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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 826 · 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 6, 10, ?, 18, 22? (a) 14 (b) 13 (c) 18 (d) 15
  2. 2.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 256 (b) 128 (c) 23 (d) 136
  3. 3.What is the 25th term of the AP 19, 21, 23, 25, …? (a) 50 (b) 48 (c) 69 (d) 67
  4. 4.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 14 (b) 16 (c) 15 (d) 18
  5. 5.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 432 (b) 402 (c) 61 (d) 804
  6. 6.What is the sum of all the whole numbers from 1 to 82? (a) 3321 (b) 3362 (c) 6806 (d) 3403
  7. 7.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 117 (b) 234 (c) 118 (d) 17
  8. 8.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 497 (d) 465
  9. 9.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 78 (b) 144 (c) 17 (d) 72
  10. 10.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 29 (b) 24 (c) 25 (d) 23
  11. 11.What is the 31st term of the AP 17, 23, 29, 35, …? (a) 203 (b) 186 (c) 180 (d) 197
  12. 12.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 231 (b) 234 (c) 36 (d) 462
  13. 13.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 190 (b) 175 (c) 31 (d) 350
  14. 14.What is the 21st term of the AP 3, 9, 15, 21, …? (a) 120 (b) 126 (c) 123 (d) 129
  15. 15.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 60 (b) 18 (c) 120 (d) 63
  16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 506 (d) 484
  17. 17.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 25 (b) 23 (c) 28 (d) 24
  18. 18.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 102 (b) 27 (c) 174 (d) 87
  19. 19.What is the 27th term of the AP 15, 19, 23, 27, …? (a) 108 (b) 123 (c) 104 (d) 119
  20. 20.What is the 18th term of the AP 11, 18, 25, 32, …? (a) 119 (b) 126 (c) 130 (d) 137
  21. 21.Which term of the AP 11, 13, 15, 17, … is 47? (a) 21st (b) 20th (c) 19th (d) 18th
  22. 22.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1771 (c) 1711 (d) 1770
  23. 23.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 162 (c) 81 (d) 96
  24. 24.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 8190 (c) 4050 (d) 4095
  25. 25.What is the 34th term of the AP 13, 22, 31, 40, …? (a) 306 (b) 297 (c) 310 (d) 319
  26. 26.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 288 (b) 160 (c) 32 (d) 144
  27. 27.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 2256 (c) 1128 (d) 1129
  28. 28.What is the 12th term of the AP 8, 17, 26, 35, …? (a) 99 (b) 116 (c) 108 (d) 107
  29. 29.What is the 39th term of the AP 10, 14, 18, 22, …? (a) 152 (b) 162 (c) 166 (d) 156
  30. 30.What is the 22nd term of the AP 7, 11, 15, 19, …? (a) 95 (b) 84 (c) 91 (d) 88
  31. 31.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2048 (c) 2080 (d) 2016
  32. 32.What is the 19th term of the AP 12, 20, 28, 36, …? (a) 144 (b) 156 (c) 164 (d) 152
  33. 33.What is the 20th term of the AP 20, 24, 28, 32, …? (a) 80 (b) 100 (c) 96 (d) 76
  34. 34.What is the 16th term of the AP 5, 14, 23, 32, …? (a) 144 (b) 135 (c) 149 (d) 140
  35. 35.What is the 13th term of the AP 17, 26, 35, 44, …? (a) 117 (b) 108 (c) 134 (d) 125
  36. 36.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 162 (b) 39 (c) 288 (d) 144
  37. 37.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 324 (d) 171
  38. 38.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 47 (c) 297 (d) 319
  39. 39.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 24 (b) 32 (c) 23 (d) 25
  40. 40.What is the sum of all the whole numbers from 1 to 46? (a) 1081 (b) 2162 (c) 1058 (d) 1035

Answer key

  1. 14
  2. 128
  3. 67
  4. 15
  5. 402
  6. 3403
  7. 117
  8. 496
  9. 72
  10. 24
  11. 197
  12. 231
  13. 175
  14. 123
  15. 60
  16. 484
  17. 24
  18. 87
  19. 119
  20. 130
  21. 19th
  22. 1770
  23. 81
  24. 4095
  25. 310
  26. 144
  27. 1128
  28. 107
  29. 162
  30. 91
  31. 2080
  32. 156
  33. 96
  34. 140
  35. 125
  36. 144
  37. 324
  38. 297
  39. 24
  40. 1081

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