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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 35 · 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 sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2926 (c) 2850 (d) 5852
  2. 2.What is the 35th term of the AP 5, 8, 11, 14, …? (a) 105 (b) 102 (c) 107 (d) 110
  3. 3.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 406 (c) 378 (d) 812
  4. 4.Which term of the AP 1, 5, 9, 13, … is 105? (a) 28th (b) 27th (c) 26th (d) 29th
  5. 5.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 26 (b) 252 (c) 126 (d) 129
  6. 6.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 3540 (c) 1711 (d) 1770
  7. 7.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3828 (d) 3916
  8. 8.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 65 (b) 418 (c) 770 (d) 385
  9. 9.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4278 (c) 4232 (d) 4186
  10. 10.What is the 17th term of the AP 14, 17, 20, 23, …? (a) 62 (b) 48 (c) 51 (d) 65
  11. 11.What is the 37th term of the AP 17, 23, 29, 35, …? (a) 239 (b) 216 (c) 233 (d) 222
  12. 12.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 612 (c) 324 (d) 42
  13. 13.What is the 14th term of the AP 10, 14, 18, 22, …? (a) 62 (b) 66 (c) 52 (d) 56
  14. 14.Which term of the AP 1, 7, 13, 19, … is 169? (a) 28th (b) 30th (c) 31st (d) 29th
  15. 15.What is the 26th term of the AP 15, 24, 33, 42, …? (a) 249 (b) 240 (c) 225 (d) 234
  16. 16.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 13 (c) 50 (d) 45
  17. 17.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 105 (b) 27 (c) 210 (d) 119
  18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  19. 19.What is the missing term in the AP 15, 18, ?, 24, 27? (a) 21 (b) 22 (c) 20 (d) 24
  20. 20.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 20 (b) 18 (c) 21 (d) 19
  21. 21.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 40 (c) 41 (d) 10
  22. 22.What is the 40th term of the AP 3, 6, 9, 12, …? (a) 120 (b) 121 (c) 117 (d) 123
  23. 23.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 120 (c) 240 (d) 105
  24. 24.What is the 17th term of the AP 15, 18, 21, 24, …? (a) 48 (b) 66 (c) 63 (d) 51
  25. 25.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 3422 (c) 1711 (d) 1682
  26. 26.Which term of the AP 8, 16, 24, 32, … is 184? (a) 23rd (b) 22nd (c) 25th (d) 24th
  27. 27.What is the 37th term of the AP 19, 28, 37, 46, …? (a) 343 (b) 352 (c) 333 (d) 324
  28. 28.What is the 11th term of the AP 20, 28, 36, 44, …? (a) 108 (b) 80 (c) 88 (d) 100
  29. 29.What is the 21st term of the AP 9, 17, 25, 33, …? (a) 160 (b) 168 (c) 177 (d) 169
  30. 30.What is the 28th term of the AP 16, 21, 26, 31, …? (a) 135 (b) 156 (c) 151 (d) 140
  31. 31.What is the 34th term of the AP 19, 22, 25, 28, …? (a) 99 (b) 118 (c) 121 (d) 102
  32. 32.What is the 33rd term of the AP 1, 10, 19, 28, …? (a) 288 (b) 297 (c) 298 (d) 289
  33. 33.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 19 (b) 16 (c) 14 (d) 15
  34. 34.What is the 15th term of the AP 9, 17, 25, 33, …? (a) 129 (b) 121 (c) 120 (d) 112
  35. 35.Which term of the AP 15, 17, 19, 21, … is 45? (a) 17th (b) 18th (c) 15th (d) 16th
  36. 36.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 378 (d) 756
  37. 37.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3528 (c) 3570 (d) 3486
  38. 38.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 16 (b) 23 (c) 17 (d) 18
  39. 39.What is the 36th term of the AP 7, 12, 17, 22, …? (a) 175 (b) 180 (c) 187 (d) 182
  40. 40.What is the 25th term of the AP 2, 5, 8, 11, …? (a) 74 (b) 75 (c) 72 (d) 77

Answer key

  1. 2926
  2. 107
  3. 406
  4. 27th
  5. 126
  6. 1770
  7. 3916
  8. 385
  9. 4278
  10. 62
  11. 233
  12. 306
  13. 62
  14. 29th
  15. 240
  16. 45
  17. 105
  18. 256
  19. 21
  20. 19
  21. 40
  22. 120
  23. 120
  24. 63
  25. 1711
  26. 23rd
  27. 343
  28. 100
  29. 169
  30. 151
  31. 118
  32. 289
  33. 15
  34. 121
  35. 16th
  36. 729
  37. 3570
  38. 17
  39. 182
  40. 74

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