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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 259 · 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.Which term of the AP 9, 12, 15, 18, … is 120? (a) 39th (b) 38th (c) 40th (d) 37th
  2. 2.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 75 (b) 20 (c) 84 (d) 150
  3. 3.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 12 (b) 17 (c) 11 (d) 10
  4. 4.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1711 (c) 1771 (d) 1770
  5. 5.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  6. 6.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 17 (b) 81 (c) 90 (d) 162
  7. 7.What is the 23rd term of the AP 4, 9, 14, 19, …? (a) 115 (b) 110 (c) 114 (d) 119
  8. 8.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3486 (c) 3403 (d) 6972
  9. 9.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 326 (c) 650 (d) 300
  10. 10.What is the 14th term of the AP 3, 9, 15, 21, …? (a) 81 (b) 84 (c) 78 (d) 87
  11. 11.What is the 31st term of the AP 18, 26, 34, 42, …? (a) 266 (b) 240 (c) 248 (d) 258
  12. 12.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 162 (b) 306 (c) 25 (d) 153
  13. 13.What is the 39th term of the AP 7, 9, 11, 13, …? (a) 76 (b) 78 (c) 85 (d) 83
  14. 14.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 1711 (c) 3422 (d) 1682
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
  16. 16.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 120 (c) 272 (d) 128
  17. 17.What is the 40th term of the AP 20, 23, 26, 29, …? (a) 140 (b) 137 (c) 117 (d) 120
  18. 18.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 114 (b) 27 (c) 102 (d) 204
  19. 19.What is the 28th term of the AP 2, 4, 6, 8, …? (a) 56 (b) 54 (c) 58 (d) 57
  20. 20.What is the 40th term of the AP 18, 27, 36, 45, …? (a) 378 (b) 369 (c) 351 (d) 360
  21. 21.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 45 (d) 90
  22. 22.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 10 (b) 11 (c) 14 (d) 12
  23. 23.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 6 (b) 10 (c) 8 (d) 7
  24. 24.What is the 13th term of the AP 2, 6, 10, 14, …? (a) 50 (b) 54 (c) 52 (d) 48
  25. 25.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3081 (c) 3003 (d) 6162
  26. 26.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 16 (b) 13 (c) 14 (d) 12
  27. 27.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 210 (d) 196
  28. 28.Which term of the AP 14, 16, 18, 20, … is 58? (a) 23rd (b) 24th (c) 22nd (d) 29th
  29. 29.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 204 (b) 120 (c) 32 (d) 102
  30. 30.What is the 40th term of the AP 3, 11, 19, 27, …? (a) 315 (b) 320 (c) 323 (d) 312
  31. 31.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 3906 (c) 1953 (d) 1922
  32. 32.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 285 (b) 570 (c) 51 (d) 310
  33. 33.What is the 17th term of the AP 14, 22, 30, 38, …? (a) 150 (b) 128 (c) 142 (d) 136
  34. 34.What is the 28th term of the AP 15, 23, 31, 39, …? (a) 216 (b) 224 (c) 239 (d) 231
  35. 35.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 140 (b) 22 (c) 80 (d) 70
  36. 36.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 75 (b) 27 (c) 150 (d) 90
  37. 37.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 32 (b) 40 (c) 30 (d) 31
  38. 38.What is the 15th term of the AP 2, 9, 16, 23, …? (a) 98 (b) 100 (c) 107 (d) 105
  39. 39.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 26 (b) 25 (c) 34 (d) 27
  40. 40.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 26 (b) 324 (c) 171 (d) 162

Answer key

  1. 38th
  2. 75
  3. 11
  4. 1770
  5. 256
  6. 81
  7. 114
  8. 3486
  9. 325
  10. 81
  11. 258
  12. 153
  13. 83
  14. 1711
  15. 400
  16. 136
  17. 137
  18. 102
  19. 56
  20. 369
  21. 81
  22. 11
  23. 7
  24. 50
  25. 3081
  26. 13
  27. 196
  28. 23rd
  29. 102
  30. 315
  31. 1953
  32. 285
  33. 142
  34. 231
  35. 70
  36. 75
  37. 31
  38. 100
  39. 26
  40. 162

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