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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 798 · 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 8 terms of the AP 2, 7, 12, …? (a) 312 (b) 37 (c) 156 (d) 176
  2. 2.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 21 (b) 20 (c) 19 (d) 25
  3. 3.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 21 (b) 224 (c) 120 (d) 112
  4. 4.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 72 (b) 128 (c) 15 (d) 64
  5. 5.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 138 (c) 17 (d) 144
  6. 6.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 20 (b) 18 (c) 25 (d) 19
  7. 7.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 169 (c) 25 (d) 91
  8. 8.What is the 37th term of the AP 3, 6, 9, 12, …? (a) 111 (b) 114 (c) 112 (d) 108
  9. 9.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2775 (c) 2850 (d) 2851
  10. 10.What is the sum of all the whole numbers from 1 to 69? (a) 2416 (b) 4830 (c) 2415 (d) 2346
  11. 11.What is the 26th term of the AP 8, 12, 16, 20, …? (a) 112 (b) 100 (c) 104 (d) 108
  12. 12.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 87 (b) 27 (c) 174 (d) 102
  13. 13.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 276 (d) 529
  14. 14.What is the 31st term of the AP 8, 15, 22, 29, …? (a) 210 (b) 218 (c) 225 (d) 217
  15. 15.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 33 (c) 153 (d) 306
  16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 462 (d) 441
  17. 17.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 32 (b) 31 (c) 39 (d) 30
  18. 18.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 62 (b) 700 (c) 380 (d) 350
  19. 19.Which term of the AP 3, 6, 9, 12, … is 48? (a) 17th (b) 16th (c) 18th (d) 15th
  20. 20.What is the 12th term of the AP 3, 8, 13, 18, …? (a) 55 (b) 60 (c) 58 (d) 63
  21. 21.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 13 (b) 110 (c) 56 (d) 55
  22. 22.What is the 15th term of the AP 13, 15, 17, 19, …? (a) 41 (b) 28 (c) 43 (d) 30
  23. 23.What is the 17th term of the AP 1, 5, 9, 13, …? (a) 68 (b) 69 (c) 65 (d) 64
  24. 24.What is the 23rd term of the AP 7, 9, 11, 13, …? (a) 53 (b) 44 (c) 51 (d) 46
  25. 25.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 1953 (d) 2016
  26. 26.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 65 (b) 60 (c) 22 (d) 120
  27. 27.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 406 (d) 812
  28. 28.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 470 (b) 37 (c) 250 (d) 235
  29. 29.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 59 (b) 640 (c) 320 (d) 350
  30. 30.What is the missing term in the AP 15, 20, ?, 30, 35? (a) 26 (b) 24 (c) 25 (d) 30
  31. 31.What is the 13th term of the AP 1, 7, 13, 19, …? (a) 72 (b) 73 (c) 79 (d) 78
  32. 32.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 75 (b) 84 (c) 150 (d) 20
  33. 33.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 154 (b) 286 (c) 143 (d) 23
  34. 34.What is the 16th term of the AP 2, 5, 8, 11, …? (a) 50 (b) 48 (c) 45 (d) 47
  35. 35.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 252 (b) 36 (c) 234 (d) 468
  36. 36.What is the 31st term of the AP 10, 18, 26, 34, …? (a) 248 (b) 258 (c) 250 (d) 240
  37. 37.What is the 20th term of the AP 10, 18, 26, 34, …? (a) 160 (b) 152 (c) 170 (d) 162
  38. 38.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 56 (b) 372 (c) 684 (d) 342
  39. 39.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 160 (b) 32 (c) 288 (d) 144
  40. 40.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 13 (b) 17 (c) 14 (d) 12

Answer key

  1. 156
  2. 20
  3. 112
  4. 64
  5. 138
  6. 19
  7. 169
  8. 111
  9. 2850
  10. 2415
  11. 108
  12. 87
  13. 529
  14. 218
  15. 289
  16. 441
  17. 31
  18. 350
  19. 16th
  20. 58
  21. 55
  22. 41
  23. 65
  24. 51
  25. 2016
  26. 60
  27. 406
  28. 235
  29. 320
  30. 25
  31. 73
  32. 75
  33. 143
  34. 47
  35. 234
  36. 250
  37. 162
  38. 342
  39. 144
  40. 13

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