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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 690 · 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 all the whole numbers from 1 to 62? (a) 1953 (b) 1891 (c) 3906 (d) 1922
  2. 2.What is the 31st term of the AP 13, 19, 25, 31, …? (a) 199 (b) 193 (c) 186 (d) 180
  3. 3.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 66 (b) 17 (c) 57 (d) 114
  4. 4.What is the 23rd term of the AP 2, 7, 12, 17, …? (a) 117 (b) 115 (c) 112 (d) 110
  5. 5.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
  6. 6.Which term of the AP 19, 21, 23, 25, … is 55? (a) 21st (b) 18th (c) 19th (d) 20th
  7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 529 (d) 45
  8. 8.What is the 10th term of the AP 18, 21, 24, 27, …? (a) 27 (b) 45 (c) 48 (d) 30
  9. 9.What is the 29th term of the AP 1, 9, 17, 25, …? (a) 233 (b) 224 (c) 225 (d) 232
  10. 10.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 450 (c) 435 (d) 930
  11. 11.What is the 27th term of the AP 14, 16, 18, 20, …? (a) 54 (b) 52 (c) 66 (d) 68
  12. 12.What is the 14th term of the AP 11, 18, 25, 32, …? (a) 109 (b) 91 (c) 102 (d) 98
  13. 13.What is the 30th term of the AP 6, 9, 12, 15, …? (a) 93 (b) 90 (c) 96 (d) 87
  14. 14.What is the 21st term of the AP 11, 16, 21, 26, …? (a) 116 (b) 100 (c) 105 (d) 111
  15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 324 (d) 171
  16. 16.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 100 (b) 99 (c) 198 (d) 14
  17. 17.Which term of the AP 9, 12, 15, 18, … is 45? (a) 15th (b) 14th (c) 13th (d) 12th
  18. 18.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 576 (d) 47
  19. 19.What is the 36th term of the AP 9, 13, 17, 21, …? (a) 140 (b) 153 (c) 144 (d) 149
  20. 20.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 10 (b) 11 (c) 9 (d) 13
  21. 21.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 243 (c) 225 (d) 450
  22. 22.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 484 (d) 253
  23. 23.What is the 26th term of the AP 11, 13, 15, 17, …? (a) 61 (b) 50 (c) 63 (d) 52
  24. 24.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  25. 25.What is the 34th term of the AP 4, 8, 12, 16, …? (a) 137 (b) 140 (c) 132 (d) 136
  26. 26.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 81 (b) 96 (c) 26 (d) 162
  27. 27.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 2701 (c) 5550 (d) 2775
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 13 (d) 56
  29. 29.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 812 (d) 406
  30. 30.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 903 (c) 946 (d) 1892
  31. 31.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 8 (b) 7 (c) 6 (d) 10
  32. 32.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 528 (b) 286 (c) 44 (d) 264
  33. 33.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 660 (b) 352 (c) 50 (d) 330
  34. 34.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 16 (b) 10 (c) 11 (d) 12
  35. 35.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 4 (b) 5 (c) 6 (d) 8
  36. 36.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 71 (b) 912 (c) 492 (d) 456
  37. 37.What is the missing term in the AP 17, 24, 31, ?, 45? (a) 38 (b) 45 (c) 37 (d) 39
  38. 38.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 13 (b) 12 (c) 16 (d) 14
  39. 39.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
  40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 351 (d) 51

Answer key

  1. 1953
  2. 193
  3. 57
  4. 112
  5. 144
  6. 19th
  7. 529
  8. 45
  9. 225
  10. 465
  11. 66
  12. 102
  13. 93
  14. 111
  15. 324
  16. 99
  17. 13th
  18. 576
  19. 149
  20. 10
  21. 225
  22. 484
  23. 61
  24. 64
  25. 136
  26. 81
  27. 2775
  28. 49
  29. 406
  30. 946
  31. 7
  32. 264
  33. 330
  34. 11
  35. 5
  36. 456
  37. 38
  38. 13
  39. 225
  40. 676

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