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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 510 · 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.Which term of the AP 20, 26, 32, 38, … is 200? (a) 32nd (b) 30th (c) 33rd (d) 31st
  2. 2.What is the 32nd term of the AP 9, 12, 15, 18, …? (a) 102 (b) 105 (c) 93 (d) 96
  3. 3.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1892 (c) 1891 (d) 3782
  4. 4.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 72 (d) 36
  5. 5.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1225 (c) 1275 (d) 1250
  6. 6.Which term of the AP 16, 20, 24, 28, … is 164? (a) 38th (b) 37th (c) 39th (d) 41st
  7. 7.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 81 (b) 90 (c) 162 (d) 17
  8. 8.What is the 26th term of the AP 7, 14, 21, 28, …? (a) 189 (b) 175 (c) 183 (d) 182
  9. 9.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 741 (c) 780 (d) 1560
  10. 10.Which term of the AP 11, 20, 29, 38, … is 245? (a) 28th (b) 29th (c) 26th (d) 27th
  11. 11.What is the missing term in the AP 3, 10, 17, ?, 31? (a) 25 (b) 23 (c) 24 (d) 31
  12. 12.What is the 29th term of the AP 19, 25, 31, 37, …? (a) 168 (b) 174 (c) 193 (d) 187
  13. 13.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 253 (b) 275 (c) 43 (d) 506
  14. 14.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 28 (b) 32 (c) 26 (d) 27
  15. 15.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 6480 (c) 3200 (d) 3240
  16. 16.What is the 31st term of the AP 14, 16, 18, 20, …? (a) 62 (b) 74 (c) 60 (d) 76
  17. 17.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 41 (b) 250 (c) 460 (d) 230
  18. 18.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 44 (b) 54 (c) 45 (d) 46
  19. 19.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 8190 (c) 4050 (d) 4095
  20. 20.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 29 (b) 35 (c) 28 (d) 30
  21. 21.Which term of the AP 12, 18, 24, 30, … is 90? (a) 14th (b) 15th (c) 16th (d) 13th
  22. 22.What is the 35th term of the AP 19, 23, 27, 31, …? (a) 159 (b) 155 (c) 136 (d) 140
  23. 23.What is the 34th term of the AP 8, 17, 26, 35, …? (a) 314 (b) 306 (c) 297 (d) 305
  24. 24.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 12 (b) 75 (c) 80 (d) 150
  25. 25.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 65 (b) 385 (c) 770 (d) 418
  26. 26.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 66 (c) 156 (d) 78
  27. 27.What is the 19th term of the AP 6, 12, 18, 24, …? (a) 120 (b) 115 (c) 108 (d) 114
  28. 28.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 40 (b) 275 (c) 278 (d) 550
  29. 29.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 450 (b) 45 (c) 225 (d) 230
  30. 30.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 33 (b) 34 (c) 39 (d) 32
  31. 31.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  32. 32.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 35 (b) 36 (c) 37 (d) 43
  33. 33.What is the 13th term of the AP 9, 15, 21, 27, …? (a) 87 (b) 72 (c) 81 (d) 78
  34. 34.What is the 26th term of the AP 4, 11, 18, 25, …? (a) 175 (b) 179 (c) 182 (d) 186
  35. 35.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 28 (b) 19 (c) 21 (d) 20
  36. 36.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 406 (c) 870 (d) 435
  37. 37.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 11 (b) 15 (c) 10 (d) 12
  38. 38.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 72 (c) 36 (d) 11
  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 13th term of the AP 20, 27, 34, 41, …? (a) 91 (b) 84 (c) 111 (d) 104

Answer key

  1. 31st
  2. 102
  3. 1891
  4. 64
  5. 1275
  6. 38th
  7. 81
  8. 182
  9. 780
  10. 27th
  11. 24
  12. 187
  13. 253
  14. 27
  15. 3240
  16. 74
  17. 230
  18. 45
  19. 4095
  20. 29
  21. 14th
  22. 155
  23. 305
  24. 75
  25. 385
  26. 78
  27. 114
  28. 275
  29. 225
  30. 33
  31. 25
  32. 36
  33. 81
  34. 179
  35. 20
  36. 435
  37. 11
  38. 36
  39. 3003
  40. 104

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