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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 744 · 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 93? (a) 4278 (b) 8742 (c) 4371 (d) 4372
  2. 2.What is the 19th term of the AP 20, 25, 30, 35, …? (a) 90 (b) 110 (c) 95 (d) 115
  3. 3.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 272 (c) 136 (d) 120
  4. 4.What is the 15th term of the AP 20, 23, 26, 29, …? (a) 62 (b) 45 (c) 42 (d) 65
  5. 5.What is the 31st term of the AP 1, 6, 11, 16, …? (a) 150 (b) 151 (c) 156 (d) 155
  6. 6.What is the 17th term of the AP 1, 6, 11, 16, …? (a) 85 (b) 81 (c) 86 (d) 80
  7. 7.What is the 10th term of the AP 5, 11, 17, 23, …? (a) 60 (b) 54 (c) 59 (d) 65
  8. 8.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 600 (d) 576
  9. 9.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 561 (d) 578
  10. 10.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 110 (d) 55
  11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  12. 12.What is the 29th term of the AP 15, 19, 23, 27, …? (a) 131 (b) 112 (c) 127 (d) 116
  13. 13.What is the 11th term of the AP 2, 7, 12, 17, …? (a) 50 (b) 55 (c) 57 (d) 52
  14. 14.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2926 (c) 2850 (d) 5852
  15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 870 (d) 435
  16. 16.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 529 (c) 45 (d) 552
  17. 17.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 15 (b) 10 (c) 12 (d) 11
  18. 18.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 154 (c) 306 (d) 136
  19. 19.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3003 (c) 6162 (d) 3081
  20. 20.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 180 (b) 168 (c) 25 (d) 336
  21. 21.Which term of the AP 16, 21, 26, 31, … is 181? (a) 36th (b) 34th (c) 35th (d) 33rd
  22. 22.Which term of the AP 5, 9, 13, 17, … is 57? (a) 13th (b) 15th (c) 16th (d) 14th
  23. 23.What is the 39th term of the AP 20, 29, 38, 47, …? (a) 371 (b) 342 (c) 362 (d) 351
  24. 24.What is the sum of all the whole numbers from 1 to 92? (a) 4278 (b) 8556 (c) 4232 (d) 4186
  25. 25.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 450 (b) 230 (c) 45 (d) 225
  26. 26.What is the 40th term of the AP 19, 25, 31, 37, …? (a) 240 (b) 259 (c) 234 (d) 253
  27. 27.What is the 31st term of the AP 5, 11, 17, 23, …? (a) 191 (b) 180 (c) 185 (d) 186
  28. 28.What is the 23rd term of the AP 11, 17, 23, 29, …? (a) 138 (b) 132 (c) 143 (d) 149
  29. 29.What is the 38th term of the AP 16, 24, 32, 40, …? (a) 320 (b) 296 (c) 304 (d) 312
  30. 30.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 36 (b) 234 (c) 468 (d) 252
  31. 31.Which term of the AP 13, 17, 21, 25, … is 101? (a) 24th (b) 22nd (c) 25th (d) 23rd
  32. 32.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 27 (b) 28 (c) 26 (d) 36
  33. 33.What is the 10th term of the AP 17, 25, 33, 41, …? (a) 97 (b) 89 (c) 72 (d) 80
  34. 34.Which term of the AP 12, 19, 26, 33, … is 166? (a) 24th (b) 22nd (c) 25th (d) 23rd
  35. 35.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 85 (b) 80 (c) 26 (d) 160
  36. 36.What is the 26th term of the AP 19, 27, 35, 43, …? (a) 200 (b) 219 (c) 227 (d) 208
  37. 37.What is the 36th term of the AP 8, 13, 18, 23, …? (a) 175 (b) 183 (c) 188 (d) 180
  38. 38.What is the 40th term of the AP 12, 15, 18, 21, …? (a) 132 (b) 129 (c) 120 (d) 117
  39. 39.What is the 19th term of the AP 18, 21, 24, 27, …? (a) 54 (b) 57 (c) 72 (d) 75
  40. 40.What is the 11th term of the AP 10, 19, 28, 37, …? (a) 109 (b) 99 (c) 100 (d) 90

Answer key

  1. 4371
  2. 110
  3. 136
  4. 62
  5. 151
  6. 81
  7. 59
  8. 576
  9. 595
  10. 100
  11. 36
  12. 127
  13. 52
  14. 2926
  15. 841
  16. 529
  17. 11
  18. 153
  19. 3081
  20. 168
  21. 34th
  22. 14th
  23. 362
  24. 4278
  25. 225
  26. 253
  27. 185
  28. 143
  29. 312
  30. 234
  31. 23rd
  32. 27
  33. 89
  34. 23rd
  35. 80
  36. 219
  37. 183
  38. 129
  39. 72
  40. 100

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