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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 246 · 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 25th term of the AP 2, 5, 8, 11, …? (a) 77 (b) 75 (c) 74 (d) 72
  2. 2.What is the 31st term of the AP 17, 24, 31, 38, …? (a) 217 (b) 210 (c) 234 (d) 227
  3. 3.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 27 (b) 32 (c) 26 (d) 25
  4. 4.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 210 (b) 112 (c) 21 (d) 105
  5. 5.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 30 (b) 31 (c) 36 (d) 29
  6. 6.Which term of the AP 14, 16, 18, 20, … is 36? (a) 13th (b) 12th (c) 11th (d) 18th
  7. 7.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 34 (b) 44 (c) 35 (d) 36
  8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  9. 9.Which term of the AP 15, 17, 19, 21, … is 41? (a) 16th (b) 13th (c) 15th (d) 14th
  10. 10.What is the 32nd term of the AP 9, 12, 15, 18, …? (a) 96 (b) 102 (c) 105 (d) 93
  11. 11.What is the 15th term of the AP 20, 28, 36, 44, …? (a) 112 (b) 132 (c) 120 (d) 140
  12. 12.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 36 (b) 147 (c) 152 (d) 294
  13. 13.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 96 (b) 26 (c) 81 (d) 162
  14. 14.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 396 (b) 53 (c) 372 (d) 744
  15. 15.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 366 (b) 396 (c) 732 (d) 58
  16. 16.Which term of the AP 16, 22, 28, 34, … is 88? (a) 12th (b) 14th (c) 13th (d) 15th
  17. 17.What is the 28th term of the AP 2, 5, 8, 11, …? (a) 81 (b) 84 (c) 83 (d) 86
  18. 18.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 25 (b) 24 (c) 26 (d) 32
  19. 19.What is the 25th term of the AP 17, 21, 25, 29, …? (a) 117 (b) 96 (c) 113 (d) 100
  20. 20.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 562 (c) 1122 (d) 528
  21. 21.What is the missing term in the AP 10, 13, 16, ?, 22? (a) 18 (b) 22 (c) 19 (d) 20
  22. 22.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1485 (c) 3080 (d) 1540
  23. 23.What is the 11th term of the AP 2, 9, 16, 23, …? (a) 77 (b) 72 (c) 70 (d) 79
  24. 24.What is the 20th term of the AP 17, 19, 21, 23, …? (a) 38 (b) 55 (c) 40 (d) 57
  25. 25.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 342 (c) 171 (d) 153
  26. 26.What is the missing term in the AP 18, ?, 28, 33, 38? (a) 22 (b) 23 (c) 24 (d) 28
  27. 27.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 105 (c) 120 (d) 121
  28. 28.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 406 (d) 812
  29. 29.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 216 (b) 17 (c) 112 (d) 108
  30. 30.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 162 (b) 82 (c) 81 (d) 13
  31. 31.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 49 (b) 261 (c) 266 (d) 522
  32. 32.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 102 (b) 27 (c) 174 (d) 87
  33. 33.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 80 (b) 16 (c) 72 (d) 144
  34. 34.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  35. 35.What is the 38th term of the AP 11, 19, 27, 35, …? (a) 304 (b) 296 (c) 307 (d) 315
  36. 36.What is the 16th term of the AP 5, 12, 19, 26, …? (a) 110 (b) 117 (c) 112 (d) 105
  37. 37.What is the 22nd term of the AP 4, 13, 22, 31, …? (a) 189 (b) 198 (c) 202 (d) 193
  38. 38.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 320 (c) 25 (d) 170
  39. 39.What is the missing term in the AP 16, 22, 28, ?, 40? (a) 34 (b) 35 (c) 33 (d) 40
  40. 40.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 306 (c) 154 (d) 153

Answer key

  1. 74
  2. 227
  3. 26
  4. 105
  5. 30
  6. 12th
  7. 35
  8. 36
  9. 14th
  10. 102
  11. 132
  12. 147
  13. 81
  14. 372
  15. 366
  16. 13th
  17. 83
  18. 25
  19. 113
  20. 561
  21. 19
  22. 1540
  23. 72
  24. 55
  25. 171
  26. 23
  27. 120
  28. 784
  29. 108
  30. 81
  31. 261
  32. 87
  33. 72
  34. 121
  35. 307
  36. 110
  37. 193
  38. 160
  39. 34
  40. 153

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