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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 90 · 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 14th term of the AP 1, 10, 19, 28, …? (a) 117 (b) 127 (c) 126 (d) 118
  2. 2.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 3828 (d) 7832
  3. 3.What is the 34th term of the AP 15, 23, 31, 39, …? (a) 272 (b) 287 (c) 264 (d) 279
  4. 4.What is the 25th term of the AP 12, 18, 24, 30, …? (a) 150 (b) 162 (c) 156 (d) 144
  5. 5.What is the 39th term of the AP 4, 13, 22, 31, …? (a) 346 (b) 342 (c) 355 (d) 351
  6. 6.What is the 30th term of the AP 19, 22, 25, 28, …? (a) 106 (b) 90 (c) 109 (d) 87
  7. 7.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 18 (b) 300 (c) 156 (d) 150
  8. 8.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 49 (b) 341 (c) 638 (d) 319
  9. 9.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 351 (d) 51
  10. 10.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 11 (b) 14 (c) 13 (d) 12
  11. 11.Which term of the AP 9, 12, 15, 18, … is 111? (a) 37th (b) 36th (c) 35th (d) 34th
  12. 12.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 12 (b) 50 (c) 51 (d) 100
  13. 13.What is the 27th term of the AP 19, 28, 37, 46, …? (a) 253 (b) 234 (c) 243 (d) 262
  14. 14.What is the 17th term of the AP 9, 17, 25, 33, …? (a) 145 (b) 136 (c) 137 (d) 128
  15. 15.What is the 34th term of the AP 17, 22, 27, 32, …? (a) 170 (b) 165 (c) 187 (d) 182
  16. 16.Which term of the AP 13, 16, 19, 22, … is 124? (a) 37th (b) 39th (c) 40th (d) 38th
  17. 17.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 612 (b) 306 (c) 333 (d) 58
  18. 18.What is the 28th term of the AP 11, 14, 17, 20, …? (a) 95 (b) 81 (c) 84 (d) 92
  19. 19.What is the 31st term of the AP 5, 13, 21, 29, …? (a) 253 (b) 240 (c) 248 (d) 245
  20. 20.Which term of the AP 5, 13, 21, 29, … is 205? (a) 25th (b) 27th (c) 28th (d) 26th
  21. 21.What is the 28th term of the AP 7, 13, 19, 25, …? (a) 168 (b) 162 (c) 169 (d) 175
  22. 22.What is the 38th term of the AP 8, 12, 16, 20, …? (a) 156 (b) 148 (c) 160 (d) 152
  23. 23.What is the 25th term of the AP 20, 22, 24, 26, …? (a) 50 (b) 70 (c) 48 (d) 68
  24. 24.Which term of the AP 12, 15, 18, 21, … is 69? (a) 21st (b) 20th (c) 19th (d) 23rd
  25. 25.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
  26. 26.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 154 (c) 136 (d) 153
  27. 27.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 49 (d) 13
  28. 28.What is the 16th term of the AP 2, 8, 14, 20, …? (a) 96 (b) 92 (c) 90 (d) 98
  29. 29.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 276 (c) 600 (d) 300
  30. 30.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 230 (b) 16 (c) 120 (d) 115
  31. 31.What is the 24th term of the AP 20, 29, 38, 47, …? (a) 207 (b) 216 (c) 236 (d) 227
  32. 32.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 396 (b) 34 (c) 198 (d) 201
  33. 33.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 50 (c) 26 (d) 25
  34. 34.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 5550 (c) 2701 (d) 2738
  35. 35.What is the 39th term of the AP 19, 22, 25, 28, …? (a) 114 (b) 117 (c) 136 (d) 133
  36. 36.What is the 39th term of the AP 15, 18, 21, 24, …? (a) 114 (b) 117 (c) 132 (d) 129
  37. 37.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 154 (b) 165 (c) 24 (d) 308
  38. 38.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 19 (b) 90 (c) 84 (d) 168
  39. 39.What is the 21st term of the AP 20, 23, 26, 29, …? (a) 63 (b) 80 (c) 83 (d) 60
  40. 40.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 200 (b) 100 (c) 32 (d) 115

Answer key

  1. 118
  2. 3916
  3. 279
  4. 156
  5. 346
  6. 106
  7. 150
  8. 319
  9. 676
  10. 12
  11. 35th
  12. 50
  13. 253
  14. 137
  15. 182
  16. 38th
  17. 306
  18. 92
  19. 245
  20. 26th
  21. 169
  22. 156
  23. 68
  24. 20th
  25. 729
  26. 153
  27. 49
  28. 92
  29. 300
  30. 115
  31. 227
  32. 198
  33. 25
  34. 2775
  35. 133
  36. 129
  37. 154
  38. 84
  39. 80
  40. 100

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