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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 800 · 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 sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 210 (d) 105
  2. 2.What is the 22nd term of the AP 6, 10, 14, 18, …? (a) 84 (b) 88 (c) 94 (d) 90
  3. 3.What is the 32nd term of the AP 8, 14, 20, 26, …? (a) 186 (b) 194 (c) 200 (d) 192
  4. 4.Which term of the AP 7, 15, 23, 31, … is 319? (a) 41st (b) 39th (c) 40th (d) 42nd
  5. 5.Which term of the AP 15, 20, 25, 30, … is 180? (a) 35th (b) 33rd (c) 36th (d) 34th
  6. 6.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 300 (d) 325
  7. 7.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 23 (b) 256 (c) 128 (d) 136
  8. 8.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 45 (d) 552
  9. 9.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 192 (b) 360 (c) 26 (d) 180
  10. 10.What is the 32nd term of the AP 18, 27, 36, 45, …? (a) 288 (b) 279 (c) 306 (d) 297
  11. 11.What is the 15th term of the AP 16, 22, 28, 34, …? (a) 90 (b) 100 (c) 84 (d) 106
  12. 12.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 121 (b) 16 (c) 242 (d) 122
  13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729
  14. 14.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 22 (b) 20 (c) 19 (d) 18
  15. 15.What is the 34th term of the AP 20, 26, 32, 38, …? (a) 204 (b) 218 (c) 224 (d) 198
  16. 16.Which term of the AP 20, 29, 38, 47, … is 182? (a) 19th (b) 20th (c) 18th (d) 21st
  17. 17.What is the 38th term of the AP 7, 9, 11, 13, …? (a) 74 (b) 83 (c) 76 (d) 81
  18. 18.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1770 (c) 1830 (d) 1800
  19. 19.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 210 (b) 24 (c) 105 (d) 108
  20. 20.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2279 (c) 2211 (d) 2278
  21. 21.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 70 (b) 8 (c) 36 (d) 35
  22. 22.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 153 (c) 154 (d) 306
  23. 23.What is the missing term in the AP 10, 18, 26, ?, 42? (a) 42 (b) 33 (c) 34 (d) 35
  24. 24.What is the missing term in the AP 20, ?, 32, 38, 44? (a) 32 (b) 27 (c) 26 (d) 25
  25. 25.What is the sum of all the whole numbers from 1 to 37? (a) 703 (b) 704 (c) 1406 (d) 666
  26. 26.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 240 (d) 120
  27. 27.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 99 (b) 100 (c) 198 (d) 14
  28. 28.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 105 (b) 200 (c) 100 (d) 30
  29. 29.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 29 (b) 35 (c) 31 (d) 30
  30. 30.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 351 (d) 702
  31. 31.What is the 12th term of the AP 7, 11, 15, 19, …? (a) 44 (b) 48 (c) 55 (d) 51
  32. 32.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2775 (c) 2851 (d) 2850
  33. 33.What is the 12th term of the AP 13, 19, 25, 31, …? (a) 79 (b) 85 (c) 66 (d) 72
  34. 34.Which term of the AP 7, 10, 13, 16, … is 64? (a) 20th (b) 21st (c) 19th (d) 22nd
  35. 35.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 9 (d) 30
  36. 36.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 364 (b) 44 (c) 203 (d) 182
  37. 37.What is the sum of all the whole numbers from 1 to 21? (a) 462 (b) 232 (c) 231 (d) 210
  38. 38.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 37 (b) 250 (c) 235 (d) 470
  39. 39.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 19 (b) 18 (c) 20 (d) 21
  40. 40.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 16 (b) 20 (c) 17 (d) 15

Answer key

  1. 196
  2. 90
  3. 194
  4. 40th
  5. 34th
  6. 325
  7. 128
  8. 529
  9. 180
  10. 297
  11. 100
  12. 121
  13. 729
  14. 19
  15. 218
  16. 19th
  17. 81
  18. 1830
  19. 105
  20. 2278
  21. 35
  22. 153
  23. 34
  24. 26
  25. 703
  26. 225
  27. 99
  28. 100
  29. 30
  30. 676
  31. 51
  32. 2850
  33. 79
  34. 20th
  35. 25
  36. 182
  37. 231
  38. 235
  39. 19
  40. 16

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