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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 947 · 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 11 terms of the AP 8, 12, 16, …? (a) 616 (b) 330 (c) 308 (d) 48
  2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  3. 3.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 34 (b) 162 (c) 324 (d) 180
  4. 4.What is the 28th term of the AP 12, 21, 30, 39, …? (a) 264 (b) 252 (c) 255 (d) 243
  5. 5.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 64 (d) 36
  6. 6.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  7. 7.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 357 (b) 352 (c) 704 (d) 57
  8. 8.What is the 13th term of the AP 11, 18, 25, 32, …? (a) 102 (b) 91 (c) 95 (d) 84
  9. 9.Which term of the AP 20, 25, 30, 35, … is 120? (a) 22nd (b) 21st (c) 24th (d) 20th
  10. 10.What is the 29th term of the AP 3, 9, 15, 21, …? (a) 174 (b) 171 (c) 168 (d) 177
  11. 11.What is the 28th term of the AP 12, 15, 18, 21, …? (a) 81 (b) 93 (c) 96 (d) 84
  12. 12.What is the 20th term of the AP 7, 14, 21, 28, …? (a) 141 (b) 140 (c) 133 (d) 147
  13. 13.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 11 (b) 14 (c) 9 (d) 10
  14. 14.What is the 34th term of the AP 20, 26, 32, 38, …? (a) 204 (b) 198 (c) 224 (d) 218
  15. 15.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 1891 (c) 3782 (d) 1830
  16. 16.What is the 23rd term of the AP 6, 10, 14, 18, …? (a) 94 (b) 98 (c) 88 (d) 92
  17. 17.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 16 (b) 17 (c) 15 (d) 20
  18. 18.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 190 (c) 110 (d) 95
  19. 19.Which term of the AP 4, 8, 12, 16, … is 156? (a) 38th (b) 40th (c) 41st (d) 39th
  20. 20.What is the 17th term of the AP 18, 24, 30, 36, …? (a) 96 (b) 114 (c) 120 (d) 102
  21. 21.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1081 (c) 1129 (d) 1128
  22. 22.What is the 24th term of the AP 17, 20, 23, 26, …? (a) 69 (b) 72 (c) 86 (d) 89
  23. 23.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 10 (b) 11 (c) 14 (d) 12
  24. 24.What is the 20th term of the AP 7, 9, 11, 13, …? (a) 38 (b) 47 (c) 45 (d) 40
  25. 25.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 306 (b) 25 (c) 153 (d) 162
  26. 26.What is the 22nd term of the AP 12, 15, 18, 21, …? (a) 66 (b) 75 (c) 63 (d) 78
  27. 27.What is the 39th term of the AP 12, 14, 16, 18, …? (a) 88 (b) 76 (c) 90 (d) 78
  28. 28.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 468 (b) 261 (c) 50 (d) 234
  29. 29.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 600 (c) 300 (d) 288
  30. 30.What is the 10th term of the AP 19, 23, 27, 31, …? (a) 36 (b) 40 (c) 55 (d) 59
  31. 31.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 18 (b) 120 (c) 63 (d) 60
  32. 32.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 170 (c) 180 (d) 340
  33. 33.What is the sum of all the whole numbers from 1 to 46? (a) 2162 (b) 1035 (c) 1081 (d) 1058
  34. 34.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 6 (b) 5 (c) 7 (d) 4
  35. 35.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 78 (c) 12 (d) 77
  36. 36.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 29 (b) 30 (c) 38 (d) 31
  37. 37.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 841 (d) 870
  38. 38.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 17 (b) 84 (c) 154 (d) 77
  39. 39.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 154 (d) 306
  40. 40.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 72 (c) 66 (d) 78

Answer key

  1. 308
  2. 49
  3. 162
  4. 255
  5. 64
  6. 169
  7. 352
  8. 95
  9. 21st
  10. 171
  11. 93
  12. 140
  13. 10
  14. 218
  15. 1891
  16. 94
  17. 16
  18. 95
  19. 39th
  20. 114
  21. 1128
  22. 86
  23. 11
  24. 45
  25. 153
  26. 75
  27. 88
  28. 234
  29. 300
  30. 55
  31. 60
  32. 170
  33. 1081
  34. 5
  35. 77
  36. 30
  37. 841
  38. 77
  39. 153
  40. 78

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