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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 539 · 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 14th term of the AP 1, 5, 9, 13, …? (a) 57 (b) 56 (c) 52 (d) 53
  2. 2.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 512 (c) 1056 (d) 528
  3. 3.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 12 (c) 73 (d) 72
  4. 4.What is the 12th term of the AP 11, 17, 23, 29, …? (a) 72 (b) 66 (c) 77 (d) 83
  5. 5.What is the 18th term of the AP 9, 14, 19, 24, …? (a) 85 (b) 94 (c) 90 (d) 99
  6. 6.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 1560 (c) 741 (d) 780
  7. 7.What is the 14th term of the AP 17, 23, 29, 35, …? (a) 84 (b) 95 (c) 101 (d) 78
  8. 8.What is the 14th term of the AP 7, 13, 19, 25, …? (a) 78 (b) 84 (c) 85 (d) 91
  9. 9.Which term of the AP 8, 16, 24, 32, … is 128? (a) 18th (b) 16th (c) 15th (d) 17th
  10. 10.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 57 (c) 354 (d) 384
  11. 11.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
  12. 12.What is the 13th term of the AP 20, 25, 30, 35, …? (a) 85 (b) 80 (c) 60 (d) 65
  13. 13.What is the 36th term of the AP 1, 5, 9, 13, …? (a) 140 (b) 145 (c) 144 (d) 141
  14. 14.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 27 (b) 28 (c) 33 (d) 26
  15. 15.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 58 (b) 110 (c) 17 (d) 55
  16. 16.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 207 (b) 39 (c) 225 (d) 414
  17. 17.Which term of the AP 14, 18, 22, 26, … is 130? (a) 29th (b) 32nd (c) 30th (d) 31st
  18. 18.What is the 31st term of the AP 18, 23, 28, 33, …? (a) 168 (b) 150 (c) 173 (d) 155
  19. 19.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 18 (b) 286 (c) 143 (d) 144
  20. 20.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 180 (c) 13 (d) 90
  21. 21.What is the 33rd term of the AP 10, 13, 16, 19, …? (a) 106 (b) 109 (c) 99 (d) 96
  22. 22.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 435 (d) 870
  23. 23.What is the 26th term of the AP 15, 23, 31, 39, …? (a) 200 (b) 215 (c) 208 (d) 223
  24. 24.What is the 19th term of the AP 6, 9, 12, 15, …? (a) 54 (b) 60 (c) 63 (d) 57
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 625 (d) 325
  26. 26.What is the 24th term of the AP 6, 12, 18, 24, …? (a) 145 (b) 150 (c) 144 (d) 138
  27. 27.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  28. 28.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 256 (d) 136
  29. 29.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 95 (b) 25 (c) 85 (d) 170
  30. 30.What is the 30th term of the AP 6, 9, 12, 15, …? (a) 87 (b) 96 (c) 93 (d) 90
  31. 31.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 396 (b) 38 (c) 216 (d) 198
  32. 32.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 36 (b) 66 (c) 8 (d) 33
  33. 33.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 24 (b) 288 (c) 144 (d) 153
  34. 34.What is the 19th term of the AP 1, 9, 17, 25, …? (a) 153 (b) 144 (c) 152 (d) 145
  35. 35.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 132 (c) 55 (d) 67
  36. 36.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 231 (d) 441
  37. 37.What is the missing term in the AP 3, 8, 13, ?, 23? (a) 18 (b) 23 (c) 19 (d) 17
  38. 38.Which term of the AP 3, 12, 21, 30, … is 264? (a) 30th (b) 32nd (c) 31st (d) 29th
  39. 39.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 2926 (c) 6006 (d) 3003
  40. 40.What is the 26th term of the AP 8, 15, 22, 29, …? (a) 183 (b) 182 (c) 190 (d) 175

Answer key

  1. 53
  2. 528
  3. 72
  4. 77
  5. 94
  6. 780
  7. 95
  8. 85
  9. 16th
  10. 354
  11. 729
  12. 80
  13. 141
  14. 27
  15. 55
  16. 207
  17. 30th
  18. 168
  19. 143
  20. 90
  21. 106
  22. 841
  23. 215
  24. 60
  25. 625
  26. 144
  27. 529
  28. 256
  29. 85
  30. 93
  31. 198
  32. 33
  33. 144
  34. 145
  35. 66
  36. 441
  37. 18
  38. 30th
  39. 3003
  40. 183

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