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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 284 · 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 16, ?, 30, 37, 44? (a) 23 (b) 24 (c) 22 (d) 30
  2. 2.Which term of the AP 1, 5, 9, 13, … is 57? (a) 16th (b) 17th (c) 15th (d) 14th
  3. 3.What is the sum of all the whole numbers from 1 to 66? (a) 2145 (b) 4422 (c) 2178 (d) 2211
  4. 4.What is the 35th term of the AP 8, 10, 12, 14, …? (a) 76 (b) 68 (c) 78 (d) 70
  5. 5.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 132 (d) 121
  6. 6.Which term of the AP 18, 27, 36, 45, … is 243? (a) 27th (b) 25th (c) 28th (d) 26th
  7. 7.What is the 25th term of the AP 2, 6, 10, 14, …? (a) 100 (b) 98 (c) 96 (d) 102
  8. 8.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 1332 (c) 648 (d) 666
  9. 9.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2017 (c) 2016 (d) 4032
  10. 10.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 231 (b) 30 (c) 220 (d) 440
  11. 11.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 112 (b) 31 (c) 224 (d) 117
  12. 12.What is the 14th term of the AP 11, 17, 23, 29, …? (a) 78 (b) 84 (c) 89 (d) 95
  13. 13.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 11 (b) 9 (c) 8 (d) 10
  14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  15. 15.Which term of the AP 14, 23, 32, 41, … is 338? (a) 36th (b) 38th (c) 39th (d) 37th
  16. 16.What is the sum of all the whole numbers from 1 to 70? (a) 4970 (b) 2485 (c) 2450 (d) 2415
  17. 17.What is the missing term in the AP 13, 21, 29, ?, 45? (a) 36 (b) 38 (c) 45 (d) 37
  18. 18.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 930 (c) 465 (d) 59
  19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 484 (d) 506
  20. 20.What is the 16th term of the AP 3, 12, 21, 30, …? (a) 147 (b) 144 (c) 135 (d) 138
  21. 21.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 132 (c) 67 (d) 66
  22. 22.What is the 33rd term of the AP 17, 24, 31, 38, …? (a) 241 (b) 231 (c) 248 (d) 224
  23. 23.Which term of the AP 19, 25, 31, 37, … is 193? (a) 31st (b) 32nd (c) 29th (d) 30th
  24. 24.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 69 (b) 14 (c) 72 (d) 138
  25. 25.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
  26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  27. 27.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 42 (c) 198 (d) 203
  28. 28.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 126 (b) 29 (c) 114 (d) 228
  29. 29.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 49 (d) 13
  30. 30.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 176 (b) 88 (c) 89 (d) 13
  31. 31.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 1327 (c) 1326 (d) 2652
  32. 32.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 120 (b) 60 (c) 61 (d) 14
  33. 33.What is the 21st term of the AP 4, 11, 18, 25, …? (a) 144 (b) 147 (c) 151 (d) 140
  34. 34.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 39 (b) 288 (c) 270 (d) 540
  35. 35.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 3487 (c) 3486 (d) 6972
  36. 36.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 95 (b) 28 (c) 80 (d) 160
  37. 37.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 11 (c) 42 (d) 36
  38. 38.What is the 14th term of the AP 5, 9, 13, 17, …? (a) 57 (b) 56 (c) 61 (d) 52
  39. 39.What is the 35th term of the AP 3, 9, 15, 21, …? (a) 213 (b) 204 (c) 210 (d) 207
  40. 40.What is the 15th term of the AP 7, 15, 23, 31, …? (a) 127 (b) 120 (c) 112 (d) 119

Answer key

  1. 23
  2. 15th
  3. 2211
  4. 76
  5. 121
  6. 26th
  7. 98
  8. 666
  9. 2016
  10. 220
  11. 112
  12. 89
  13. 9
  14. 144
  15. 37th
  16. 2485
  17. 37
  18. 900
  19. 484
  20. 138
  21. 66
  22. 241
  23. 30th
  24. 69
  25. 841
  26. 529
  27. 198
  28. 114
  29. 49
  30. 88
  31. 1326
  32. 60
  33. 144
  34. 270
  35. 3486
  36. 80
  37. 36
  38. 57
  39. 207
  40. 119

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