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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 204 · 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 32nd term of the AP 17, 25, 33, 41, …? (a) 248 (b) 256 (c) 265 (d) 273
  2. 2.Which term of the AP 1, 5, 9, 13, … is 149? (a) 39th (b) 38th (c) 40th (d) 37th
  3. 3.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 128 (c) 136 (d) 120
  4. 4.What is the sum of all the whole numbers from 1 to 83? (a) 3486 (b) 6972 (c) 3487 (d) 3403
  5. 5.What is the 29th term of the AP 14, 22, 30, 38, …? (a) 246 (b) 224 (c) 238 (d) 232
  6. 6.What is the 10th term of the AP 12, 19, 26, 33, …? (a) 82 (b) 63 (c) 75 (d) 70
  7. 7.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 4186 (c) 8556 (d) 4278
  8. 8.What is the 12th term of the AP 18, 25, 32, 39, …? (a) 77 (b) 95 (c) 102 (d) 84
  9. 9.What is the sum of all the whole numbers from 1 to 15? (a) 120 (b) 121 (c) 240 (d) 105
  10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 11 (d) 42
  11. 11.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 1953 (c) 2016 (d) 2017
  12. 12.What is the 21st term of the AP 15, 20, 25, 30, …? (a) 115 (b) 100 (c) 105 (d) 120
  13. 13.What is the 27th term of the AP 17, 23, 29, 35, …? (a) 173 (b) 156 (c) 162 (d) 179
  14. 14.What is the 12th term of the AP 10, 15, 20, 25, …? (a) 70 (b) 60 (c) 55 (d) 65
  15. 15.What is the 33rd term of the AP 19, 28, 37, 46, …? (a) 316 (b) 288 (c) 297 (d) 307
  16. 16.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 144 (b) 24 (c) 136 (d) 272
  17. 17.What is the 19th term of the AP 2, 5, 8, 11, …? (a) 57 (b) 54 (c) 56 (d) 59
  18. 18.What is the 14th term of the AP 14, 20, 26, 32, …? (a) 84 (b) 92 (c) 78 (d) 98
  19. 19.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 5 (b) 9 (c) 7 (d) 6
  20. 20.What is the 37th term of the AP 9, 18, 27, 36, …? (a) 334 (b) 342 (c) 324 (d) 333
  21. 21.What is the 20th term of the AP 9, 14, 19, 24, …? (a) 100 (b) 109 (c) 104 (d) 95
  22. 22.What is the 32nd term of the AP 18, 22, 26, 30, …? (a) 146 (b) 142 (c) 128 (d) 124
  23. 23.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 136 (b) 240 (c) 29 (d) 120
  24. 24.What is the 10th term of the AP 8, 17, 26, 35, …? (a) 81 (b) 98 (c) 90 (d) 89
  25. 25.What is the 30th term of the AP 2, 8, 14, 20, …? (a) 180 (b) 182 (c) 176 (d) 174
  26. 26.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 23 (b) 15 (c) 17 (d) 16
  27. 27.Which term of the AP 7, 10, 13, 16, … is 103? (a) 35th (b) 34th (c) 32nd (d) 33rd
  28. 28.What is the 36th term of the AP 3, 6, 9, 12, …? (a) 111 (b) 108 (c) 109 (d) 105
  29. 29.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 90 (d) 17
  30. 30.What is the 32nd term of the AP 3, 5, 7, 9, …? (a) 67 (b) 64 (c) 62 (d) 65
  31. 31.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 23 (b) 19 (c) 21 (d) 20
  32. 32.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 26 (b) 171 (c) 162 (d) 324
  33. 33.What is the 24th term of the AP 13, 22, 31, 40, …? (a) 216 (b) 207 (c) 229 (d) 220
  34. 34.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 380 (b) 37 (c) 190 (d) 210
  35. 35.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 73 (b) 144 (c) 12 (d) 72
  36. 36.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 144 (b) 17 (c) 138 (d) 276
  37. 37.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
  38. 38.What is the 10th term of the AP 6, 14, 22, 30, …? (a) 78 (b) 80 (c) 72 (d) 86
  39. 39.What is the 25th term of the AP 6, 10, 14, 18, …? (a) 102 (b) 106 (c) 100 (d) 96
  40. 40.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 376 (b) 208 (c) 188 (d) 41

Answer key

  1. 265
  2. 38th
  3. 136
  4. 3486
  5. 238
  6. 75
  7. 4278
  8. 95
  9. 120
  10. 36
  11. 2016
  12. 115
  13. 173
  14. 65
  15. 307
  16. 136
  17. 56
  18. 92
  19. 6
  20. 333
  21. 104
  22. 142
  23. 120
  24. 89
  25. 176
  26. 16
  27. 33rd
  28. 108
  29. 81
  30. 65
  31. 20
  32. 162
  33. 220
  34. 190
  35. 72
  36. 138
  37. 400
  38. 78
  39. 102
  40. 188

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