# MCQs for Class 10 Maths Chapter 5 Arithmetic Progressions

MCQs for **Class 10 Maths Chapter 5 Arithmetic Progressions**: In this article, we have covered all the important MCQs for Free for Class 10 Term 1 2021-22 Board Exams. In accordance with the latest pattern, Padhle is here with MCQ Questions for Class 10.

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# MCQs for Class 10 Maths Chapter 5 Arithmetic Progressions

1. The nth term of an A.P. is given by an = 3 + 4n. The common difference is

(a) 7

(b) 3

(c) 4

(d) 1

Answer: (c) 4

2. In an AP, if d = –4, n = 7, a_{n} = 4, then a is

(a) 6

(b) 7

(c) 20

(d) 28

Answer: (d) 28

3. In an Arithmetic Progression, if a=28, d=-4, n=7, then an is:

(a)4

(b)5

(c)3

(d)7

Answer: (a) 4

4. The sum of the first 15 multiples of 8 is

(a) 920

(b) 860

(c) 900

(d) 960

Answer: (d) 960

5. The nth term of an A.P. is given by an = 3 + 4n. The common difference is

(a) 7

(b) 3

(c) 4

(d) 1

Answer: (c) 4

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6. The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

(a) 5

(b) 6

(c) 7

(d) 8

Answer: (b) 6

7. The (n – 1)th term of an A.P. is given by 7,12,17, 22,… is

(a) 5n + 2

(b) 5n + 3

(c) 5n – 5

(d) 5n – 3

Answer: (d) 5n – 3

8. If p, q, r and s are in A.P. then r – q is

(a) s – p

(b) s – q

(c) s – r

(d) none of these

Answer: (c) s – r

9. In an AP, if a = 3.5, d = 0, n = 101, then an will be

(a) 0

(b) 3.5

(c) 103.5

(d) 104.5

Answer: (b) 3.5

10. .If a=10 and d=10, then first four terms will be:

(a)10,30,50,60

(b)10,20,30,40

(c)10,15,20,25

(d)10,18,20,30

Answer: (b)10,20,30,40

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11. Next term of the AP √2, 3√2, 5√2, ……. is

(a) 2√7

(b) 6√2

(c) 9√2

(d) 7√2

Answer: (d) 7√2

12. If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are

(a) 2, 4, 6

(b) 1, 5, 3

(c) 2, 8, 4

(d) 2, 3, 4

Answer: (d) 2 ,3 ,4

13. If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is

(a) 13

(b) 9

(c) 21

(d) 17

Answer: (c) 21

14. The number of two digit numbers divisible by 5 is

(a) 19

(b) 18

(c) 16

(d) 17

Answer: (b) 18

15. The nth term of an A.P. 5, 2, -1, -4, -7 … is

(a) 2n + 5

(b) 2n – 5

(c) 8 – 3n

(d) 3n – 8

Answer: c

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16. The first four terms of an AP, whose first term is –2 and the common difference is –2, are

(a) – 2, 0, 2, 4

(b) – 2, 4, – 8, 16

(c) – 2, – 4, – 6, – 8

(d) – 2, – 4, – 8, –16

Answer: (c)– 2, – 4, – 6, – 8

17. The first term and common difference for the A.P. 3,1,-1,-3 is:

(a)1 and 3

(b)-1 and 3

(c)3 and -2

(d)2 and 3

Answer: (c) 3 and -2

18. First four terms of the sequence a_{n} = 2n + 3 are

(a) 3, 5, 7, 9

(b) 5, 7, 9, 11

(c) 5, 8, 11, 14

(d) 1, 3, 5, 7

Answer: (b) 5, 7, 9, 11

19. The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is

(a) -955

(b) -945

(c) -950

(d) -965

Answer: (a) -955

20. If 7th and 13th term of an A.P. are 34 and 64 respectively, then its 18th term is

(a) 87

(b) 88

(c) 89

(d) 90

Answer: (c) 89

21. What is the sum of the first 50 multiples of 3?

(a) 3255

(b) 3825

(c) 4325

(d) 4455

Answer: (b) 3825

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22. Find the sum of 12 terms of an A.P. whose nth term is given by a_{n} = 3n + 4

(a) 262

(b) 272

(c) 282

(d) 292

Answer: (a) 262

23. The famous mathematician associated with finding the sum of the first 100 natural numbers is

(a) Pythagoras

(b) Newton

(c) Gauss

(d) Euclid

Answer: (c) Gauss

24. 30th term of the A.P: 10,7, 4, …, is

(a)97

(b)77

(c)-77

(d)-87

Answer:(c) -77

25. 20th term of the AP -5, -3, -1, 1, is

(a) 33

(b) 30

(c) 20

(d) 25

Answer: (a) 33

26. The sum of all two digit odd numbers is

(a) 2575

(b) 2475

(c) 2524

(d) 2425

Answer: (b) 2475

27. If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is

(a) ab/2(b-a)

(b) ab/b-a

(c) 3ab/2(b-a)

(d) none

Answer: (c) 3ab/2(b-a)

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28. If 7th and 13th terms of an A.P. be 34 and 64, respectively, then it’s 18th term is :

(a) 87

(b) 88

(c) 89

(d) 90

Answer: (c) 89

29. The sum of first n odd natural numbers is

(a) 2n²

(b) 2n + 1

(c) 2n – 1

(d) n²

Answer: (d) n^{2}

30. 11th term of the A.P. -3, -1/2, ,2 …. Is

(a)28

(b)22

(c)-38

(d)-48

Answer: (b)22

31. If nth term of an AP is 7 – 4n, then its common difference is

(a) 4

(b) -4

(c) 3

(d) 11

Answer: (d) 11

32. nth term of the sequence a, a + d, a + 2d,… is

(a) a + nd

(b) a – (n – 1)d

(c) a + (n – 1)d

(d) n + nd

Answer: (a) a + nd

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33. If the sum of n terms of an A.P. is then its nth term is

(a) 4n – 3

(b) 3n – 4

(c) 4n + 3

(d) 3n + 4

Answer: (c) 4n + 3

34. The weights of 11 students selected for a team are noted in ascending order and are in A. P. The lowest value is 45 Kg, and the middle value is 55 Kg. What is the difference between the two values placed consecutively ?

(a) 4

(b) 2

(c) 6

(d) 3

Answer: (b) 2

35. If (p + q)th term of an A.P. is m and (p – q)tn term is n, then pth term is

(a) mn

(b) m/n

(c) ½(m-n)

(d) ½(m+n)

Answer:(d) ½(m+n)

36. The 11th term of the A.P -5 , -5/2 , 0 , 5/2 is…

(a) –20

(b) 20

(c) –30

(d) 30

Answer: (b) 20

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37 . The missing terms in AP: __, 13, __, 3 are:

(a)11 and 9

(b)17 and 9

(c)18 and 8

(d)18 and 9

Answer: (c)18 and 8

38. If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be

(a) A + B

(b) A – B

(c) 2A

(d) 2B

Answer: (d) 2B

39. The 10th term from the end of the A.P. 4, 9,14, …, 254 is

(a) 209

(b) 205

(c) 214

(d) 213

Answer: (a) 209

40. If 3 times the third term of an A.P. is equal to 5 times the fifth term. Then its 8th term is

(a) 0

(b) 1

(c) 2

(d) 3

Answer: (a) 0

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41. If 2x, x + 10, 3x + 2 are in A.P., then x is equal to

(a) 0

(b) 2

(c) 4

(d) 6

Answer: (d) 6

42. If a, b, c are in A.P. then a−b/b−c is equal to

(a) 1

(b) b/a

(c) a/c

(d) c/a

Answer: (a) 1

43. The 21st term of the AP whose first two terms are –3 and 4 is

(a) 17

(b) 137

(c) 143

(d) –143

Answer: (b) 137

44. Which term of the A.P. 3, 8, 13, 18, … is 78?

(a)12th

(b)13th

(c)15th

(d)16th

Answer: (d) 16th

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45. The 10th term of the sequence √3, √12, √27; …… is

(a) √243

(b) √300

(c) √363

(d) √432

Answer: (b) √300

46. The sum of all odd integers between 2 and 100 divisible by 3 is

(a) 17

(b) 867

(c) 876

(d) 786

Answer: (b) 867

47. In an A.P., am+n + am-n is equal to

(a) 0

(b) 1

(c) 2am

(d) am

Answer: (c) 2am

48. If p, q, r are in AP, then p3 + r3 – 8q3 is equal to

(a) 4pqr

(b) -6pqr

(c) 2pqr

(d) 8pqr

Answer: (b) -6pqr

49. If a, b, c, d, e are in A.P., then the value of a – 4b + 6c – 4d + e is

(a) 0

(b) 1

(c) -1.

(d) 2

Answer: (a) 0

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50. If the common difference of an AP is 5, then what is a_{18} – a_{13}?

(a) 5

(b) 20

(c) 25

(d) 30

Answer: (c) 25

51. If 17th term of an A.P. exceeds its 10th term by 7. The common difference is:

(a)1

(b)2

(c)3

(d)4

Answer: (a) 1

52. Sum of n terms of the series √2 + √8 + √18+ √32 + …… is

(a) n(n+2)/√2

(b) √2 n(n+1)

(c) n(n+1)/√2

(d) 1

Answer: (c)n(n+1)/√2

53. If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then 18th term

(a) 18

(b) 9

(c) 77

(d) 0

Answer: (d) 0

54. If pth term of an A.P. 1/q is and qth term is 1/p then the sum of pq terms is

(a) p-q/2

(b) p+q/2

(c) pq+½

(d) pq-½

Answer: (c) pq+½

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55. nth term of the sequence a, a + d, a + 2d,… is

(a) a + nd

(b) a – (n – 1)d

(c) a + (n – 1)d

(d) n + nd

Answer: (a) a + nd

56. The sum of first 16 terms of the AP: 10, 6, 2,… is

(a) –320

(b) 320

(c) –352

(d) –400

Answer: (a) -320

57. The number of multiples of 4 between 10 and 250 is:

(a)50

(b)40

(c)60

(d)30

Answer: (c) 60

58. If p – 1, p + 3, 3p – 1 are in AP, then p is equal to

(a) 4

(b) -4

(c) 2

(d) -2

Answer: (a) 4

59. The list of numbers -10, -6, -2, 2, … is

(a) an AP with d = -16

(b) an AP with d = 4

(c) an AP with d = -4

(d) not an AP

Answer: (b) an AP with d = 4

60. If the sum of first n even natural number is equal to k times the sum of first n odd natural number then value of k will be

(a) 1/n

(b) n-1/n

(c) n+1/2n

(d) n+1/n

Answer: (d) n+1/n

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61. An athlete wants to improve his stamina, so he decides to increase the distance he runs by half a kilometer every day. If he starts with 5 km on first day, find how much he runs on the 10 th day

(a) 6 Km

(b) 7.5 Km

(c) 9.5 Km

(d) 10 Km

Answer: (c) 9.5 Km

62. The middle most term (s) of the AP:–11, –7, –3, …, 49 is:

(a) 18, 20

(b) 19, 23

(c) 17, 21

(d) 23, 25

Answer: (c) 17, 21

63. 20th term from the last term of the A.P. 3, 8, 13, …, 253 is:

(a)147

(b)151

(c)154

(d)158

Answer: (d)158

64. The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to.

(a) 10

(b) 11

(c) 12

(d) 13

Answer: (b) 11

65. Two APs have the same common difference. . The first term of one of these is -1 and that of the other is -8. Then the difference between their 4th terms is

(a) -1

(b) -8

(c) 7

(d) -9

Answer:(c) 7

66. The number of terms of an A.P. 3, 7, 11, 15… to be taken so that the sum is 406 is

(a) 5

(b) 10

(c) 12

(d) 14

Answer: (d) 14

67. If the sum of n terms of an AP is 3n2+5n then which of its terms is 164?

(a) 27th

(b) 29th

(c) 28th

(c) 26th

Answer: (a) 27th

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68. In an AP if a = 1, a_{n} = 20 and S_{n} = 399, then n is

(a) 19

(b) 21

(c) 38

(d) 42

Answer: (c) 38

69. The sum of the first five multiples of 3 is:

(a)45

(b)55

(c)65

(d)75

Answer: (a) 45

70. If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be

(a) m + n

(b) -(m + n)

(c) m – n

(d) 0

Answer: (b) -(m + n)

71.For the common difference of an AP is 3, then a_{20} – a_{15} is

(a) 5

(b) 3

(c) 15

(d) 20

Answer: (c) 15

72. The common difference of the AP

(a) p

(b) -p

(c) -1

(d) 1

Answer: (c) -1

73. The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is

(a) 508th

(b) 502th

(c) 501th

(d) none of these

Answer: (d) none of these

74. If p, q, r, s, t are the terms of an A.P. with common difference -1 the relation between p and t is:

(a) t = p – 5

(b) t = p – 4

(c) t = p – 6

(d) t = p + 4

Answer: (b) t = p – 4

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75. If sum of n terms of an A.P. is then common difference of the A.P. is

(a) 3

(b) 4

(c) 6

(d) 7

Answer: (c) 6

76. For an A.P the sum of first 30 terms is -1155,the common difference is -3and the thirtieth term is -82. What is the first term?

(a) 10

(b) 8

(c) 5

(d) 12

Answer: (c) 5

77.If nth term of an AP is given by f_{n} = 3n + 4, find the common difference of the AP

(a) 3

(b) 2

(c) 4

(d) 7

Answer: (a) 3

78. Find the next two terms of the A.P.:- -10, -6,-2…

(a) 4,8

(b) -4,-8

(c) 2,6

(d) 6,10

Answer: (c) 2,6

79. Sum of all natural numbers lying between 250 and 1000 which are exactly divisible by 3 is

(a) 157365

(b) 153657

(c) 156375

(d) 155637

Answer: (c) 156375

80. How many terms of AP 54, 51, 48… are required to give a sum of 513?

(a) 21 or 25

(b) 22 or 23

(c) 23 or 24

(d) 18 or 19

Answer: (d) 18 or 19

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