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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 68 · 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 57? (a) 1653 (b) 1654 (c) 3306 (d) 1596
  2. 2.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 240 (c) 121 (d) 120
  3. 3.Which term of the AP 3, 6, 9, 12, … is 114? (a) 38th (b) 40th (c) 37th (d) 39th
  4. 4.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 18 (b) 270 (c) 140 (d) 135
  5. 5.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 17 (d) 45
  6. 6.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 234 (b) 239 (c) 468 (d) 46
  7. 7.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 41 (b) 80 (c) 10 (d) 40
  8. 8.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 780 (c) 820 (d) 1640
  9. 9.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 15 (b) 110 (c) 220 (d) 111
  10. 10.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 144 (b) 136 (c) 272 (d) 24
  11. 11.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 676 (d) 51
  12. 12.What is the 40th term of the AP 12, 18, 24, 30, …? (a) 240 (b) 234 (c) 252 (d) 246
  13. 13.What is the 26th term of the AP 15, 19, 23, 27, …? (a) 100 (b) 115 (c) 104 (d) 119
  14. 14.Which term of the AP 19, 22, 25, 28, … is 55? (a) 14th (b) 12th (c) 13th (d) 15th
  15. 15.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 6 (b) 5 (c) 7 (d) 11
  16. 16.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 300 (d) 47
  17. 17.What is the 18th term of the AP 11, 13, 15, 17, …? (a) 36 (b) 45 (c) 34 (d) 47
  18. 18.What is the 27th term of the AP 4, 9, 14, 19, …? (a) 134 (b) 139 (c) 130 (d) 135
  19. 19.What is the 15th term of the AP 20, 26, 32, 38, …? (a) 90 (b) 84 (c) 104 (d) 110
  20. 20.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 96 (b) 54 (c) 13 (d) 48
  21. 21.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 814 (b) 67 (c) 407 (d) 440
  22. 22.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 31 (b) 350 (c) 190 (d) 175
  23. 23.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 7 (b) 9 (c) 6 (d) 5
  24. 24.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 225 (b) 450 (c) 45 (d) 230
  25. 25.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 108 (c) 216 (d) 109
  26. 26.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 23 (b) 186 (c) 93 (d) 102
  27. 27.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 270 (b) 35 (c) 135 (d) 150
  28. 28.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 136 (d) 272
  29. 29.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 756 (d) 53
  30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  31. 31.What is the 40th term of the AP 6, 15, 24, 33, …? (a) 360 (b) 366 (c) 357 (d) 351
  32. 32.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 13 (b) 11 (c) 12 (d) 17
  33. 33.Which term of the AP 9, 11, 13, 15, … is 31? (a) 12th (b) 13th (c) 14th (d) 11th
  34. 34.What is the sum of all the whole numbers from 1 to 20? (a) 190 (b) 200 (c) 420 (d) 210
  35. 35.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 150 (b) 300 (c) 24 (d) 160
  36. 36.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 8 (b) 9 (c) 13 (d) 10
  37. 37.What is the missing term in the AP 8, 10, 12, ?, 16? (a) 13 (b) 14 (c) 15 (d) 16
  38. 38.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 16 (b) 18 (c) 15 (d) 14
  39. 39.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 17 (b) 19 (c) 23 (d) 18
  40. 40.What is the sum of all the whole numbers from 1 to 44? (a) 968 (b) 1980 (c) 990 (d) 946

Answer key

  1. 1653
  2. 120
  3. 38th
  4. 135
  5. 81
  6. 234
  7. 40
  8. 820
  9. 110
  10. 136
  11. 676
  12. 246
  13. 115
  14. 13th
  15. 6
  16. 576
  17. 45
  18. 134
  19. 104
  20. 48
  21. 407
  22. 175
  23. 6
  24. 225
  25. 108
  26. 93
  27. 135
  28. 256
  29. 729
  30. 841
  31. 357
  32. 12
  33. 12th
  34. 210
  35. 150
  36. 9
  37. 14
  38. 15
  39. 18
  40. 990

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