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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 80 · 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.Which term of the AP 17, 20, 23, 26, … is 68? (a) 17th (b) 18th (c) 20th (d) 19th
  2. 2.What is the 26th term of the AP 8, 11, 14, 17, …? (a) 83 (b) 86 (c) 78 (d) 75
  3. 3.What is the 12th term of the AP 12, 19, 26, 33, …? (a) 77 (b) 89 (c) 84 (d) 96
  4. 4.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 722 (c) 741 (d) 1482
  5. 5.What is the 17th term of the AP 14, 20, 26, 32, …? (a) 116 (b) 102 (c) 110 (d) 96
  6. 6.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 22 (b) 23 (c) 24 (d) 21
  7. 7.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 14 (b) 12 (c) 13 (d) 19
  8. 8.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 1568 (c) 1540 (d) 3192
  9. 9.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 108 (b) 216 (c) 120 (d) 28
  10. 10.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 726 (c) 58 (d) 363
  11. 11.What is the 25th term of the AP 3, 6, 9, 12, …? (a) 75 (b) 72 (c) 76 (d) 78
  12. 12.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 3306 (c) 1654 (d) 1653
  13. 13.What is the 34th term of the AP 16, 19, 22, 25, …? (a) 118 (b) 99 (c) 102 (d) 115
  14. 14.Which term of the AP 19, 23, 27, 31, … is 171? (a) 41st (b) 39th (c) 40th (d) 38th
  15. 15.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1953 (c) 1891 (d) 1922
  16. 16.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 37 (b) 312 (c) 176 (d) 156
  17. 17.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 45 (b) 11 (c) 46 (d) 90
  18. 18.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 55 (d) 110
  19. 19.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 102 (c) 14 (d) 108
  20. 20.What is the 21st term of the AP 14, 19, 24, 29, …? (a) 105 (b) 114 (c) 119 (d) 100
  21. 21.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 189 (b) 35 (c) 171 (d) 342
  22. 22.What is the missing term in the AP 19, 25, 31, ?, 43? (a) 37 (b) 43 (c) 36 (d) 38
  23. 23.What is the missing term in the AP 15, ?, 21, 24, 27? (a) 17 (b) 21 (c) 18 (d) 19
  24. 24.What is the 17th term of the AP 4, 11, 18, 25, …? (a) 112 (b) 119 (c) 123 (d) 116
  25. 25.What is the 23rd term of the AP 2, 9, 16, 23, …? (a) 161 (b) 163 (c) 156 (d) 154
  26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 276 (d) 529
  27. 27.What is the 29th term of the AP 10, 15, 20, 25, …? (a) 145 (b) 140 (c) 155 (d) 150
  28. 28.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 62 (b) 352 (c) 704 (d) 385
  29. 29.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 1431 (c) 1378 (d) 2862
  30. 30.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 676 (d) 351
  31. 31.What is the 13th term of the AP 12, 14, 16, 18, …? (a) 36 (b) 38 (c) 24 (d) 26
  32. 32.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 561 (c) 562 (d) 528
  33. 33.What is the 16th term of the AP 2, 5, 8, 11, …? (a) 48 (b) 50 (c) 47 (d) 45
  34. 34.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4372 (c) 4371 (d) 8742
  35. 35.What is the 17th term of the AP 1, 7, 13, 19, …? (a) 96 (b) 97 (c) 103 (d) 102
  36. 36.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 352 (b) 57 (c) 357 (d) 704
  37. 37.What is the 12th term of the AP 18, 22, 26, 30, …? (a) 44 (b) 66 (c) 62 (d) 48
  38. 38.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 89 (b) 176 (c) 88 (d) 13
  39. 39.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4656 (c) 4754 (d) 4753
  40. 40.What is the 13th term of the AP 10, 15, 20, 25, …? (a) 65 (b) 60 (c) 75 (d) 70

Answer key

  1. 18th
  2. 83
  3. 89
  4. 741
  5. 110
  6. 22
  7. 13
  8. 1596
  9. 108
  10. 363
  11. 75
  12. 1653
  13. 115
  14. 39th
  15. 1953
  16. 156
  17. 45
  18. 100
  19. 102
  20. 114
  21. 171
  22. 37
  23. 18
  24. 116
  25. 156
  26. 529
  27. 150
  28. 352
  29. 1431
  30. 676
  31. 36
  32. 561
  33. 47
  34. 4371
  35. 97
  36. 352
  37. 62
  38. 88
  39. 4753
  40. 70

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