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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 122 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the 10th term of the AP 12, 15, 18, 21, …? (a) 42 (b) 30 (c) 27 (d) 39
  2. 2.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 25 (b) 24 (c) 28 (d) 26
  3. 3.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 812 (d) 406
  5. 5.What is the 23rd term of the AP 6, 9, 12, 15, …? (a) 75 (b) 72 (c) 69 (d) 66
  6. 6.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 53 (b) 44 (c) 45 (d) 43
  7. 7.Which term of the AP 12, 17, 22, 27, … is 182? (a) 35th (b) 37th (c) 34th (d) 36th
  8. 8.What is the 39th term of the AP 2, 5, 8, 11, …? (a) 116 (b) 114 (c) 117 (d) 119
  9. 9.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 6972 (c) 3403 (d) 3486
  10. 10.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 946 (c) 968 (d) 1980
  11. 11.Which term of the AP 12, 19, 26, 33, … is 278? (a) 40th (b) 38th (c) 39th (d) 41st
  12. 12.What is the sum of all the whole numbers from 1 to 88? (a) 3916 (b) 3872 (c) 7832 (d) 3828
  13. 13.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 25 (b) 26 (c) 24 (d) 34
  14. 14.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 23 (b) 24 (c) 32 (d) 25
  15. 15.Which term of the AP 15, 21, 27, 33, … is 87? (a) 13th (b) 12th (c) 14th (d) 15th
  16. 16.What is the 25th term of the AP 12, 19, 26, 33, …? (a) 175 (b) 168 (c) 180 (d) 187
  17. 17.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 22 (b) 92 (c) 104 (d) 184
  18. 18.What is the sum of all the whole numbers from 1 to 15? (a) 120 (b) 240 (c) 121 (d) 105
  19. 19.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
  20. 20.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 11 (c) 65 (d) 70
  21. 21.What is the 12th term of the AP 4, 13, 22, 31, …? (a) 112 (b) 108 (c) 103 (d) 99
  22. 22.What is the 16th term of the AP 20, 22, 24, 26, …? (a) 30 (b) 50 (c) 52 (d) 32
  23. 23.What is the 24th term of the AP 11, 16, 21, 26, …? (a) 131 (b) 115 (c) 120 (d) 126
  24. 24.What is the 16th term of the AP 8, 17, 26, 35, …? (a) 144 (b) 143 (c) 152 (d) 135
  25. 25.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 282 (b) 40 (c) 564 (d) 300
  26. 26.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 31 (b) 32 (c) 30 (d) 39
  27. 27.What is the 15th term of the AP 20, 24, 28, 32, …? (a) 80 (b) 76 (c) 56 (d) 60
  28. 28.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 256 (d) 31
  29. 29.What is the 19th term of the AP 7, 13, 19, 25, …? (a) 114 (b) 115 (c) 108 (d) 121
  30. 30.What is the missing term in the AP 10, ?, 20, 25, 30? (a) 20 (b) 14 (c) 15 (d) 16
  31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 49 (d) 56
  32. 32.Which term of the AP 10, 13, 16, 19, … is 112? (a) 37th (b) 34th (c) 35th (d) 36th
  33. 33.What is the 25th term of the AP 1, 6, 11, 16, …? (a) 121 (b) 126 (c) 125 (d) 120
  34. 34.What is the 15th term of the AP 20, 22, 24, 26, …? (a) 28 (b) 30 (c) 48 (d) 50
  35. 35.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 5550 (c) 2775 (d) 2701
  36. 36.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2279 (c) 2278 (d) 2211
  37. 37.Which term of the AP 14, 20, 26, 32, … is 128? (a) 22nd (b) 19th (c) 20th (d) 21st
  38. 38.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 30 (b) 26 (c) 27 (d) 25
  39. 39.What is the 32nd term of the AP 20, 29, 38, 47, …? (a) 299 (b) 279 (c) 308 (d) 288
  40. 40.What is the missing term in the AP 20, 29, ?, 47, 56? (a) 37 (b) 39 (c) 47 (d) 38

Answer key

  1. 39
  2. 25
  3. 25
  4. 784
  5. 72
  6. 44
  7. 35th
  8. 116
  9. 3486
  10. 990
  11. 39th
  12. 3916
  13. 25
  14. 24
  15. 13th
  16. 180
  17. 92
  18. 120
  19. 225
  20. 65
  21. 103
  22. 50
  23. 126
  24. 143
  25. 282
  26. 31
  27. 76
  28. 256
  29. 115
  30. 15
  31. 49
  32. 35th
  33. 121
  34. 48
  35. 2775
  36. 2278
  37. 20th
  38. 26
  39. 299
  40. 38

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