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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 108 · 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 the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 31 (d) 136
  2. 2.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 5 (b) 10 (c) 6 (d) 7
  3. 3.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 47 (c) 297 (d) 319
  4. 4.What is the 11th term of the AP 9, 11, 13, 15, …? (a) 31 (b) 29 (c) 22 (d) 20
  5. 5.What is the 11th term of the AP 5, 10, 15, 20, …? (a) 60 (b) 50 (c) 55 (d) 56
  6. 6.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 4005 (c) 4006 (d) 3916
  7. 7.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1352 (c) 1378 (d) 1326
  8. 8.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 168 (b) 24 (c) 96 (d) 84
  9. 9.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 11 (b) 9 (c) 10 (d) 12
  10. 10.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 21 (b) 24 (c) 22 (d) 23
  11. 11.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 448 (b) 49 (c) 248 (d) 224
  12. 12.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 16 (b) 12 (c) 13 (d) 14
  13. 13.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 120 (b) 30 (c) 240 (d) 132
  14. 14.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 55 (c) 132 (d) 67
  15. 15.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 20 (b) 18 (c) 27 (d) 19
  16. 16.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 171 (b) 162 (c) 324 (d) 26
  17. 17.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 10 (b) 12 (c) 11 (d) 13
  18. 18.What is the 16th term of the AP 18, 23, 28, 33, …? (a) 80 (b) 75 (c) 93 (d) 98
  19. 19.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2851 (c) 2850 (d) 5700
  20. 20.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 512 (c) 496 (d) 528
  21. 21.What is the 38th term of the AP 15, 24, 33, 42, …? (a) 357 (b) 333 (c) 348 (d) 342
  22. 22.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 198 (b) 19 (c) 99 (d) 108
  23. 23.Which term of the AP 11, 13, 15, 17, … is 45? (a) 19th (b) 18th (c) 20th (d) 17th
  24. 24.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 216 (b) 204 (c) 28 (d) 408
  25. 25.What is the 17th term of the AP 11, 15, 19, 23, …? (a) 75 (b) 64 (c) 79 (d) 68
  26. 26.Which term of the AP 17, 21, 25, 29, … is 121? (a) 29th (b) 27th (c) 26th (d) 28th
  27. 27.What is the 32nd term of the AP 12, 18, 24, 30, …? (a) 198 (b) 204 (c) 186 (d) 192
  28. 28.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 336 (b) 168 (c) 39 (d) 173
  29. 29.What is the 35th term of the AP 2, 9, 16, 23, …? (a) 245 (b) 247 (c) 240 (d) 238
  30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  31. 31.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 65 (b) 16 (c) 60 (d) 120
  32. 32.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1128 (c) 1176 (d) 1152
  33. 33.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 784 (d) 812
  34. 34.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 24 (b) 22 (c) 21 (d) 23
  35. 35.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 19 (b) 24 (c) 20 (d) 21
  36. 36.What is the 26th term of the AP 4, 10, 16, 22, …? (a) 154 (b) 150 (c) 160 (d) 156
  37. 37.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 96 (c) 81 (d) 162
  38. 38.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1327 (c) 1275 (d) 1326
  39. 39.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 12 (b) 13 (c) 14 (d) 18
  40. 40.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 552 (b) 276 (c) 45 (d) 300

Answer key

  1. 256
  2. 6
  3. 297
  4. 29
  5. 55
  6. 4005
  7. 1378
  8. 84
  9. 10
  10. 22
  11. 224
  12. 13
  13. 120
  14. 66
  15. 19
  16. 162
  17. 11
  18. 93
  19. 2850
  20. 528
  21. 348
  22. 99
  23. 18th
  24. 204
  25. 75
  26. 27th
  27. 198
  28. 168
  29. 240
  30. 225
  31. 60
  32. 1176
  33. 784
  34. 22
  35. 20
  36. 154
  37. 81
  38. 1326
  39. 13
  40. 276

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