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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 502 · 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 34th term of the AP 3, 6, 9, 12, …? (a) 103 (b) 99 (c) 102 (d) 105
  2. 2.What is the 25th term of the AP 18, 25, 32, 39, …? (a) 168 (b) 193 (c) 175 (d) 186
  3. 3.Which term of the AP 19, 27, 35, 43, … is 307? (a) 36th (b) 38th (c) 37th (d) 39th
  4. 4.What is the 28th term of the AP 4, 13, 22, 31, …? (a) 252 (b) 247 (c) 243 (d) 256
  5. 5.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 17 (b) 14 (c) 13 (d) 12
  6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 45 (d) 17
  7. 7.What is the 40th term of the AP 2, 9, 16, 23, …? (a) 282 (b) 280 (c) 273 (d) 275
  8. 8.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 3655 (c) 7482 (d) 3698
  9. 9.Which term of the AP 6, 11, 16, 21, … is 66? (a) 12th (b) 15th (c) 14th (d) 13th
  10. 10.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 9 (b) 11 (c) 13 (d) 10
  11. 11.What is the 13th term of the AP 4, 9, 14, 19, …? (a) 65 (b) 64 (c) 60 (d) 69
  12. 12.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 15 (c) 12 (d) 11
  13. 13.What is the 25th term of the AP 13, 22, 31, 40, …? (a) 225 (b) 238 (c) 229 (d) 216
  14. 14.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 191 (c) 190 (d) 380
  15. 15.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 703 (c) 741 (d) 722
  16. 16.What is the 25th term of the AP 2, 4, 6, 8, …? (a) 52 (b) 51 (c) 48 (d) 50
  17. 17.What is the 22nd term of the AP 11, 17, 23, 29, …? (a) 132 (b) 143 (c) 137 (d) 126
  18. 18.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 576 (d) 600
  19. 19.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 90 (b) 28 (c) 95 (d) 180
  20. 20.What is the 35th term of the AP 5, 13, 21, 29, …? (a) 285 (b) 272 (c) 280 (d) 277
  21. 21.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 595 (c) 631 (d) 630
  22. 22.Which term of the AP 1, 5, 9, 13, … is 49? (a) 14th (b) 12th (c) 15th (d) 13th
  23. 23.What is the 26th term of the AP 2, 4, 6, 8, …? (a) 53 (b) 54 (c) 50 (d) 52
  24. 24.What is the 30th term of the AP 6, 9, 12, 15, …? (a) 87 (b) 90 (c) 96 (d) 93
  25. 25.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 496 (c) 512 (d) 528
  26. 26.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 135 (b) 22 (c) 252 (d) 126
  27. 27.Which term of the AP 9, 12, 15, 18, … is 96? (a) 30th (b) 32nd (c) 29th (d) 31st
  28. 28.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 51 (c) 572 (d) 286
  29. 29.What is the 25th term of the AP 2, 7, 12, 17, …? (a) 122 (b) 125 (c) 127 (d) 120
  30. 30.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  31. 31.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 432 (b) 216 (c) 240 (d) 48
  32. 32.What is the 35th term of the AP 3, 12, 21, 30, …? (a) 309 (b) 306 (c) 318 (d) 315
  33. 33.Which term of the AP 2, 7, 12, 17, … is 187? (a) 40th (b) 38th (c) 39th (d) 37th
  34. 34.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 38 (b) 198 (c) 216 (d) 396
  35. 35.What is the 18th term of the AP 15, 18, 21, 24, …? (a) 69 (b) 51 (c) 54 (d) 66
  36. 36.What is the 37th term of the AP 8, 13, 18, 23, …? (a) 188 (b) 180 (c) 185 (d) 193
  37. 37.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 60 (c) 10 (d) 30
  38. 38.What is the 13th term of the AP 8, 12, 16, 20, …? (a) 60 (b) 52 (c) 56 (d) 48
  39. 39.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28
  40. 40.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 93 (b) 186 (c) 23 (d) 102

Answer key

  1. 102
  2. 186
  3. 37th
  4. 247
  5. 13
  6. 81
  7. 275
  8. 3741
  9. 13th
  10. 10
  11. 64
  12. 11
  13. 229
  14. 190
  15. 741
  16. 50
  17. 137
  18. 576
  19. 90
  20. 277
  21. 630
  22. 13th
  23. 52
  24. 93
  25. 528
  26. 126
  27. 30th
  28. 286
  29. 122
  30. 400
  31. 216
  32. 309
  33. 38th
  34. 198
  35. 66
  36. 188
  37. 30
  38. 56
  39. 49
  40. 93

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