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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 873 · 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 8, 14, 20, 26, … is 212? (a) 37th (b) 36th (c) 35th (d) 34th
  2. 2.What is the 38th term of the AP 5, 14, 23, 32, …? (a) 338 (b) 333 (c) 342 (d) 347
  3. 3.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 147 (b) 294 (c) 39 (d) 168
  4. 4.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 175 (b) 154 (c) 308 (d) 40
  5. 5.Which term of the AP 9, 15, 21, 27, … is 117? (a) 21st (b) 20th (c) 18th (d) 19th
  6. 6.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 16 (c) 121 (d) 242
  7. 7.What is the 12th term of the AP 11, 14, 17, 20, …? (a) 33 (b) 44 (c) 47 (d) 36
  8. 8.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 37 (b) 32 (c) 31 (d) 30
  9. 9.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 3200 (c) 6480 (d) 3160
  10. 10.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
  11. 11.What is the 21st term of the AP 20, 29, 38, 47, …? (a) 209 (b) 200 (c) 189 (d) 180
  12. 12.What is the 23rd term of the AP 19, 27, 35, 43, …? (a) 184 (b) 203 (c) 195 (d) 176
  13. 13.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 180 (b) 99 (c) 90 (d) 18
  14. 14.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 20 (b) 19 (c) 18 (d) 23
  15. 15.What is the 39th term of the AP 7, 9, 11, 13, …? (a) 76 (b) 85 (c) 78 (d) 83
  16. 16.What is the 18th term of the AP 6, 11, 16, 21, …? (a) 96 (b) 90 (c) 91 (d) 85
  17. 17.What is the 30th term of the AP 19, 21, 23, 25, …? (a) 58 (b) 60 (c) 79 (d) 77
  18. 18.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 1056 (c) 496 (d) 528
  19. 19.What is the 29th term of the AP 16, 18, 20, 22, …? (a) 58 (b) 72 (c) 74 (d) 56
  20. 20.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 496 (d) 992
  21. 21.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 75 (b) 80 (c) 150 (d) 12
  22. 22.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 92 (b) 182 (c) 16 (d) 91
  23. 23.What is the 15th term of the AP 13, 18, 23, 28, …? (a) 75 (b) 83 (c) 88 (d) 70
  24. 24.Which term of the AP 10, 18, 26, 34, … is 298? (a) 38th (b) 39th (c) 37th (d) 36th
  25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 171 (d) 324
  26. 26.What is the 17th term of the AP 13, 19, 25, 31, …? (a) 96 (b) 102 (c) 109 (d) 115
  27. 27.What is the 26th term of the AP 13, 22, 31, 40, …? (a) 234 (b) 238 (c) 247 (d) 225
  28. 28.What is the 32nd term of the AP 5, 8, 11, 14, …? (a) 101 (b) 98 (c) 96 (d) 93
  29. 29.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 19 (b) 9 (c) 10 (d) 11
  30. 30.What is the 17th term of the AP 15, 22, 29, 36, …? (a) 119 (b) 127 (c) 134 (d) 112
  31. 31.Which term of the AP 18, 26, 34, 42, … is 138? (a) 15th (b) 17th (c) 16th (d) 18th
  32. 32.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 2415 (c) 2416 (d) 4830
  33. 33.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 240 (d) 120
  34. 34.Which term of the AP 2, 4, 6, 8, … is 22? (a) 10th (b) 13th (c) 11th (d) 12th
  35. 35.What is the 29th term of the AP 9, 12, 15, 18, …? (a) 96 (b) 84 (c) 93 (d) 87
  36. 36.Which term of the AP 15, 23, 31, 39, … is 103? (a) 12th (b) 13th (c) 11th (d) 14th
  37. 37.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 55 (d) 19
  38. 38.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 57 (d) 870
  39. 39.Which term of the AP 7, 11, 15, 19, … is 159? (a) 41st (b) 40th (c) 38th (d) 39th
  40. 40.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 66 (b) 792 (c) 429 (d) 396

Answer key

  1. 35th
  2. 338
  3. 147
  4. 154
  5. 19th
  6. 121
  7. 44
  8. 31
  9. 3240
  10. 121
  11. 200
  12. 195
  13. 90
  14. 19
  15. 83
  16. 91
  17. 77
  18. 528
  19. 72
  20. 496
  21. 75
  22. 91
  23. 83
  24. 37th
  25. 324
  26. 109
  27. 238
  28. 98
  29. 10
  30. 127
  31. 16th
  32. 2415
  33. 225
  34. 11th
  35. 93
  36. 12th
  37. 100
  38. 841
  39. 39th
  40. 396

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