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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 353 · 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.Which term of the AP 11, 13, 15, 17, … is 37? (a) 13th (b) 14th (c) 16th (d) 15th
  2. 2.What is the 38th term of the AP 15, 24, 33, 42, …? (a) 357 (b) 333 (c) 342 (d) 348
  3. 3.What is the 14th term of the AP 17, 20, 23, 26, …? (a) 59 (b) 56 (c) 39 (d) 42
  4. 4.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 9 (b) 36 (c) 70 (d) 35
  5. 5.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 288 (b) 156 (c) 23 (d) 144
  6. 6.What is the 24th term of the AP 14, 21, 28, 35, …? (a) 161 (b) 175 (c) 182 (d) 168
  7. 7.What is the 11th term of the AP 14, 21, 28, 35, …? (a) 84 (b) 70 (c) 77 (d) 91
  8. 8.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 22 (b) 21 (c) 20 (d) 19
  9. 9.What is the 18th term of the AP 10, 13, 16, 19, …? (a) 51 (b) 64 (c) 61 (d) 54
  10. 10.What is the 13th term of the AP 6, 11, 16, 21, …? (a) 60 (b) 71 (c) 65 (d) 66
  11. 11.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 18 (b) 23 (c) 19 (d) 17
  12. 12.What is the 17th term of the AP 11, 16, 21, 26, …? (a) 80 (b) 85 (c) 96 (d) 91
  13. 13.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 220 (b) 440 (c) 231 (d) 30
  14. 14.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 231 (d) 441
  15. 15.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 253 (c) 506 (d) 231
  16. 16.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2851 (c) 5700 (d) 2850
  17. 17.Which term of the AP 4, 11, 18, 25, … is 88? (a) 12th (b) 13th (c) 14th (d) 15th
  18. 18.What is the 23rd term of the AP 2, 4, 6, 8, …? (a) 46 (b) 44 (c) 47 (d) 48
  19. 19.What is the 32nd term of the AP 16, 18, 20, 22, …? (a) 80 (b) 62 (c) 64 (d) 78
  20. 20.Which term of the AP 9, 17, 25, 33, … is 321? (a) 42nd (b) 40th (c) 41st (d) 39th
  21. 21.What is the 25th term of the AP 16, 23, 30, 37, …? (a) 175 (b) 184 (c) 168 (d) 191
  22. 22.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 2312 (c) 4692 (d) 2346
  23. 23.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 496 (c) 1056 (d) 512
  24. 24.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 572 (b) 51 (c) 291 (d) 286
  25. 25.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 22 (b) 21 (c) 25 (d) 20
  26. 26.What is the 25th term of the AP 18, 21, 24, 27, …? (a) 72 (b) 90 (c) 75 (d) 93
  27. 27.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 31 (b) 40 (c) 32 (d) 30
  28. 28.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 414 (b) 225 (c) 207 (d) 39
  29. 29.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 180 (c) 340 (d) 170
  30. 30.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3200 (c) 6480 (d) 3240
  31. 31.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 231 (c) 462 (d) 210
  32. 32.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 1568 (c) 1540 (d) 3192
  33. 33.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 15 (b) 120 (c) 66 (d) 60
  34. 34.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 72 (b) 138 (c) 69 (d) 14
  35. 35.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 105 (c) 120 (d) 240
  36. 36.What is the 34th term of the AP 2, 6, 10, 14, …? (a) 138 (b) 136 (c) 134 (d) 132
  37. 37.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 484 (d) 253
  38. 38.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 280 (b) 520 (c) 44 (d) 260
  39. 39.What is the 12th term of the AP 1, 4, 7, 10, …? (a) 37 (b) 36 (c) 34 (d) 33
  40. 40.What is the 10th term of the AP 2, 11, 20, 29, …? (a) 81 (b) 90 (c) 83 (d) 92

Answer key

  1. 14th
  2. 348
  3. 56
  4. 35
  5. 144
  6. 175
  7. 84
  8. 20
  9. 61
  10. 66
  11. 18
  12. 91
  13. 220
  14. 441
  15. 253
  16. 2850
  17. 13th
  18. 46
  19. 78
  20. 40th
  21. 184
  22. 2346
  23. 528
  24. 286
  25. 21
  26. 90
  27. 31
  28. 207
  29. 170
  30. 3240
  31. 231
  32. 1596
  33. 60
  34. 69
  35. 120
  36. 134
  37. 484
  38. 260
  39. 34
  40. 83

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