MATHEMATICS CLASS- 10
MCQ- CH-5(Arithmetic Progressions)
Class 10 Mathematics
Chapter 5: Arithmetic Progressions
50 Board-Level MCQs with Answers and Solutions
Q1. Which of the following is an Arithmetic Progression (A.P.)?
(a) 2, 4, 8, 16
(b) 3, 7, 11, 15
(c) 1, 4, 9, 16
(d) 2, 6, 18, 54
Answer: (b) 3, 7, 11, 15
Solution: The common difference is 4.
Q2. The common difference of 5, 9, 13, 17, ... is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (c) 4
Q3. The first term of the A.P. 7, 12, 17, 22, ... is
(a) 5
(b) 7
(c) 12
(d) 17
Answer: (b) 7
Q4. Find the 10th term of the A.P. 2, 5, 8, 11, ...
(a) 26
(b) 27
(c) 29
(d) 30
Answer: (c) 29
Solution: a = 2, d = 3.
a₁₀ = a + 9d = 2 + 27 = 29.
Q5. The common difference of the A.P. 15, 11, 7, 3, ... is
(a) 4
(b) -4
(c) -3
(d) 3
Answer: (b) -4
Q6. Find the 15th term of the A.P. 4, 9, 14, 19, ...
(a) 69
(b) 70
(c) 74
(d) 79
Answer: (c) 74
Solution: a₁₅ = 4 + 14 × 5 = 74.
Q7. Which term of the A.P. 3, 8, 13, 18, ... is 63?
(a) 11th
(b) 12th
(c) 13th
(d) 14th
Answer: (c) 13th
Solution: 63 = 3 + (n−1)5 ⇒ n = 13.
Q8. The 20th term of the A.P. 1, 3, 5, 7, ... is
(a) 37
(b) 39
(c) 41
(d) 43
Answer: (b) 39
Q9. The sum of first 10 natural numbers is
(a) 45
(b) 50
(c) 55
(d) 60
Answer: (c) 55
Solution: S₁₀ = 10(11)/2 = 55.
Q10. The sum of first 20 even numbers is
(a) 400
(b) 420
(c) 440
(d) 460
Answer: (b) 420
Q11. The 25th term of the A.P. 7, 10, 13, ... is
(a) 76
(b) 77
(c) 79
(d) 80
Answer: (c) 79
Q12. The sum of first 15 terms of the A.P. 2, 4, 6, ... is
(a) 220
(b) 230
(c) 240
(d) 250
Answer: (c) 240
Q13. Find the common difference if a = 6 and a₁₂ = 50.
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (b) 4
Solution: 50 = 6 + 11d ⇒ d = 4.
Q14. The 50th term of the A.P. 5, 8, 11, ... is
(a) 149
(b) 150
(c) 152
(d) 155
Answer: (c) 152
Q15. The sum of first n natural numbers is
(a) n(n−1)/2
(b) n(n+1)/2
(c) n²
(d) (n+1)/2
Answer: (b)
Q16. Which term of the A.P. 4, 7, 10, ... is 52?
(a) 15th
(b) 16th
(c) 17th
(d) 18th
Answer: (c) 17th
Q17. The sum of first 12 terms of 3, 6, 9, ... is
(a) 216
(b) 225
(c) 234
(d) 240
Answer: (c) 234
Q18. The common difference of −2, 1, 4, 7, ... is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (b) 3
Q19. The first term of an A.P. is 8 and d = 5. The 11th term is
(a) 53
(b) 56
(c) 58
(d) 60
Answer: (c) 58
Q20. The sum of first 25 odd numbers is
(a) 525
(b) 600
(c) 625
(d) 650
Answer: (c) 625
Solution: Sum of first n odd numbers = n².
Q21. The 18th term of the A.P. 10, 7, 4, 1, ... is
(a) -41
(b) -42
(c) -43
(d) -44
Answer: (a) -41
Q22. If the 7th term of an A.P. is 31 and d = 4, then the first term is
(a) 5
(b) 6
(c) 7
(d) 8
Answer: (c) 7
Q23. Find the sum of first 30 multiples of 3.
(a) 1365
(b) 1395
(c) 1400
(d) 1450
Answer: (b) 1395
Q24. Which term of the A.P. 11, 15, 19, ... is 95?
(a) 20th
(b) 21st
(c) 22nd
(d) 23rd
Answer: (c) 22nd
Q25. The sum of first 50 natural numbers is
(a) 1225
(b) 1250
(c) 1275
(d) 1300
Answer: (c) 1275
Q26. (CBSE PYQ) If the nth term of an A.P. is 4n + 1, then its common difference is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (c) 4
Q27. The middle term of the A.P. 2, 4, 6, ..., 40 is
(a) 20
(b) 21
(c) 22
(d) 24
Answer: (b) 21
Q28. The sum of first 15 multiples of 4 is
(a) 450
(b) 460
(c) 480
(d) 500
Answer: (c) 480
Q29. If a = 12 and d = -2, then a₁₀ equals
(a) -4
(b) -6
(c) -8
(d) -10
Answer: (b) -6
Q30. The sum of first 100 natural numbers is
(a) 4950
(b) 5000
(c) 5050
(d) 5100
Answer: (c) 5050
Q31. (CBSE PYQ) If the 5th term of an A.P. is 18 and the 9th term is 30, then d equals
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (b) 3
Q32. Find the sum of first 20 terms of 5, 10, 15, ...
(a) 950
(b) 1000
(c) 1050
(d) 1100
Answer: (c) 1050
Q33. Which term of the A.P. 8, 13, 18, ... is 98?
(a) 18th
(b) 19th
(c) 20th
(d) 21st
Answer: (b) 19th
Q34. The sum of first 40 even numbers is
(a) 1600
(b) 1640
(c) 1680
(d) 1720
Answer: (b) 1640
Q35. If a = 3 and d = 7, then a₂₀ equals
(a) 129
(b) 130
(c) 136
(d) 140
Answer: (c) 136
Q36. (CBSE PYQ) The sum of first n odd numbers is
(a) n²
(b) n(n+1)
(c) n(n−1)
(d) 2n²
Answer: (a) n²
Q37. The 30th term of the A.P. 6, 11, 16, ... is
(a) 146
(b) 151
(c) 156
(d) 161
Answer: (b) 151
Q38. The sum of first 12 odd numbers is
(a) 132
(b) 144
(c) 156
(d) 168
Answer: (b) 144
Q39. A.P. stands for
(a) Arithmetic Progression
(b) Algebraic Process
(c) Arithmetic Process
(d) Algebraic Progression
Answer: (a)
Q40. If the common difference of an A.P. is zero, then the sequence is
(a) Increasing
(b) Decreasing
(c) Constant
(d) None
Answer: (c)
Q41. Three numbers are in A.P. If their sum is 24 and middle term is 8, then the numbers are
(a) 6, 8, 10
(b) 5, 8, 11
(c) 4, 8, 12
(d) 3, 8, 13
Answer: (a)
Q42. (CBSE PYQ) Which term of the A.P. 21, 18, 15, ... is zero?
(a) 6th
(b) 7th
(c) 8th
(d) 9th
Answer: (c) 8th
Q43. The sum of first 25 terms of 1, 2, 3, ... is
(a) 300
(b) 315
(c) 325
(d) 350
Answer: (b) 325
Q44. The common difference of 100, 90, 80, ... is
(a) 10
(b) -10
(c) -20
(d) 20
Answer: (b)
Q45. The 12th term of the A.P. 1, 4, 7, ... is
(a) 31
(b) 32
(c) 33
(d) 34
Answer: (d) 34
Q46. The sum of first 15 natural numbers is
(a) 110
(b) 115
(c) 120
(d) 125
Answer: (c) 120
Q47. If a = 7 and d = 7, then a₁₅ equals
(a) 98
(b) 100
(c) 105
(d) 110
Answer: (c) 105
Q48. The sum of first 10 multiples of 5 is
(a) 250
(b) 275
(c) 300
(d) 325
Answer: (b) 275
Q49. The nth term formula of an A.P. is
(a) a + nd
(b) a + (n−1)d
(c) a − nd
(d) nd
Answer: (b)
Q50. Which statement is true?
(a) Every sequence is an A.P.
(b) Common difference of an A.P. is constant.
(c) Sum formula cannot be used in A.P.
(d) An A.P. always increases.
Answer: (b) Common difference of an A.P. is constant.
Solution: The defining property of an Arithmetic Progression is a constant common difference.