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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 359 · 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 19th term of the AP 6, 15, 24, 33, …? (a) 162 (b) 168 (c) 171 (d) 177
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 64 (d) 36
  3. 3.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 7482 (c) 3655 (d) 3698
  4. 4.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 31 (b) 41 (c) 33 (d) 32
  5. 5.Which term of the AP 12, 15, 18, 21, … is 120? (a) 40th (b) 36th (c) 38th (d) 37th
  6. 6.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 2346 (c) 4830 (d) 2416
  7. 7.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 13 (b) 14 (c) 20 (d) 15
  8. 8.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 682 (b) 61 (c) 374 (d) 341
  9. 9.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 418 (b) 209 (c) 29 (d) 220
  10. 10.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 180 (b) 90 (c) 13 (d) 96
  11. 11.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 990 (c) 1980 (d) 968
  12. 12.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 264 (b) 150 (c) 132 (d) 37
  13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  14. 14.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 243 (b) 41 (c) 225 (d) 450
  15. 15.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 812 (c) 392 (d) 406
  16. 16.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 171 (c) 162 (d) 342
  17. 17.What is the 16th term of the AP 10, 17, 24, 31, …? (a) 122 (b) 112 (c) 115 (d) 105
  18. 18.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 506 (d) 253
  19. 19.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2279 (c) 2211 (d) 4556
  20. 20.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 19 (b) 155 (c) 154 (d) 308
  21. 21.What is the 27th term of the AP 1, 4, 7, 10, …? (a) 78 (b) 79 (c) 81 (d) 82
  22. 22.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 900 (d) 59
  23. 23.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 24 (b) 33 (c) 25 (d) 26
  24. 24.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 8 (b) 10 (c) 9 (d) 13
  25. 25.What is the 17th term of the AP 1, 3, 5, 7, …? (a) 32 (b) 33 (c) 35 (d) 34
  26. 26.What is the 37th term of the AP 17, 25, 33, 41, …? (a) 288 (b) 296 (c) 313 (d) 305
  27. 27.What is the sum of the first 8 terms of the AP 10, 13, 16, …? (a) 176 (b) 31 (c) 164 (d) 328
  28. 28.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 5 (b) 3 (c) 4 (d) 6
  29. 29.What is the 17th term of the AP 17, 22, 27, 32, …? (a) 102 (b) 97 (c) 80 (d) 85
  30. 30.What is the 11th term of the AP 20, 26, 32, 38, …? (a) 66 (b) 60 (c) 80 (d) 86
  31. 31.What is the 11th term of the AP 1, 6, 11, 16, …? (a) 50 (b) 55 (c) 51 (d) 56
  32. 32.What is the 33rd term of the AP 12, 19, 26, 33, …? (a) 236 (b) 231 (c) 224 (d) 243
  33. 33.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3656 (c) 3570 (d) 3655
  34. 34.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 200 (b) 100 (c) 23 (d) 112
  35. 35.What is the 39th term of the AP 20, 27, 34, 41, …? (a) 266 (b) 273 (c) 286 (d) 293
  36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 435 (d) 841
  37. 37.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 15 (b) 14 (c) 13 (d) 21
  38. 38.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  39. 39.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 120 (b) 204 (c) 102 (d) 32
  40. 40.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 180 (b) 90 (c) 99 (d) 18

Answer key

  1. 168
  2. 64
  3. 3741
  4. 32
  5. 37th
  6. 2415
  7. 14
  8. 341
  9. 209
  10. 90
  11. 990
  12. 132
  13. 729
  14. 225
  15. 406
  16. 171
  17. 115
  18. 484
  19. 2278
  20. 154
  21. 79
  22. 900
  23. 25
  24. 9
  25. 33
  26. 305
  27. 164
  28. 4
  29. 97
  30. 80
  31. 51
  32. 236
  33. 3655
  34. 100
  35. 286
  36. 841
  37. 14
  38. 225
  39. 102
  40. 90

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