. Which of the following is true for a G.P.?

39. What is the sum of the first 5 terms of the G.P. 2, 6, 18, 54, 162?

40. In a Fibonacci sequence, what is the 10th term if the first two terms are both 1?

41. What is the sum of the series 2 + 4 + 6 + 8 + ... + 20?

42. What is the 7th term of the sequence defined by an=4n−3a_n = 4n - 3an​=4n−3?

43. If a3=27a_3 = 27a3​=27 in a geometric progression, and the first term is 3, what is the common ratio?

44. In an arithmetic progression, the sum of the first 15 terms is 105, and the first term is 2. What is the common difference?

45. The first term of a geometric progression is 8, and the 8th term is 512. What is the common ratio?

46. If an=2n−1a_n = 2n - 1an​=2n−1, what is the 15th term?

47. A sequence is defined by an=n2a_n = n^2an​=n2. What is the 6th term?

48. The 3rd term of an arithmetic sequence is 9, and the 8th term is 24. What is the common difference?

49. The sum of the first nnn terms of a geometric progression is given by Sn=5×(1−3n)S_n = 5 \times (1 - 3^n)Sn​=5×(1−3n). What is the first term if r=3r = 3r=3?

50. The sum of the first 8 terms of a geometric series is 15, and the first term is 1. What is the common ratio?

51. If the sum of the first nnn terms of a sequence is given by Sn=n2+nS_n = n^2 + nSn​=n2+n, what is the sum of the first 4 terms?

52. The first four terms of an arithmetic progression are 7, 12, 17, 22. What is the common difference?

53. A geometric progression starts with 5, and the 4th term is 80. What is the common ratio?

54. If a1=2a_1 = 2a1​=2, a2=4a_2 = 4a2​=4, a3=8a_3 = 8a3​=8, then what is a5a_5a5​ in the geometric progression?

55. If the sum of the first nnn terms of an arithmetic sequence is 3n+23n + 23n+2, what is the first term if n=5n = 5n=5?

56. In an arithmetic progression, the 5th term is 20, and the 15th term is 50. What is the common difference?

57. If the 6th term of a geometric progression is 54 and the first term is 3, what is the common ratio?

58. What is the sum of the first 10 terms of the sequence 5,10,15,20,…5, 10, 15, 20, \ldots5,10,15,20,…?

59. The sum of an arithmetic series with first term a1=5a_1 = 5a1​=5, last term an=50a_n = 50an​=50, and 20 terms is calculated to be 525. What is the common difference?

60. A sequence is defined by an=2na_n = 2^nan​=2n. What is the sum of the first 4 terms?

61. In an arithmetic progression, the 4th term is 10, and the 8th term is 22. What is the common difference?

62. The first term of a geometric progression is 3, and the common ratio is 2. What is the 5th term?

63. What is the 10th term of the sequence an=3n−1a_n = 3n - 1an​=3n−1?

64. The first term of an arithmetic progression is 7, and the common difference is 5. What is the 12th term?

65. In a geometric progression, the first term is 2 and the common ratio is 12\frac{1}{2}21​. What is the 6th term?

66. The sum of the first 4 terms of an arithmetic progression is 40, and the first term is 6. What is the common difference?

67. In a geometric progression, the first term is 4, and the common ratio is 14\frac{1}{4}41​. What is the sum of the first 6 terms?

68. The first three terms of a geometric progression are 1, 2, 4. What is the 7th term?

69. The sum of the first 6 terms of a sequence is 72, and the first term is 6. What is the common ratio?

70. In a Fibonacci sequence, the first two terms are 1 and 1. What is the 7th term?

71. What is the common ratio of the geometric progression 3, 9, 27, 81, ...?

72. The 4th term of an arithmetic progression is 14, and the common difference is 2. What is the first term?

73. If the sum of the first 5 terms of a geometric progression is 121 and the first term is 3, what is the common ratio?

74. The nth term of a geometric progression is given by an=3×2n−1a_n = 3 \times 2^{n-1}an​=3×2n−1. What is the 6th term?

75. The first term of a sequence is 10, and the 5th term is 22. What is the common difference of the arithmetic progression?

76. If the first term of a geometric progression is 5 and the 6th term is 125, what is the common ratio?

77. In an arithmetic progression, the 2nd term is 5 and the 6th term is 15. What is the common difference?

78. If the first two terms of a sequence are 1 and 4, and the common difference is 3, what is the 10th term?

4. In a G.P., the first term $a = 3$ and the common ratio $r = 2$ . What is the 5th term?

5. If the nth term of a sequence is given by $a_n = 2n - 1$ , what is the 10th term?

6. What is the sum of the first n terms of a G.P. if the first term is $a$ , the common ratio is $r$ , and $r \neq 1$ ?

8. What is a geometric mean (G.M.) of two positive numbers $a$ and $b$ ?

11. In an arithmetic progression, the 7th term is 20 and the 12th term is 40. What is the common difference $d$ ?

12. The nth term of a sequence is $a_n = 5n - 2$ . What is the 8th term of the sequence?

13. In a geometric progression, the first term is 3 and the common ratio is $\frac{1}{3}$ . What is the 4th term?

14. What is the 10th term of the sequence defined by $a_n = 3n + 2$ ?

15. The sum of the first five terms of a G.P. is 121, and the first term is 3. What is the common ratio $r$ ?

19. What is the 7th term of the sequence defined by $a_n = 2^n$ ?

21. The sum of the first 5 terms of an arithmetic progression is 50, and the first term is 10. What is the common difference $d$ ?

23. If the nth term of an arithmetic progression is $a_n = 3n - 1$ , what is the 6th term?

29. If the nth term of a sequence is given by $a_n = 3n + 1$ , what is the 5th term?

34. The nth term of a sequence is $a_n = 2n^2 + 1$ . What is the 4th term of the sequence?

36. In a G.P., the first term is 1, and the common ratio is $\frac{1}{3}$ . What is the sum of the first 5 terms?

42. What is the 7th term of the sequence defined by $a_n = 4n - 3$ ?

43. If $a_3 = 27$ in a geometric progression, and the first term is 3, what is the common ratio?

46. If $a_n = 2n - 1$ , what is the 15th term?

47. A sequence is defined by $a_n = n^2$ . What is the 6th term?

49. The sum of the first $n$ terms of a geometric progression is given by $S_n = 5 \times (1 - 3^n)$ . What is the first term if $r = 3$ ?

51. If the sum of the first $n$ terms of a sequence is given by $S_n = n^2 + n$ , what is the sum of the first 4 terms?

54. If $a_1 = 2$ , $a_2 = 4$ , $a_3 = 8$ , then what is $a_5$ in the geometric progression?

55. If the sum of the first $n$ terms of an arithmetic sequence is $3n + 2$ , what is the first term if $n = 5$ ?

58. What is the sum of the first 10 terms of the sequence $5, 10, 15, 20, \ldots$ ?

59. The sum of an arithmetic series with first term $a_1 = 5$ , last term $a_n = 50$ , and 20 terms is calculated to be 525. What is the common difference?

60. A sequence is defined by $a_n = 2^n$ . What is the sum of the first 4 terms?

63. What is the 10th term of the sequence $a_n = 3n - 1$ ?

65. In a geometric progression, the first term is 2 and the common ratio is $\frac{1}{2}$ . What is the 6th term?

67. In a geometric progression, the first term is 4, and the common ratio is $\frac{1}{4}$ . What is the sum of the first 6 terms?

74. The nth term of a geometric progression is given by $a_n = 3 \times 2^{n-1}$ . What is the 6th term?

80. If the sum of the first $n$ terms of an arithmetic progression is given by $S_n = 4n + 3$ , what is the 10th term?