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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 646 · 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 7, 14, ?, 28, 35? (a) 22 (b) 28 (c) 20 (d) 21
  2. 2.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 156 (c) 66 (d) 72
  3. 3.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 150 (b) 27 (c) 75 (d) 90
  4. 4.What is the 39th term of the AP 19, 23, 27, 31, …? (a) 152 (b) 175 (c) 156 (d) 171
  5. 5.What is the 30th term of the AP 10, 12, 14, 16, …? (a) 70 (b) 60 (c) 58 (d) 68
  6. 6.What is the 15th term of the AP 13, 15, 17, 19, …? (a) 28 (b) 30 (c) 41 (d) 43
  7. 7.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 28 (b) 29 (c) 30 (d) 38
  8. 8.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 8 (b) 7 (c) 5 (d) 6
  9. 9.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 43 (b) 53 (c) 44 (d) 45
  10. 10.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 54 (b) 108 (c) 10 (d) 55
  11. 11.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 378 (c) 351 (d) 756
  12. 12.Which term of the AP 12, 17, 22, 27, … is 187? (a) 35th (b) 37th (c) 38th (d) 36th
  13. 13.What is the 38th term of the AP 2, 10, 18, 26, …? (a) 298 (b) 304 (c) 296 (d) 306
  14. 14.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 462 (b) 429 (c) 69 (d) 858
  15. 15.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 49 (d) 28
  16. 16.Which term of the AP 20, 22, 24, 26, … is 52? (a) 18th (b) 16th (c) 26th (d) 17th
  17. 17.What is the 17th term of the AP 20, 26, 32, 38, …? (a) 102 (b) 116 (c) 96 (d) 122
  18. 18.What is the 30th term of the AP 18, 25, 32, 39, …? (a) 210 (b) 203 (c) 228 (d) 221
  19. 19.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 136 (b) 28 (c) 266 (d) 133
  20. 20.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
  21. 21.Which term of the AP 19, 23, 27, 31, … is 63? (a) 11th (b) 12th (c) 14th (d) 13th
  22. 22.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 22 (b) 21 (c) 27 (d) 20
  23. 23.What is the 32nd term of the AP 7, 9, 11, 13, …? (a) 64 (b) 71 (c) 62 (d) 69
  24. 24.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 286 (b) 143 (c) 144 (d) 18
  25. 25.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
  26. 26.Which term of the AP 12, 16, 20, 24, … is 64? (a) 13th (b) 15th (c) 16th (d) 14th
  27. 27.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4561 (c) 4560 (d) 4465
  28. 28.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3403 (c) 3362 (d) 3321
  29. 29.What is the 22nd term of the AP 7, 14, 21, 28, …? (a) 161 (b) 155 (c) 154 (d) 147
  30. 30.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 312 (b) 156 (c) 168 (d) 30
  31. 31.Which term of the AP 18, 21, 24, 27, … is 93? (a) 27th (b) 31st (c) 25th (d) 26th
  32. 32.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 57 (c) 435 (d) 870
  33. 33.What is the 36th term of the AP 7, 15, 23, 31, …? (a) 280 (b) 287 (c) 295 (d) 288
  34. 34.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 190 (b) 350 (c) 31 (d) 175
  35. 35.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 480 (b) 42 (c) 260 (d) 240
  36. 36.What is the 39th term of the AP 7, 11, 15, 19, …? (a) 163 (b) 159 (c) 156 (d) 152
  37. 37.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 70 (b) 20 (c) 140 (d) 73
  38. 38.What is the 17th term of the AP 4, 10, 16, 22, …? (a) 96 (b) 100 (c) 106 (d) 102
  39. 39.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 57 (c) 114 (d) 12
  40. 40.Which term of the AP 18, 22, 26, 30, … is 130? (a) 30th (b) 29th (c) 31st (d) 28th

Answer key

  1. 21
  2. 78
  3. 75
  4. 171
  5. 68
  6. 41
  7. 29
  8. 6
  9. 44
  10. 54
  11. 378
  12. 36th
  13. 298
  14. 429
  15. 49
  16. 17th
  17. 116
  18. 221
  19. 133
  20. 361
  21. 12th
  22. 21
  23. 69
  24. 143
  25. 676
  26. 14th
  27. 4560
  28. 3403
  29. 154
  30. 156
  31. 26th
  32. 841
  33. 287
  34. 175
  35. 240
  36. 159
  37. 70
  38. 100
  39. 57
  40. 29th

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