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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 219 · 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 38th term of the AP 14, 16, 18, 20, …? (a) 76 (b) 74 (c) 90 (d) 88
  2. 2.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3403 (c) 3486 (d) 3487
  3. 3.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 156 (b) 144 (c) 288 (d) 23
  4. 4.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 306 (c) 154 (d) 153
  5. 5.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 588 (b) 41 (c) 294 (d) 312
  6. 6.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 198 (b) 15 (c) 100 (d) 99
  7. 7.What is the 31st term of the AP 1, 3, 5, 7, …? (a) 60 (b) 62 (c) 63 (d) 61
  8. 8.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 528 (c) 1056 (d) 496
  9. 9.Which term of the AP 7, 9, 11, 13, … is 69? (a) 31st (b) 32nd (c) 34th (d) 33rd
  10. 10.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 252 (b) 48 (c) 257 (d) 504
  11. 11.Which term of the AP 4, 7, 10, 13, … is 40? (a) 13th (b) 12th (c) 15th (d) 14th
  12. 12.What is the 21st term of the AP 4, 12, 20, 28, …? (a) 160 (b) 172 (c) 168 (d) 164
  13. 13.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 140 (b) 70 (c) 24 (d) 75
  14. 14.What is the sum of all the whole numbers from 1 to 58? (a) 1711 (b) 1682 (c) 1653 (d) 3422
  15. 15.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 930 (c) 465 (d) 450
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  17. 17.What is the missing term in the AP 10, ?, 28, 37, 46? (a) 19 (b) 18 (c) 28 (d) 20
  18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 153 (d) 33
  19. 19.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 110 (b) 13 (c) 55 (d) 56
  20. 20.Which term of the AP 20, 23, 26, 29, … is 104? (a) 29th (b) 30th (c) 31st (d) 28th
  21. 21.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 57 (b) 297 (c) 594 (d) 324
  22. 22.What is the 34th term of the AP 10, 15, 20, 25, …? (a) 170 (b) 175 (c) 165 (d) 180
  23. 23.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 18 (b) 16 (c) 22 (d) 17
  24. 24.What is the sum of all the whole numbers from 1 to 51? (a) 1326 (b) 2652 (c) 1275 (d) 1327
  25. 25.What is the 11th term of the AP 7, 15, 23, 31, …? (a) 88 (b) 87 (c) 95 (d) 80
  26. 26.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 432 (b) 228 (c) 29 (d) 216
  27. 27.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 10 (b) 13 (c) 9 (d) 8
  28. 28.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1152 (c) 1176 (d) 2352
  29. 29.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
  30. 30.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 20 (b) 150 (c) 84 (d) 75
  31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  32. 32.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 6 (b) 8 (c) 5 (d) 7
  33. 33.Which term of the AP 4, 9, 14, 19, … is 134? (a) 26th (b) 27th (c) 28th (d) 29th
  34. 34.What is the 26th term of the AP 5, 7, 9, 11, …? (a) 57 (b) 55 (c) 52 (d) 50
  35. 35.Which term of the AP 3, 5, 7, 9, … is 73? (a) 37th (b) 35th (c) 38th (d) 36th
  36. 36.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 78 (b) 75 (c) 21 (d) 150
  37. 37.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 66 (c) 132 (d) 67
  38. 38.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 55 (c) 100 (d) 50
  39. 39.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 406 (d) 812
  40. 40.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 30 (b) 9 (c) 25 (d) 50

Answer key

  1. 88
  2. 3486
  3. 144
  4. 153
  5. 294
  6. 99
  7. 61
  8. 528
  9. 32nd
  10. 252
  11. 13th
  12. 164
  13. 70
  14. 1711
  15. 465
  16. 64
  17. 19
  18. 289
  19. 55
  20. 29th
  21. 297
  22. 175
  23. 17
  24. 1326
  25. 87
  26. 216
  27. 9
  28. 1176
  29. 441
  30. 75
  31. 784
  32. 6
  33. 27th
  34. 55
  35. 36th
  36. 75
  37. 66
  38. 50
  39. 406
  40. 25

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