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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 580 · 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 the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 729 (c) 53 (d) 378
  2. 2.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4753 (c) 4851 (d) 4802
  3. 3.What is the missing term in the AP 4, 12, 20, ?, 36? (a) 27 (b) 29 (c) 28 (d) 36
  4. 4.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 14 (b) 16 (c) 15 (d) 19
  5. 5.What is the 10th term of the AP 3, 6, 9, 12, …? (a) 27 (b) 31 (c) 30 (d) 33
  6. 6.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 435 (c) 406 (d) 870
  7. 7.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 3080 (c) 1485 (d) 1541
  8. 8.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3081 (c) 6162 (d) 3003
  9. 9.What is the missing term in the AP 16, 18, 20, ?, 24? (a) 21 (b) 24 (c) 22 (d) 23
  10. 10.What is the sum of all the whole numbers from 1 to 84? (a) 3570 (b) 3486 (c) 7140 (d) 3528
  11. 11.What is the 40th term of the AP 20, 22, 24, 26, …? (a) 100 (b) 98 (c) 80 (d) 78
  12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  13. 13.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 110 (d) 19
  14. 14.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 638 (b) 319 (c) 49 (d) 341
  15. 15.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 595 (c) 1260 (d) 630
  16. 16.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 189 (b) 378 (c) 210 (d) 45
  17. 17.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 456 (b) 30 (c) 228 (d) 240
  18. 18.What is the 18th term of the AP 3, 5, 7, 9, …? (a) 37 (b) 36 (c) 34 (d) 39
  19. 19.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 29 (b) 19 (c) 20 (d) 21
  20. 20.What is the 16th term of the AP 18, 22, 26, 30, …? (a) 60 (b) 82 (c) 64 (d) 78
  21. 21.What is the 11th term of the AP 12, 19, 26, 33, …? (a) 77 (b) 89 (c) 70 (d) 82
  22. 22.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 14 (b) 18 (c) 15 (d) 16
  23. 23.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 21 (b) 22 (c) 23 (d) 30
  24. 24.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 288 (b) 46 (c) 576 (d) 312
  25. 25.What is the 33rd term of the AP 15, 23, 31, 39, …? (a) 256 (b) 279 (c) 264 (d) 271
  26. 26.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 55 (b) 65 (c) 19 (d) 110
  27. 27.What is the 23rd term of the AP 5, 10, 15, 20, …? (a) 116 (b) 115 (c) 110 (d) 120
  28. 28.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 45 (d) 90
  29. 29.What is the 29th term of the AP 12, 15, 18, 21, …? (a) 87 (b) 99 (c) 84 (d) 96
  30. 30.Which term of the AP 12, 14, 16, 18, … is 70? (a) 31st (b) 29th (c) 35th (d) 30th
  31. 31.What is the 19th term of the AP 1, 6, 11, 16, …? (a) 90 (b) 96 (c) 95 (d) 91
  32. 32.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 27 (b) 23 (c) 24 (d) 25
  33. 33.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4465 (c) 4418 (d) 4371
  34. 34.What is the 13th term of the AP 10, 15, 20, 25, …? (a) 60 (b) 70 (c) 65 (d) 75
  35. 35.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 17 (b) 21 (c) 16 (d) 15
  36. 36.What is the 32nd term of the AP 5, 14, 23, 32, …? (a) 288 (b) 279 (c) 293 (d) 284
  37. 37.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4951 (c) 9900 (d) 4851
  38. 38.What is the 12th term of the AP 7, 9, 11, 13, …? (a) 31 (b) 29 (c) 22 (d) 24
  39. 39.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 59 (d) 930
  40. 40.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 75 (b) 24 (c) 140 (d) 70

Answer key

  1. 729
  2. 4851
  3. 28
  4. 15
  5. 30
  6. 435
  7. 1540
  8. 3081
  9. 22
  10. 3570
  11. 98
  12. 49
  13. 100
  14. 319
  15. 630
  16. 189
  17. 228
  18. 37
  19. 20
  20. 78
  21. 82
  22. 15
  23. 22
  24. 288
  25. 271
  26. 55
  27. 115
  28. 81
  29. 96
  30. 30th
  31. 91
  32. 24
  33. 4465
  34. 70
  35. 16
  36. 284
  37. 4950
  38. 29
  39. 900
  40. 70

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