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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 458 · 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 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  2. 2.What is the 29th term of the AP 6, 9, 12, 15, …? (a) 84 (b) 90 (c) 87 (d) 93
  3. 3.What is the 35th term of the AP 3, 7, 11, 15, …? (a) 140 (b) 143 (c) 139 (d) 136
  4. 4.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 465 (c) 930 (d) 435
  5. 5.Which term of the AP 19, 21, 23, 25, … is 85? (a) 36th (b) 34th (c) 35th (d) 33rd
  6. 6.What is the 40th term of the AP 16, 21, 26, 31, …? (a) 211 (b) 200 (c) 216 (d) 195
  7. 7.What is the 27th term of the AP 16, 18, 20, 22, …? (a) 54 (b) 70 (c) 52 (d) 68
  8. 8.What is the 27th term of the AP 17, 20, 23, 26, …? (a) 95 (b) 98 (c) 81 (d) 78
  9. 9.What is the 28th term of the AP 5, 8, 11, 14, …? (a) 86 (b) 84 (c) 81 (d) 89
  10. 10.What is the 23rd term of the AP 10, 13, 16, 19, …? (a) 66 (b) 69 (c) 76 (d) 79
  11. 11.Which term of the AP 4, 12, 20, 28, … is 92? (a) 13th (b) 11th (c) 14th (d) 12th
  12. 12.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 396 (b) 53 (c) 372 (d) 744
  13. 13.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 8 (b) 7 (c) 11 (d) 6
  14. 14.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 35 (b) 240 (c) 222 (d) 444
  15. 15.What is the 21st term of the AP 6, 15, 24, 33, …? (a) 186 (b) 189 (c) 195 (d) 180
  16. 16.What is the missing term in the AP 20, 29, 38, ?, 56? (a) 56 (b) 46 (c) 47 (d) 48
  17. 17.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 23 (b) 21 (c) 20 (d) 22
  18. 18.What is the 12th term of the AP 2, 9, 16, 23, …? (a) 79 (b) 77 (c) 86 (d) 84
  19. 19.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2926 (c) 2850 (d) 2888
  20. 20.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 25 (b) 26 (c) 35 (d) 27
  21. 21.What is the 13th term of the AP 1, 3, 5, 7, …? (a) 25 (b) 24 (c) 26 (d) 27
  22. 22.What is the 27th term of the AP 19, 23, 27, 31, …? (a) 108 (b) 123 (c) 127 (d) 104
  23. 23.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 41 (b) 460 (c) 250 (d) 230
  24. 24.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 3422 (c) 1711 (d) 1653
  25. 25.What is the 32nd term of the AP 19, 21, 23, 25, …? (a) 62 (b) 81 (c) 64 (d) 83
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  27. 27.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 96 (b) 48 (c) 13 (d) 54
  28. 28.Which term of the AP 6, 10, 14, 18, … is 38? (a) 9th (b) 11th (c) 8th (d) 10th
  29. 29.What is the 24th term of the AP 9, 16, 23, 30, …? (a) 168 (b) 177 (c) 170 (d) 161
  30. 30.What is the missing term in the AP 16, 22, 28, ?, 40? (a) 35 (b) 33 (c) 40 (d) 34
  31. 31.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 306 (d) 154
  32. 32.Which term of the AP 2, 6, 10, 14, … is 82? (a) 21st (b) 22nd (c) 20th (d) 23rd
  33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  34. 34.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 562 (c) 1122 (d) 561
  35. 35.What is the 32nd term of the AP 20, 23, 26, 29, …? (a) 116 (b) 113 (c) 96 (d) 93
  36. 36.Which term of the AP 3, 11, 19, 27, … is 275? (a) 34th (b) 36th (c) 35th (d) 37th
  37. 37.Which term of the AP 19, 27, 35, 43, … is 155? (a) 19th (b) 18th (c) 20th (d) 17th
  38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  39. 39.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 243 (b) 225 (c) 41 (d) 450
  40. 40.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 990 (c) 968 (d) 1980

Answer key

  1. 100
  2. 90
  3. 139
  4. 465
  5. 34th
  6. 211
  7. 68
  8. 95
  9. 86
  10. 76
  11. 12th
  12. 372
  13. 7
  14. 222
  15. 186
  16. 47
  17. 21
  18. 79
  19. 2926
  20. 26
  21. 25
  22. 123
  23. 230
  24. 1711
  25. 81
  26. 841
  27. 48
  28. 9th
  29. 170
  30. 34
  31. 153
  32. 21st
  33. 25
  34. 561
  35. 113
  36. 35th
  37. 18th
  38. 121
  39. 225
  40. 990

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