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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 973 · 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 61? (a) 1891 (b) 3782 (c) 1892 (d) 1830
  2. 2.Which term of the AP 9, 15, 21, 27, … is 111? (a) 19th (b) 20th (c) 18th (d) 17th
  3. 3.What is the 14th term of the AP 18, 22, 26, 30, …? (a) 52 (b) 74 (c) 56 (d) 70
  4. 4.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 1653 (c) 3306 (d) 1596
  5. 5.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 57 (c) 354 (d) 384
  6. 6.What is the 17th term of the AP 18, 24, 30, 36, …? (a) 102 (b) 114 (c) 96 (d) 120
  7. 7.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 378 (c) 756 (d) 351
  8. 8.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 52 (b) 279 (c) 252 (d) 504
  9. 9.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 198 (b) 100 (c) 99 (d) 15
  10. 10.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 96 (c) 114 (d) 192
  11. 11.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 3080 (c) 1540 (d) 1485
  12. 12.What is the 10th term of the AP 9, 18, 27, 36, …? (a) 99 (b) 91 (c) 90 (d) 81
  13. 13.Which term of the AP 8, 17, 26, 35, … is 125? (a) 15th (b) 14th (c) 16th (d) 13th
  14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 23 (d) 156
  15. 15.What is the 23rd term of the AP 8, 10, 12, 14, …? (a) 46 (b) 44 (c) 52 (d) 54
  16. 16.What is the 24th term of the AP 16, 21, 26, 31, …? (a) 136 (b) 131 (c) 120 (d) 115
  17. 17.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 12 (b) 14 (c) 13 (d) 16
  18. 18.What is the 29th term of the AP 9, 13, 17, 21, …? (a) 116 (b) 125 (c) 112 (d) 121
  19. 19.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 351 (c) 325 (d) 338
  20. 20.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 16 (b) 14 (c) 13 (d) 15
  21. 21.What is the sum of all the whole numbers from 1 to 70? (a) 4970 (b) 2415 (c) 2485 (d) 2450
  22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 90 (d) 17
  23. 23.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 792 (b) 429 (c) 396 (d) 66
  24. 24.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 21 (b) 22 (c) 19 (d) 20
  25. 25.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 22 (c) 94 (d) 182
  26. 26.What is the missing term in the AP 7, 12, 17, ?, 27? (a) 21 (b) 23 (c) 22 (d) 27
  27. 27.What is the 33rd term of the AP 4, 12, 20, 28, …? (a) 256 (b) 260 (c) 268 (d) 264
  28. 28.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 16 (b) 17 (c) 20 (d) 15
  29. 29.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 170 (b) 29 (c) 100 (d) 85
  30. 30.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 23 (b) 28 (c) 21 (d) 22
  31. 31.What is the 21st term of the AP 4, 7, 10, 13, …? (a) 64 (b) 63 (c) 60 (d) 67
  32. 32.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 40 (c) 11 (d) 35
  33. 33.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 342 (b) 171 (c) 189 (d) 35
  34. 34.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 130 (b) 75 (c) 21 (d) 65
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 66 (d) 132
  36. 36.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 35 (b) 26 (c) 25 (d) 27
  37. 37.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 156 (b) 18 (c) 78 (d) 84
  38. 38.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 55 (c) 110 (d) 50
  39. 39.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 374 (b) 187 (c) 190 (d) 32
  40. 40.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 490 (b) 245 (c) 47 (d) 270

Answer key

  1. 1891
  2. 18th
  3. 70
  4. 1653
  5. 354
  6. 114
  7. 378
  8. 252
  9. 99
  10. 96
  11. 1540
  12. 90
  13. 14th
  14. 144
  15. 52
  16. 131
  17. 13
  18. 121
  19. 351
  20. 14
  21. 2485
  22. 81
  23. 396
  24. 20
  25. 91
  26. 22
  27. 260
  28. 16
  29. 85
  30. 22
  31. 64
  32. 35
  33. 171
  34. 65
  35. 121
  36. 26
  37. 78
  38. 55
  39. 187
  40. 245

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