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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 840 · 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 all the whole numbers from 1 to 86? (a) 3741 (b) 3698 (c) 3655 (d) 7482
  2. 2.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 17 (b) 133 (c) 132 (d) 264
  3. 3.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 28 (b) 204 (c) 408 (d) 216
  4. 4.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 729 (d) 53
  5. 5.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 1326 (c) 1327 (d) 2652
  6. 6.What is the 19th term of the AP 9, 17, 25, 33, …? (a) 144 (b) 152 (c) 161 (d) 153
  7. 7.What is the 37th term of the AP 1, 8, 15, 22, …? (a) 260 (b) 259 (c) 252 (d) 253
  8. 8.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4802 (c) 4851 (d) 4753
  9. 9.What is the 28th term of the AP 3, 11, 19, 27, …? (a) 216 (b) 227 (c) 219 (d) 224
  10. 10.Which term of the AP 6, 9, 12, 15, … is 102? (a) 34th (b) 35th (c) 32nd (d) 33rd
  11. 11.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 23 (b) 24 (c) 25 (d) 22
  12. 12.What is the sum of all the whole numbers from 1 to 89? (a) 4006 (b) 3916 (c) 8010 (d) 4005
  13. 13.Which term of the AP 14, 17, 20, 23, … is 113? (a) 36th (b) 35th (c) 34th (d) 33rd
  14. 14.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 29 (b) 35 (c) 28 (d) 30
  15. 15.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 90 (b) 81 (c) 162 (d) 17
  16. 16.Which term of the AP 12, 17, 22, 27, … is 177? (a) 34th (b) 36th (c) 35th (d) 33rd
  17. 17.What is the 16th term of the AP 10, 13, 16, 19, …? (a) 58 (b) 48 (c) 55 (d) 45
  18. 18.What is the 17th term of the AP 1, 10, 19, 28, …? (a) 154 (b) 144 (c) 145 (d) 153
  19. 19.What is the 22nd term of the AP 1, 3, 5, 7, …? (a) 43 (b) 42 (c) 45 (d) 44
  20. 20.What is the 15th term of the AP 18, 21, 24, 27, …? (a) 63 (b) 45 (c) 42 (d) 60
  21. 21.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1432 (c) 1431 (d) 2862
  22. 22.What is the 22nd term of the AP 12, 15, 18, 21, …? (a) 78 (b) 66 (c) 63 (d) 75
  23. 23.What is the 38th term of the AP 13, 19, 25, 31, …? (a) 241 (b) 222 (c) 228 (d) 235
  24. 24.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 75 (c) 12 (d) 150
  25. 25.What is the 13th term of the AP 11, 20, 29, 38, …? (a) 128 (b) 119 (c) 117 (d) 108
  26. 26.Which term of the AP 13, 20, 27, 34, … is 272? (a) 39th (b) 37th (c) 40th (d) 38th
  27. 27.What is the missing term in the AP 10, 15, 20, ?, 30? (a) 30 (b) 25 (c) 24 (d) 26
  28. 28.What is the 40th term of the AP 20, 25, 30, 35, …? (a) 195 (b) 215 (c) 200 (d) 220
  29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 484 (d) 43
  30. 30.Which term of the AP 20, 28, 36, 44, … is 196? (a) 25th (b) 22nd (c) 23rd (d) 24th
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 121 (d) 132
  32. 32.What is the missing term in the AP 16, 19, ?, 25, 28? (a) 25 (b) 23 (c) 21 (d) 22
  33. 33.What is the 39th term of the AP 10, 16, 22, 28, …? (a) 238 (b) 234 (c) 244 (d) 228
  34. 34.What is the 38th term of the AP 2, 5, 8, 11, …? (a) 116 (b) 113 (c) 111 (d) 114
  35. 35.Which term of the AP 19, 23, 27, 31, … is 167? (a) 38th (b) 39th (c) 40th (d) 37th
  36. 36.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 462 (d) 441
  37. 37.What is the 13th term of the AP 10, 14, 18, 22, …? (a) 48 (b) 62 (c) 58 (d) 52
  38. 38.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 266 (b) 28 (c) 136 (d) 133
  39. 39.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 72 (b) 73 (c) 12 (d) 144
  40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 351 (d) 51

Answer key

  1. 3741
  2. 132
  3. 204
  4. 729
  5. 1326
  6. 153
  7. 253
  8. 4851
  9. 219
  10. 33rd
  11. 23
  12. 4005
  13. 34th
  14. 29
  15. 81
  16. 34th
  17. 55
  18. 145
  19. 43
  20. 60
  21. 1431
  22. 75
  23. 235
  24. 75
  25. 119
  26. 38th
  27. 25
  28. 215
  29. 484
  30. 23rd
  31. 121
  32. 22
  33. 238
  34. 113
  35. 38th
  36. 441
  37. 58
  38. 133
  39. 72
  40. 676

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