Skip to content

Class X – Arithmetic Progression (PYQs) – Solutions

Arithmetic Progression (Previous Year Questions)

1. Find the 12th term from the end of the AP: –2, – 4, – 6, …, – 100.

View Answer

Ans.

2. Find the 20th term from the last term of the AP: 3, 8, 13,…, 253.

View Answer

Ans.

3. Which term of the AP: 3, 8, 13, 18, …, is 78?

View Answer

Ans.

4. The sum of the 5th and 7th terms of an AP is 52 and the 10th term is 46. Find the AP.

View Answer

Ans.

5. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

View Answer

Ans.

6. Find the 10th term of the AP: 2, 7, 12, …

View Answer

Ans. 47

7. Find the 6th term from the end of the AP: 17, 14, 11, …, –40.

View Answer

Ans. –25

8. Which term of the AP: 21, 18, 15, … is zero?

View Answer

Ans. 8

9. Write the next term of the AP: √8, √18, √32 , ………..

View Answer

Ans. 50 or 5√2

10. For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an AP?

View Answer

Ans.

11. For what value of k will the consecutive terms 2k + 1, 3k + 3 and 5k – 1 form an AP?

View Answer

Ans.

12. Find the eleventh term from the last term of the AP: 27, 23, 19, …, –65.

View Answer

Ans. a11 = –25

13. If the first three terms of an AP are b, c and 2b, then find the ratio of b and c.

View Answer

Ans.

14. Find how many integers between 200 and 500 are divisible by 8.

View Answer

Ans.

15. Is –150 a term of the AP: 17, 12, 7, 2, …?

View Answer

Ans.

16. Find the number of two-digit numbers which are divisible by 6.

View Answer

Ans.

17. Which term of the AP: 3, 14, 25, 36, … will be 99 more than its 25th term?

View Answer

Ans.

18. Which term of the AP: 3, 15, 27, 39, … will be 120 more than its 21st term?

View Answer

Ans.

19. How many two-digit numbers are divisible by 7?

View Answer

Ans.

20. How many two digit numbers are divisible by 3?

View Answer

Ans.

21. If 1/(x + 2), 1/(x + 3) and 1/(x + 5) are in A.P, find the value of x?

View Answer

Ans.

22. How many three digit numbers are divisible by 11?

View Answer

Ans.

23. In an AP, the first term is 12 and the common difference is 6. If the last term of the AP is 252, find its middle term.

View Answer

Ans.

24. Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

View Answer

Ans.

25. The 4th term of an AP is zero. Prove that the 25th term of the AP is three times its 11th term.

View Answer

Ans.

26. Find the middle term of the AP: 6, 13, 20, …, 216.

View Answer

Ans.

27. The nth term of an AP is 6n + 2. Find its common difference

View Answer

Ans. 6

28. Find the 10th term from end of the AP: 4, 9, 14, …, 254.

View Answer

Ans. 209

29. Determine k so that k2 + 4k + 8, 2k2 + 3k + 6, 3k2 + 4k + 4 are three consecutive terms of an AP.

View Answer

Ans. k = 0

30. Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5 both.

View Answer

Ans.

31. The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle.

View Answer

Ans. 40°, 60°, 80°

32. The 8th term of an AP is 37 and its 12th term is 57. Find the AP.

View Answer

Ans. 2, 7, 12, 17, 22, …

33. The pth, qth and rth terms of an AP are a, b and c respectively. Show that a(q – r) + b(r – p) + c(p – q) = 0.

View Answer

Ans.

34. If m times the mth term of an Arithmetic Progression is equal to n times its nth term and m ≠ n, show that the (m + n)th term of the AP is zero.

View Answer

Ans.

35. The 19th term of an AP is equal to three times its sixth term. If its 9th term is 19, find the AP.

View Answer

Ans. 3, 5, 7, 9,…

36. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

View Answer

Ans. –13, –8, –3

37. The eighth term of an AP is half its second term and the eleventh term exceeds one-third of its fourth term by 1. Find the 15th term

View Answer

Ans. 3

38. If 4 times the 4th term of an AP is equal to 18 times the 18th term, then find the 22nd term.

View Answer

Ans.

39. How many terms of the AP: 9, 17, 25, … must be taken to give a sum of 636?

View Answer

Ans.

40. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n term

View Answer

Ans.

41. The sum of the first 7 terms of an AP is 63 and the sum of its next 7 terms is 161. Find the 28th term of this AP.

View Answer

Ans.

42. The sum of the first n terms of an AP is 3n2 + 6n. Find the nth term of this AP.

View Answer

Ans.

43. In an AP, the sum of first ten terms is – 150 and the sum of next ten terms is – 550. Find the AP.

View Answer

Ans.

44. If the sum of the first p terms of an AP is ap2 + bp, find its common difference.

View Answer

Ans.

45. The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference ‘d’.

View Answer

Ans.

46. The sum of the first n terms of an AP is given by Sn = 3n2 – 4n. Determine the AP and the 12th term.

View Answer

Ans.

47. If Sn denotes the sum of the first n terms of an AP, prove that S30 = 3 (S20 – S10).

View Answer

Ans.

48. The sum of n, 2n, 3n terms of an AP are S1, S2 and S3 respectively. Prove that S3 = 3(S2 – S1).

View Answer

Ans.

49. If the sum of m terms of an AP is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero.

View Answer

Ans.

50. Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

View Answer

Ans.

51. Find the sum of first 10 terms of the AP: 2, 7, 12, …

View Answer

Ans. 245

52. If the sum of first m terms of an AP is 2m2 + 3m, then what is its second term?

View Answer

Ans. 9

53. Find the sum of first 10 multiples of 6.

View Answer

Ans.

54. What is the sum of five positive integers divisible by 6?

View Answer

Ans. 90

55. If the sum of the first q terms of an AP is 2q + 3q2 , what is its common difference?

View Answer

Ans.

56. If n th term of an AP is (2n + 1), what is the sum of its first three terms.

View Answer

Ans.

57. Find the sum of first 100 natural numbers.

View Answer

Ans.

58. Find the sum of first 8 multiples of 3

View Answer

Ans.

59. Find the number of terms of the AP: 54, 51, 48, … so that their sum is 513.

View Answer

Ans. 18 or 19

60. In an AP, the first term is –4, the last term is 29 and the sum of all its terms is 150. Find its common difference.

View Answer

Ans.

61. Find the sum of all three digit natural numbers, which are multiples of 11.

View Answer

Ans.

62. The first and the last terms of an AP are 8 and 65 respectively. If sum of all its terms is 730, find its common difference.

View Answer

Ans.

63. The sum of the first n terms of an AP is 4n2 + 2n. Find the n th term of this AP.

View Answer

Ans.

64. How many terms of the AP: 18, 16, 14, … be taken so that their sum is zero?

View Answer

Ans.

65. In an AP, if S5 + S7 = 167 and S10 = 235, then find the AP, where Sn denotes the sum of its first n terms.

View Answer

Ans.

66. How many multiples of 4 lie between 10 and 250? Also find their sum.

View Answer

Ans. 60, 7800

67. Find the sum of first n terms of an AP whose n th term is 5n – 1. Hence find the sum of first 20 terms.

View Answer

Ans.

68. The sum of first six terms of an AP is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first and the thirteenth terms of the AP.

View Answer

Ans. 2 and 26

69. Find the sum of all multiples of 7 lying between 500 and 900.

View Answer

Ans. 39, 900

70. In an AP, if the 6th and 13th terms are 35 and 70 respectively, find the sum of its first 20 terms.

View Answer

Ans.

71. The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.

View Answer

Ans.

72. If the ratio of the sum of first n terms of two AP’s is (7n + 1) : (4n + 27), find the ratio of their m th terms

View Answer

Ans.

73. The digits of a positive number of three digits are in AP and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.

View Answer

Ans.

74. The sums of first n terms of three A.Ps’ are S1, S2 and S3. The first term of each AP is 5 and their common differences are 2, 4 and 6 respectively. Prove that S1 + S3 = 2S2.

View Answer

Ans.

75. The sum of the first five terms of an AP is 55 and sum of the first ten terms of this AP is 235, find the sum of its first 20 terms.

View Answer

Ans. 970

76. The sums of n terms of two APs are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 25th terms.

View Answer

Ans. 249 : 447

77. How many terms of the AP: 24, 21, 18, … must be taken so that their sum is 78?

View Answer

Ans.

78. The first term of an AP is 5, the last term is 45 and sum is 400. Find the number of terms and the common difference.

View Answer

Ans.