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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 853 · 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 17th term of the AP 19, 23, 27, 31, …? (a) 64 (b) 87 (c) 68 (d) 83
  2. 2.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 252 (b) 36 (c) 468 (d) 234
  3. 3.What is the 31st term of the AP 13, 16, 19, 22, …? (a) 106 (b) 90 (c) 103 (d) 93
  4. 4.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4560 (c) 9312 (d) 4656
  5. 5.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 630 (c) 648 (d) 1332
  6. 6.Which term of the AP 1, 5, 9, 13, … is 89? (a) 22nd (b) 24th (c) 23rd (d) 25th
  7. 7.What is the 31st term of the AP 7, 9, 11, 13, …? (a) 69 (b) 60 (c) 67 (d) 62
  8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 784 (d) 812
  9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 64 (d) 15
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 136 (d) 31
  11. 11.What is the 23rd term of the AP 4, 7, 10, 13, …? (a) 66 (b) 69 (c) 70 (d) 73
  12. 12.What is the 25th term of the AP 3, 11, 19, 27, …? (a) 192 (b) 195 (c) 200 (d) 203
  13. 13.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 880 (b) 440 (c) 70 (d) 473
  14. 14.Which term of the AP 20, 28, 36, 44, … is 188? (a) 22nd (b) 24th (c) 23rd (d) 21st
  15. 15.What is the 32nd term of the AP 7, 13, 19, 25, …? (a) 192 (b) 186 (c) 199 (d) 193
  16. 16.What is the 28th term of the AP 1, 5, 9, 13, …? (a) 108 (b) 113 (c) 112 (d) 109
  17. 17.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 105 (b) 20 (c) 196 (d) 98
  18. 18.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 168 (b) 39 (c) 294 (d) 147
  19. 19.What is the sum of all the whole numbers from 1 to 82? (a) 3321 (b) 3362 (c) 3403 (d) 6806
  20. 20.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 93 (c) 186 (d) 28
  21. 21.Which term of the AP 18, 21, 24, 27, … is 69? (a) 19th (b) 23rd (c) 17th (d) 18th
  22. 22.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 45 (b) 378 (c) 189 (d) 210
  23. 23.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 440 (b) 407 (c) 814 (d) 67
  24. 24.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 289 (d) 153
  25. 25.What is the 38th term of the AP 4, 8, 12, 16, …? (a) 152 (b) 148 (c) 153 (d) 156
  26. 26.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 24 (b) 22 (c) 29 (d) 23
  27. 27.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2592 (c) 2628 (d) 2556
  28. 28.What is the 20th term of the AP 16, 20, 24, 28, …? (a) 80 (b) 92 (c) 96 (d) 76
  29. 29.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 1327 (c) 1326 (d) 2652
  30. 30.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 21 (b) 18 (c) 16 (d) 17
  31. 31.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 224 (b) 22 (c) 112 (d) 119
  32. 32.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 78 (b) 150 (c) 21 (d) 75
  33. 33.What is the 12th term of the AP 5, 8, 11, 14, …? (a) 38 (b) 36 (c) 41 (d) 33
  34. 34.What is the 15th term of the AP 10, 17, 24, 31, …? (a) 115 (b) 105 (c) 108 (d) 98
  35. 35.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 18 (b) 168 (c) 91 (d) 84
  36. 36.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 612 (c) 42 (d) 324
  37. 37.What is the 39th term of the AP 8, 13, 18, 23, …? (a) 195 (b) 190 (c) 198 (d) 203
  38. 38.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 351 (d) 676
  39. 39.What is the 26th term of the AP 15, 18, 21, 24, …? (a) 78 (b) 93 (c) 75 (d) 90
  40. 40.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 11 (b) 17 (c) 12 (d) 10

Answer key

  1. 83
  2. 234
  3. 103
  4. 4656
  5. 666
  6. 23rd
  7. 67
  8. 784
  9. 64
  10. 256
  11. 70
  12. 195
  13. 440
  14. 22nd
  15. 193
  16. 109
  17. 98
  18. 147
  19. 3403
  20. 93
  21. 18th
  22. 189
  23. 407
  24. 289
  25. 152
  26. 23
  27. 2628
  28. 92
  29. 1326
  30. 17
  31. 112
  32. 75
  33. 38
  34. 108
  35. 84
  36. 306
  37. 198
  38. 676
  39. 90
  40. 11

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