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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 351 · 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 29th term of the AP 12, 21, 30, 39, …? (a) 252 (b) 261 (c) 264 (d) 273
  2. 2.Which term of the AP 9, 13, 17, 21, … is 133? (a) 32nd (b) 34th (c) 31st (d) 33rd
  3. 3.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 200 (b) 370 (c) 32 (d) 185
  4. 4.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 59 (b) 408 (c) 378 (d) 756
  5. 5.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 20 (b) 90 (c) 180 (d) 96
  6. 6.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 1035 (c) 1081 (d) 2162
  7. 7.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 198 (b) 114 (c) 99 (d) 29
  8. 8.What is the 24th term of the AP 1, 5, 9, 13, …? (a) 92 (b) 96 (c) 97 (d) 93
  9. 9.What is the 23rd term of the AP 11, 14, 17, 20, …? (a) 77 (b) 80 (c) 66 (d) 69
  10. 10.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 540 (c) 504 (d) 1008
  11. 11.What is the 34th term of the AP 14, 18, 22, 26, …? (a) 150 (b) 146 (c) 136 (d) 132
  12. 12.What is the 35th term of the AP 8, 10, 12, 14, …? (a) 68 (b) 70 (c) 78 (d) 76
  13. 13.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  14. 14.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 882 (c) 861 (d) 1806
  15. 15.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 20 (b) 24 (c) 22 (d) 21
  16. 16.Which term of the AP 16, 22, 28, 34, … is 106? (a) 18th (b) 15th (c) 17th (d) 16th
  17. 17.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 15 (b) 16 (c) 18 (d) 14
  18. 18.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  19. 19.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 10100 (d) 5000
  20. 20.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 85 (b) 26 (c) 160 (d) 80
  21. 21.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  22. 22.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 78 (b) 14 (c) 77 (d) 154
  23. 23.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 300 (b) 46 (c) 280 (d) 560
  24. 24.What is the 23rd term of the AP 20, 28, 36, 44, …? (a) 196 (b) 184 (c) 176 (d) 204
  25. 25.What is the 37th term of the AP 11, 16, 21, 26, …? (a) 196 (b) 191 (c) 185 (d) 180
  26. 26.What is the 13th term of the AP 12, 18, 24, 30, …? (a) 90 (b) 84 (c) 78 (d) 72
  27. 27.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 11 (b) 15 (c) 12 (d) 13
  28. 28.What is the 34th term of the AP 5, 8, 11, 14, …? (a) 104 (b) 102 (c) 107 (d) 99
  29. 29.What is the 16th term of the AP 12, 19, 26, 33, …? (a) 117 (b) 124 (c) 105 (d) 112
  30. 30.What is the 32nd term of the AP 5, 9, 13, 17, …? (a) 128 (b) 129 (c) 124 (d) 133
  31. 31.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 46 (b) 45 (c) 9 (d) 90
  32. 32.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 22 (b) 29 (c) 21 (d) 20
  33. 33.Which term of the AP 17, 24, 31, 38, … is 73? (a) 9th (b) 8th (c) 10th (d) 11th
  34. 34.What is the 16th term of the AP 18, 27, 36, 45, …? (a) 144 (b) 135 (c) 153 (d) 162
  35. 35.What is the 26th term of the AP 8, 11, 14, 17, …? (a) 78 (b) 75 (c) 83 (d) 86
  36. 36.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 51 (d) 351
  37. 37.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 36 (b) 34 (c) 35 (d) 43
  38. 38.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 136 (c) 154 (d) 153
  39. 39.What is the 28th term of the AP 17, 23, 29, 35, …? (a) 162 (b) 179 (c) 185 (d) 168
  40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 812 (d) 55

Answer key

  1. 264
  2. 32nd
  3. 185
  4. 378
  5. 90
  6. 1081
  7. 99
  8. 93
  9. 77
  10. 504
  11. 146
  12. 76
  13. 576
  14. 903
  15. 21
  16. 16th
  17. 15
  18. 324
  19. 5050
  20. 80
  21. 225
  22. 77
  23. 280
  24. 196
  25. 191
  26. 84
  27. 12
  28. 104
  29. 117
  30. 129
  31. 45
  32. 21
  33. 9th
  34. 153
  35. 83
  36. 676
  37. 35
  38. 153
  39. 179
  40. 784

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