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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 827 · 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 8, 16, 24, ?, 40? (a) 31 (b) 40 (c) 33 (d) 32
  2. 2.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 2017 (c) 1953 (d) 4032
  3. 3.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 184 (b) 92 (c) 22 (d) 104
  4. 4.What is the 21st term of the AP 9, 14, 19, 24, …? (a) 114 (b) 109 (c) 100 (d) 105
  5. 5.Which term of the AP 18, 26, 34, 42, … is 122? (a) 13th (b) 15th (c) 14th (d) 16th
  6. 6.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 30 (b) 180 (c) 330 (d) 165
  7. 7.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 7 (b) 6 (c) 9 (d) 8
  8. 8.What is the 40th term of the AP 18, 27, 36, 45, …? (a) 369 (b) 378 (c) 360 (d) 351
  9. 9.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 352 (b) 43 (c) 200 (d) 176
  10. 10.What is the 20th term of the AP 4, 13, 22, 31, …? (a) 175 (b) 184 (c) 171 (d) 180
  11. 11.What is the 10th term of the AP 20, 26, 32, 38, …? (a) 54 (b) 74 (c) 60 (d) 80
  12. 12.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2211 (c) 4422 (d) 2145
  13. 13.What is the 35th term of the AP 3, 10, 17, 24, …? (a) 245 (b) 248 (c) 241 (d) 238
  14. 14.What is the 37th term of the AP 7, 15, 23, 31, …? (a) 296 (b) 295 (c) 303 (d) 288
  15. 15.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 722 (c) 1482 (d) 703
  16. 16.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 470 (c) 235 (d) 260
  17. 17.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 110 (b) 55 (c) 60 (d) 21
  18. 18.What is the 12th term of the AP 9, 18, 27, 36, …? (a) 117 (b) 109 (c) 99 (d) 108
  19. 19.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 18 (b) 286 (c) 144 (d) 143
  20. 20.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 35 (b) 36 (c) 37 (d) 44
  21. 21.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 22 (b) 96 (c) 87 (d) 174
  22. 22.What is the 23rd term of the AP 13, 16, 19, 22, …? (a) 69 (b) 66 (c) 79 (d) 82
  23. 23.What is the 35th term of the AP 3, 8, 13, 18, …? (a) 170 (b) 178 (c) 173 (d) 175
  24. 24.What is the 34th term of the AP 11, 13, 15, 17, …? (a) 68 (b) 66 (c) 79 (d) 77
  25. 25.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 26 (b) 27 (c) 33 (d) 25
  26. 26.What is the missing term in the AP 15, 23, 31, ?, 47? (a) 39 (b) 38 (c) 47 (d) 40
  27. 27.What is the 20th term of the AP 9, 11, 13, 15, …? (a) 38 (b) 40 (c) 47 (d) 49
  28. 28.What is the missing term in the AP 3, 11, 19, ?, 35? (a) 26 (b) 28 (c) 27 (d) 35
  29. 29.What is the 26th term of the AP 4, 6, 8, 10, …? (a) 50 (b) 56 (c) 54 (d) 52
  30. 30.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 756 (d) 53
  31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 81 (d) 17
  32. 32.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 204 (b) 32 (c) 102 (d) 120
  33. 33.What is the 12th term of the AP 7, 11, 15, 19, …? (a) 48 (b) 44 (c) 55 (d) 51
  34. 34.What is the 36th term of the AP 2, 8, 14, 20, …? (a) 210 (b) 212 (c) 218 (d) 216
  35. 35.What is the 26th term of the AP 2, 4, 6, 8, …? (a) 54 (b) 50 (c) 52 (d) 53
  36. 36.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 182 (d) 91
  37. 37.What is the 24th term of the AP 8, 14, 20, 26, …? (a) 138 (b) 152 (c) 146 (d) 144
  38. 38.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 756 (d) 378
  39. 39.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 16 (b) 20 (c) 17 (d) 15
  40. 40.Which term of the AP 17, 20, 23, 26, … is 107? (a) 32nd (b) 30th (c) 31st (d) 33rd

Answer key

  1. 32
  2. 2016
  3. 92
  4. 109
  5. 14th
  6. 165
  7. 7
  8. 369
  9. 176
  10. 175
  11. 74
  12. 2211
  13. 241
  14. 295
  15. 741
  16. 235
  17. 55
  18. 108
  19. 143
  20. 36
  21. 87
  22. 79
  23. 173
  24. 77
  25. 26
  26. 39
  27. 47
  28. 27
  29. 54
  30. 729
  31. 81
  32. 102
  33. 51
  34. 212
  35. 52
  36. 169
  37. 146
  38. 378
  39. 16
  40. 31st

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