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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 398 · 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 21st term of the AP 10, 14, 18, 22, …? (a) 94 (b) 80 (c) 90 (d) 84
  2. 2.What is the 21st term of the AP 9, 12, 15, 18, …? (a) 69 (b) 60 (c) 72 (d) 63
  3. 3.What is the 22nd term of the AP 4, 7, 10, 13, …? (a) 63 (b) 70 (c) 66 (d) 67
  4. 4.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 9702 (c) 4753 (d) 4851
  5. 5.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 156 (c) 23 (d) 78
  6. 6.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 6806 (c) 3321 (d) 3403
  7. 7.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 528 (c) 512 (d) 496
  8. 8.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  9. 9.What is the 40th term of the AP 15, 23, 31, 39, …? (a) 327 (b) 312 (c) 320 (d) 335
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  12. 12.What is the 34th term of the AP 3, 11, 19, 27, …? (a) 272 (b) 267 (c) 264 (d) 275
  13. 13.What is the 33rd term of the AP 14, 21, 28, 35, …? (a) 245 (b) 231 (c) 224 (d) 238
  14. 14.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 432 (b) 216 (c) 240 (d) 48
  15. 15.Which term of the AP 11, 19, 27, 35, … is 187? (a) 23rd (b) 22nd (c) 24th (d) 25th
  16. 16.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 40 (b) 234 (c) 216 (d) 432
  17. 17.Which term of the AP 18, 20, 22, 24, … is 70? (a) 35th (b) 26th (c) 28th (d) 27th
  18. 18.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 90 (b) 96 (c) 20 (d) 180
  19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 289 (d) 306
  20. 20.What is the 23rd term of the AP 3, 12, 21, 30, …? (a) 198 (b) 210 (c) 201 (d) 207
  21. 21.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 722 (c) 703 (d) 1482
  22. 22.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 231 (d) 210
  23. 23.What is the 12th term of the AP 13, 15, 17, 19, …? (a) 22 (b) 24 (c) 37 (d) 35
  24. 24.What is the 39th term of the AP 20, 25, 30, 35, …? (a) 215 (b) 190 (c) 210 (d) 195
  25. 25.What is the 23rd term of the AP 3, 5, 7, 9, …? (a) 44 (b) 47 (c) 46 (d) 49
  26. 26.What is the 37th term of the AP 16, 18, 20, 22, …? (a) 90 (b) 74 (c) 88 (d) 72
  27. 27.Which term of the AP 16, 19, 22, 25, … is 133? (a) 40th (b) 41st (c) 42nd (d) 39th
  28. 28.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 78 (c) 77 (d) 12
  29. 29.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 29 (d) 225
  30. 30.What is the missing term in the AP 15, ?, 21, 24, 27? (a) 21 (b) 19 (c) 18 (d) 17
  31. 31.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 68 (b) 12 (c) 72 (d) 136
  32. 32.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 170 (b) 29 (c) 100 (d) 85
  33. 33.What is the 28th term of the AP 10, 13, 16, 19, …? (a) 91 (b) 94 (c) 84 (d) 81
  34. 34.Which term of the AP 18, 23, 28, 33, … is 128? (a) 25th (b) 24th (c) 23rd (d) 22nd
  35. 35.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 119 (b) 26 (c) 238 (d) 122
  36. 36.What is the 28th term of the AP 8, 11, 14, 17, …? (a) 92 (b) 84 (c) 89 (d) 81
  37. 37.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 110 (c) 120 (d) 20
  38. 38.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 26 (b) 28 (c) 27 (d) 32
  39. 39.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 424 (b) 212 (c) 44 (d) 232
  40. 40.What is the 16th term of the AP 1, 9, 17, 25, …? (a) 129 (b) 128 (c) 121 (d) 120

Answer key

  1. 90
  2. 69
  3. 67
  4. 4851
  5. 144
  6. 3403
  7. 528
  8. 121
  9. 327
  10. 256
  11. 81
  12. 267
  13. 238
  14. 216
  15. 23rd
  16. 216
  17. 27th
  18. 90
  19. 289
  20. 201
  21. 741
  22. 231
  23. 35
  24. 210
  25. 47
  26. 88
  27. 40th
  28. 77
  29. 225
  30. 18
  31. 68
  32. 85
  33. 91
  34. 23rd
  35. 119
  36. 89
  37. 110
  38. 27
  39. 212
  40. 121

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