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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 906 · 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 missing term in the AP 5, ?, 9, 11, 13? (a) 7 (b) 6 (c) 9 (d) 8
  2. 2.What is the 11th term of the AP 13, 20, 27, 34, …? (a) 70 (b) 83 (c) 90 (d) 77
  3. 3.What is the missing term in the AP 14, 19, 24, ?, 34? (a) 30 (b) 28 (c) 34 (d) 29
  4. 4.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 15 (b) 13 (c) 18 (d) 14
  5. 5.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 16 (b) 10 (c) 12 (d) 11
  6. 6.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4371 (c) 8930 (d) 4418
  7. 7.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4802 (c) 4851 (d) 4753
  8. 8.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 25 (b) 24 (c) 33 (d) 26
  9. 9.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 780 (c) 741 (d) 1560
  10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 289 (d) 153
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484
  12. 12.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 39 (b) 42 (c) 41 (d) 44
  13. 13.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4753 (c) 9506 (d) 4656
  14. 14.What is the 34th term of the AP 3, 5, 7, 9, …? (a) 66 (b) 68 (c) 71 (d) 69
  15. 15.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 18 (b) 14 (c) 12 (d) 13
  16. 16.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 50 (b) 10 (c) 98 (d) 49
  17. 17.What is the 37th term of the AP 15, 22, 29, 36, …? (a) 267 (b) 259 (c) 252 (d) 274
  18. 18.What is the 16th term of the AP 17, 24, 31, 38, …? (a) 112 (b) 105 (c) 129 (d) 122
  19. 19.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 600 (d) 47
  20. 20.What is the sum of all the whole numbers from 1 to 83? (a) 3486 (b) 3403 (c) 3487 (d) 6972
  21. 21.What is the 17th term of the AP 14, 17, 20, 23, …? (a) 48 (b) 51 (c) 62 (d) 65
  22. 22.What is the 23rd term of the AP 14, 18, 22, 26, …? (a) 88 (b) 92 (c) 106 (d) 102
  23. 23.What is the 29th term of the AP 5, 7, 9, 11, …? (a) 58 (b) 56 (c) 61 (d) 63
  24. 24.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 26 (b) 27 (c) 25 (d) 28
  25. 25.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 342 (c) 171 (d) 162
  26. 26.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 10 (b) 11 (c) 12 (d) 17
  27. 27.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 110 (c) 55 (d) 60
  28. 28.What is the 28th term of the AP 4, 13, 22, 31, …? (a) 256 (b) 247 (c) 252 (d) 243
  29. 29.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 1711 (c) 3422 (d) 1682
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  31. 31.What is the missing term in the AP 14, ?, 32, 41, 50? (a) 24 (b) 32 (c) 23 (d) 22
  32. 32.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 9900 (c) 4951 (d) 4950
  33. 33.What is the 25th term of the AP 14, 18, 22, 26, …? (a) 100 (b) 114 (c) 110 (d) 96
  34. 34.What is the 16th term of the AP 16, 20, 24, 28, …? (a) 64 (b) 60 (c) 80 (d) 76
  35. 35.What is the 14th term of the AP 10, 14, 18, 22, …? (a) 66 (b) 62 (c) 52 (d) 56
  36. 36.Which term of the AP 14, 22, 30, 38, … is 158? (a) 18th (b) 20th (c) 19th (d) 21st
  37. 37.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 14 (b) 16 (c) 15 (d) 21
  38. 38.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 631 (c) 595 (d) 630
  39. 39.What is the 16th term of the AP 13, 21, 29, 37, …? (a) 128 (b) 133 (c) 120 (d) 141
  40. 40.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 18 (b) 26 (c) 20 (d) 19

Answer key

  1. 7
  2. 83
  3. 29
  4. 14
  5. 11
  6. 4465
  7. 4851
  8. 25
  9. 780
  10. 289
  11. 484
  12. 41
  13. 4753
  14. 69
  15. 13
  16. 49
  17. 267
  18. 122
  19. 576
  20. 3486
  21. 62
  22. 102
  23. 61
  24. 26
  25. 171
  26. 11
  27. 55
  28. 247
  29. 1711
  30. 144
  31. 23
  32. 4950
  33. 110
  34. 76
  35. 62
  36. 19th
  37. 15
  38. 630
  39. 133
  40. 19

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