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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 154 · 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 19th term of the AP 17, 23, 29, 35, …? (a) 114 (b) 108 (c) 131 (d) 125
  2. 2.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 108 (b) 14 (c) 60 (d) 54
  3. 3.What is the 31st term of the AP 3, 7, 11, 15, …? (a) 127 (b) 124 (c) 123 (d) 120
  4. 4.Which term of the AP 5, 11, 17, 23, … is 131? (a) 21st (b) 23rd (c) 22nd (d) 24th
  5. 5.What is the 16th term of the AP 16, 19, 22, 25, …? (a) 64 (b) 61 (c) 45 (d) 48
  6. 6.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 201 (b) 198 (c) 396 (d) 33
  7. 7.What is the 17th term of the AP 17, 19, 21, 23, …? (a) 51 (b) 32 (c) 49 (d) 34
  8. 8.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1326 (c) 1378 (d) 2756
  9. 9.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 7 (b) 11 (c) 9 (d) 8
  10. 10.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 1980 (c) 968 (d) 990
  11. 11.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 66 (b) 396 (c) 792 (d) 429
  12. 12.What is the 15th term of the AP 4, 13, 22, 31, …? (a) 126 (b) 135 (c) 139 (d) 130
  13. 13.What is the 38th term of the AP 11, 17, 23, 29, …? (a) 233 (b) 239 (c) 228 (d) 222
  14. 14.What is the 12th term of the AP 5, 11, 17, 23, …? (a) 72 (b) 66 (c) 77 (d) 71
  15. 15.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 351 (c) 325 (d) 702
  16. 16.What is the 21st term of the AP 18, 23, 28, 33, …? (a) 118 (b) 100 (c) 123 (d) 105
  17. 17.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 264 (b) 22 (c) 132 (d) 143
  18. 18.What is the 14th term of the AP 17, 22, 27, 32, …? (a) 87 (b) 70 (c) 82 (d) 65
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 15 (d) 64
  20. 20.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 186 (c) 93 (d) 28
  21. 21.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 406 (c) 812 (d) 392
  22. 22.What is the 16th term of the AP 3, 8, 13, 18, …? (a) 83 (b) 80 (c) 75 (d) 78
  23. 23.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 8930 (c) 4418 (d) 4465
  24. 24.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 2450 (c) 4970 (d) 2415
  25. 25.What is the 25th term of the AP 10, 14, 18, 22, …? (a) 110 (b) 106 (c) 96 (d) 100
  26. 26.What is the 21st term of the AP 4, 8, 12, 16, …? (a) 80 (b) 88 (c) 85 (d) 84
  27. 27.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 196 (b) 105 (c) 20 (d) 98
  28. 28.What is the 28th term of the AP 11, 14, 17, 20, …? (a) 81 (b) 84 (c) 92 (d) 95
  29. 29.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 96 (b) 162 (c) 81 (d) 26
  30. 30.What is the 39th term of the AP 6, 14, 22, 30, …? (a) 310 (b) 318 (c) 304 (d) 312
  31. 31.What is the 33rd term of the AP 5, 8, 11, 14, …? (a) 101 (b) 96 (c) 99 (d) 104
  32. 32.What is the 14th term of the AP 14, 18, 22, 26, …? (a) 52 (b) 56 (c) 66 (d) 70
  33. 33.What is the 16th term of the AP 14, 21, 28, 35, …? (a) 119 (b) 126 (c) 112 (d) 105
  34. 34.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 189 (b) 336 (c) 168 (d) 42
  35. 35.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 53 (b) 305 (c) 610 (d) 330
  36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
  37. 37.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 88 (b) 44 (c) 9 (d) 48
  38. 38.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 192 (b) 27 (c) 384 (d) 204
  39. 39.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1892 (c) 1830 (d) 1891
  40. 40.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 27 (b) 26 (c) 28 (d) 33

Answer key

  1. 125
  2. 54
  3. 123
  4. 22nd
  5. 61
  6. 198
  7. 49
  8. 1378
  9. 8
  10. 990
  11. 396
  12. 130
  13. 233
  14. 71
  15. 351
  16. 118
  17. 132
  18. 82
  19. 64
  20. 93
  21. 406
  22. 78
  23. 4465
  24. 2485
  25. 106
  26. 84
  27. 98
  28. 92
  29. 81
  30. 310
  31. 101
  32. 66
  33. 119
  34. 168
  35. 305
  36. 841
  37. 44
  38. 192
  39. 1891
  40. 27

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