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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 515 · 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 31st term of the AP 7, 13, 19, 25, …? (a) 193 (b) 187 (c) 186 (d) 180
  2. 2.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
  3. 3.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 182 (b) 25 (c) 105 (d) 91
  4. 4.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 37 (b) 159 (c) 154 (d) 308
  5. 5.What is the 39th term of the AP 13, 21, 29, 37, …? (a) 325 (b) 304 (c) 312 (d) 317
  6. 6.What is the 39th term of the AP 4, 6, 8, 10, …? (a) 78 (b) 76 (c) 82 (d) 80
  7. 7.What is the 20th term of the AP 14, 21, 28, 35, …? (a) 133 (b) 140 (c) 147 (d) 154
  8. 8.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 300 (b) 45 (c) 276 (d) 552
  9. 9.What is the 16th term of the AP 1, 4, 7, 10, …? (a) 48 (b) 46 (c) 49 (d) 45
  10. 10.What is the 17th term of the AP 18, 23, 28, 33, …? (a) 98 (b) 85 (c) 80 (d) 103
  11. 11.What is the 10th term of the AP 18, 21, 24, 27, …? (a) 30 (b) 27 (c) 45 (d) 48
  12. 12.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 37 (b) 154 (c) 133 (d) 266
  13. 13.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 144 (d) 156
  14. 14.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3872 (c) 3828 (d) 3916
  15. 15.What is the missing term in the AP 18, 27, ?, 45, 54? (a) 45 (b) 37 (c) 36 (d) 35
  16. 16.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 21 (b) 13 (c) 11 (d) 12
  17. 17.What is the 25th term of the AP 17, 19, 21, 23, …? (a) 65 (b) 67 (c) 48 (d) 50
  18. 18.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 154 (c) 306 (d) 136
  19. 19.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1682 (c) 1711 (d) 1653
  20. 20.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 35 (c) 342 (d) 171
  21. 21.What is the 26th term of the AP 20, 29, 38, 47, …? (a) 225 (b) 254 (c) 245 (d) 234
  22. 22.What is the 18th term of the AP 4, 7, 10, 13, …? (a) 51 (b) 58 (c) 54 (d) 55
  23. 23.What is the 19th term of the AP 10, 16, 22, 28, …? (a) 108 (b) 124 (c) 114 (d) 118
  24. 24.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 234 (b) 132 (c) 117 (d) 32
  25. 25.What is the 34th term of the AP 6, 12, 18, 24, …? (a) 204 (b) 205 (c) 210 (d) 198
  26. 26.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1485 (c) 2970 (d) 1431
  27. 27.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 1892 (c) 3782 (d) 1830
  28. 28.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 30 (b) 32 (c) 31 (d) 40
  29. 29.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 210 (b) 190 (c) 37 (d) 380
  30. 30.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 625 (d) 49
  31. 31.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 105 (b) 27 (c) 119 (d) 210
  32. 32.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 204 (c) 32 (d) 120
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 66 (d) 21
  34. 34.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 18 (b) 19 (c) 25 (d) 17
  35. 35.What is the 35th term of the AP 3, 9, 15, 21, …? (a) 213 (b) 207 (c) 210 (d) 204
  36. 36.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 402 (b) 804 (c) 61 (d) 432
  37. 37.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 396 (b) 28 (c) 198 (d) 209
  38. 38.What is the 26th term of the AP 17, 26, 35, 44, …? (a) 242 (b) 234 (c) 251 (d) 225
  39. 39.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 18 (b) 11 (c) 10 (d) 12
  40. 40.What is the missing term in the AP 11, 14, ?, 20, 23? (a) 20 (b) 16 (c) 18 (d) 17

Answer key

  1. 187
  2. 729
  3. 91
  4. 154
  5. 317
  6. 80
  7. 147
  8. 276
  9. 46
  10. 98
  11. 45
  12. 133
  13. 144
  14. 3916
  15. 36
  16. 12
  17. 65
  18. 153
  19. 1711
  20. 324
  21. 245
  22. 55
  23. 118
  24. 117
  25. 204
  26. 1485
  27. 1891
  28. 31
  29. 190
  30. 625
  31. 105
  32. 102
  33. 121
  34. 18
  35. 207
  36. 402
  37. 198
  38. 242
  39. 11
  40. 17

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