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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 545 · 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 13th term of the AP 12, 17, 22, 27, …? (a) 72 (b) 65 (c) 77 (d) 60
  2. 2.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 595 (c) 631 (d) 630
  3. 3.What is the 23rd term of the AP 3, 8, 13, 18, …? (a) 113 (b) 115 (c) 118 (d) 110
  4. 4.What is the 36th term of the AP 8, 12, 16, 20, …? (a) 144 (b) 152 (c) 140 (d) 148
  5. 5.What is the 30th term of the AP 2, 10, 18, 26, …? (a) 234 (b) 232 (c) 240 (d) 242
  6. 6.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 20 (b) 15 (c) 13 (d) 14
  7. 7.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 506 (d) 43
  8. 8.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 12 (b) 19 (c) 11 (d) 10
  9. 9.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 17 (c) 117 (d) 118
  10. 10.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 45 (c) 55 (d) 110
  11. 11.What is the 11th term of the AP 5, 9, 13, 17, …? (a) 49 (b) 40 (c) 45 (d) 44
  12. 12.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 841 (d) 57
  13. 13.What is the 24th term of the AP 11, 13, 15, 17, …? (a) 48 (b) 46 (c) 59 (d) 57
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  15. 15.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3042 (d) 3081
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 17 (d) 90
  17. 17.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 78 (c) 156 (d) 72
  18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 31 (d) 136
  19. 19.What is the missing term in the AP 13, 16, ?, 22, 25? (a) 18 (b) 20 (c) 19 (d) 22
  20. 20.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 351 (c) 338 (d) 702
  21. 21.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 57 (b) 17 (c) 66 (d) 114
  22. 22.What is the 14th term of the AP 9, 13, 17, 21, …? (a) 56 (b) 61 (c) 65 (d) 52
  23. 23.Which term of the AP 10, 16, 22, 28, … is 208? (a) 36th (b) 35th (c) 34th (d) 33rd
  24. 24.Which term of the AP 9, 17, 25, 33, … is 153? (a) 20th (b) 18th (c) 19th (d) 21st
  25. 25.Which term of the AP 6, 14, 22, 30, … is 86? (a) 13th (b) 10th (c) 12th (d) 11th
  26. 26.Which term of the AP 19, 27, 35, 43, … is 99? (a) 10th (b) 12th (c) 13th (d) 11th
  27. 27.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 48 (b) 312 (c) 624 (d) 336
  28. 28.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 114 (b) 198 (c) 29 (d) 99
  29. 29.What is the 33rd term of the AP 10, 12, 14, 16, …? (a) 66 (b) 64 (c) 76 (d) 74
  30. 30.What is the 20th term of the AP 5, 13, 21, 29, …? (a) 152 (b) 160 (c) 157 (d) 165
  31. 31.Which term of the AP 14, 21, 28, 35, … is 266? (a) 36th (b) 39th (c) 37th (d) 38th
  32. 32.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 2162 (c) 1035 (d) 1081
  33. 33.What is the 33rd term of the AP 20, 23, 26, 29, …? (a) 119 (b) 116 (c) 99 (d) 96
  34. 34.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  35. 35.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 11 (d) 42
  36. 36.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 26 (b) 24 (c) 28 (d) 25
  37. 37.Which term of the AP 5, 11, 17, 23, … is 89? (a) 17th (b) 15th (c) 16th (d) 14th
  38. 38.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 8 (b) 6 (c) 11 (d) 7
  39. 39.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  40. 40.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 23 (b) 100 (c) 112 (d) 200

Answer key

  1. 72
  2. 630
  3. 113
  4. 148
  5. 234
  6. 14
  7. 484
  8. 11
  9. 117
  10. 55
  11. 45
  12. 841
  13. 57
  14. 121
  15. 3081
  16. 81
  17. 78
  18. 256
  19. 19
  20. 351
  21. 57
  22. 61
  23. 34th
  24. 19th
  25. 11th
  26. 11th
  27. 312
  28. 99
  29. 74
  30. 157
  31. 37th
  32. 1081
  33. 116
  34. 400
  35. 36
  36. 25
  37. 15th
  38. 7
  39. 144
  40. 100

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