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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 18 · 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 missing term in the AP 5, 13, 21, ?, 37? (a) 37 (b) 28 (c) 30 (d) 29
  2. 2.What is the 15th term of the AP 15, 22, 29, 36, …? (a) 105 (b) 113 (c) 98 (d) 120
  3. 3.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 133 (b) 29 (c) 238 (d) 119
  4. 4.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 22 (b) 184 (c) 104 (d) 92
  5. 5.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 9120 (c) 4560 (d) 4465
  6. 6.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
  7. 7.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 51 (b) 100 (c) 12 (d) 50
  8. 8.What is the 10th term of the AP 16, 20, 24, 28, …? (a) 40 (b) 36 (c) 56 (d) 52
  9. 9.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 132 (b) 27 (c) 144 (d) 264
  10. 10.Which term of the AP 5, 9, 13, 17, … is 41? (a) 11th (b) 12th (c) 9th (d) 10th
  11. 11.What is the missing term in the AP 7, ?, 23, 31, 39? (a) 23 (b) 14 (c) 16 (d) 15
  12. 12.Which term of the AP 16, 19, 22, 25, … is 61? (a) 16th (b) 18th (c) 15th (d) 17th
  13. 13.Which term of the AP 11, 13, 15, 17, … is 43? (a) 18th (b) 17th (c) 19th (d) 16th
  14. 14.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 379 (c) 756 (d) 351
  15. 15.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 702 (d) 351
  16. 16.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 85 (b) 90 (c) 170 (d) 27
  17. 17.Which term of the AP 9, 13, 17, 21, … is 125? (a) 31st (b) 29th (c) 32nd (d) 30th
  18. 18.What is the 15th term of the AP 19, 26, 33, 40, …? (a) 117 (b) 105 (c) 98 (d) 124
  19. 19.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 56 (b) 28 (c) 7 (d) 29
  20. 20.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 5000 (d) 10100
  21. 21.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 496 (c) 528 (d) 512
  22. 22.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 12 (b) 136 (c) 68 (d) 72
  23. 23.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 392 (d) 406
  24. 24.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 171 (b) 153 (c) 33 (d) 306
  25. 25.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3741 (c) 7482 (d) 3655
  26. 26.Which term of the AP 1, 10, 19, 28, … is 307? (a) 37th (b) 36th (c) 35th (d) 34th
  27. 27.What is the 10th term of the AP 11, 19, 27, 35, …? (a) 72 (b) 80 (c) 91 (d) 83
  28. 28.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2416 (c) 2346 (d) 2415
  29. 29.What is the 34th term of the AP 11, 16, 21, 26, …? (a) 165 (b) 181 (c) 170 (d) 176
  30. 30.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 25 (b) 102 (c) 90 (d) 180
  31. 31.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 10 (b) 35 (c) 60 (d) 30
  32. 32.What is the 13th term of the AP 3, 12, 21, 30, …? (a) 108 (b) 120 (c) 111 (d) 117
  33. 33.Which term of the AP 13, 20, 27, 34, … is 202? (a) 27th (b) 28th (c) 29th (d) 30th
  34. 34.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 21 (b) 19 (c) 24 (d) 20
  35. 35.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 228 (b) 29 (c) 432 (d) 216
  36. 36.What is the 39th term of the AP 4, 6, 8, 10, …? (a) 78 (b) 76 (c) 80 (d) 82
  37. 37.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 12 (b) 14 (c) 13 (d) 17
  38. 38.What is the missing term in the AP 16, ?, 30, 37, 44? (a) 24 (b) 22 (c) 30 (d) 23
  39. 39.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 1640 (c) 800 (d) 780
  40. 40.What is the 19th term of the AP 11, 14, 17, 20, …? (a) 65 (b) 57 (c) 68 (d) 54

Answer key

  1. 29
  2. 113
  3. 119
  4. 92
  5. 4560
  6. 144
  7. 50
  8. 52
  9. 132
  10. 10th
  11. 15
  12. 16th
  13. 17th
  14. 378
  15. 676
  16. 85
  17. 30th
  18. 117
  19. 28
  20. 5050
  21. 528
  22. 68
  23. 406
  24. 153
  25. 3741
  26. 35th
  27. 83
  28. 2415
  29. 176
  30. 90
  31. 30
  32. 111
  33. 28th
  34. 20
  35. 216
  36. 80
  37. 13
  38. 23
  39. 820
  40. 65

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