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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 834 · 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.Which term of the AP 7, 16, 25, 34, … is 133? (a) 14th (b) 15th (c) 16th (d) 17th
  2. 2.Which term of the AP 10, 12, 14, 16, … is 78? (a) 36th (b) 35th (c) 39th (d) 34th
  3. 3.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 378 (b) 210 (c) 189 (d) 45
  4. 4.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 325 (d) 625
  5. 5.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 19 (b) 21 (c) 20 (d) 27
  6. 6.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 184 (b) 200 (c) 368 (d) 37
  7. 7.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 14 (b) 69 (c) 138 (d) 72
  8. 8.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 1953 (d) 2016
  9. 9.What is the 17th term of the AP 3, 10, 17, 24, …? (a) 122 (b) 115 (c) 119 (d) 112
  10. 10.What is the 21st term of the AP 8, 14, 20, 26, …? (a) 134 (b) 128 (c) 120 (d) 126
  11. 11.What is the 27th term of the AP 1, 4, 7, 10, …? (a) 79 (b) 82 (c) 81 (d) 78
  12. 12.What is the 17th term of the AP 6, 10, 14, 18, …? (a) 68 (b) 64 (c) 70 (d) 74
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  14. 14.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 152 (b) 140 (c) 28 (d) 280
  15. 15.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 3656 (c) 7310 (d) 3570
  16. 16.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 171 (c) 342 (d) 162
  17. 17.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 42 (b) 264 (c) 484 (d) 242
  18. 18.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 13 (b) 176 (c) 89 (d) 88
  19. 19.What is the 22nd term of the AP 18, 25, 32, 39, …? (a) 165 (b) 154 (c) 172 (d) 147
  20. 20.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 6 (b) 8 (c) 5 (d) 4
  21. 21.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 741 (c) 1482 (d) 703
  22. 22.What is the 21st term of the AP 8, 12, 16, 20, …? (a) 92 (b) 88 (c) 80 (d) 84
  23. 23.What is the 15th term of the AP 3, 6, 9, 12, …? (a) 48 (b) 42 (c) 46 (d) 45
  24. 24.What is the 34th term of the AP 17, 23, 29, 35, …? (a) 215 (b) 198 (c) 221 (d) 204
  25. 25.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 21 (b) 15 (c) 17 (d) 16
  26. 26.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 179 (b) 352 (c) 176 (d) 31
  27. 27.What is the 40th term of the AP 15, 17, 19, 21, …? (a) 80 (b) 78 (c) 93 (d) 95
  28. 28.Which term of the AP 16, 22, 28, 34, … is 220? (a) 37th (b) 36th (c) 34th (d) 35th
  29. 29.What is the 21st term of the AP 2, 10, 18, 26, …? (a) 168 (b) 162 (c) 170 (d) 160
  30. 30.What is the 15th term of the AP 10, 12, 14, 16, …? (a) 28 (b) 38 (c) 40 (d) 30
  31. 31.Which term of the AP 16, 24, 32, 40, … is 280? (a) 35th (b) 36th (c) 33rd (d) 34th
  32. 32.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2048 (c) 4160 (d) 2080
  33. 33.Which term of the AP 4, 12, 20, 28, … is 284? (a) 37th (b) 35th (c) 38th (d) 36th
  34. 34.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 3655 (c) 7482 (d) 3698
  35. 35.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 506 (b) 38 (c) 256 (d) 253
  36. 36.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 31 (b) 29 (c) 36 (d) 30
  37. 37.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 3916 (c) 4006 (d) 4005
  38. 38.What is the missing term in the AP 9, 17, 25, ?, 41? (a) 34 (b) 32 (c) 41 (d) 33
  39. 39.What is the 13th term of the AP 6, 10, 14, 18, …? (a) 58 (b) 48 (c) 52 (d) 54
  40. 40.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 492 (b) 71 (c) 456 (d) 912

Answer key

  1. 15th
  2. 35th
  3. 189
  4. 625
  5. 20
  6. 184
  7. 69
  8. 2016
  9. 115
  10. 128
  11. 79
  12. 70
  13. 49
  14. 140
  15. 3655
  16. 171
  17. 242
  18. 88
  19. 165
  20. 5
  21. 741
  22. 88
  23. 45
  24. 215
  25. 16
  26. 176
  27. 93
  28. 35th
  29. 162
  30. 38
  31. 34th
  32. 2080
  33. 36th
  34. 3741
  35. 253
  36. 30
  37. 4005
  38. 33
  39. 54
  40. 456

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