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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 683 · 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 12th term of the AP 14, 23, 32, 41, …? (a) 99 (b) 108 (c) 113 (d) 122
  2. 2.Which term of the AP 2, 8, 14, 20, … is 200? (a) 35th (b) 33rd (c) 34th (d) 36th
  3. 3.What is the 21st term of the AP 5, 10, 15, 20, …? (a) 100 (b) 106 (c) 105 (d) 110
  4. 4.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 147 (b) 152 (c) 294 (d) 36
  5. 5.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4950 (c) 9900 (d) 4851
  6. 6.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 99 (b) 14 (c) 100 (d) 198
  7. 7.What is the 12th term of the AP 13, 19, 25, 31, …? (a) 85 (b) 79 (c) 66 (d) 72
  8. 8.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 192 (b) 384 (c) 204 (d) 27
  9. 9.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 529 (c) 45 (d) 552
  10. 10.What is the 24th term of the AP 1, 7, 13, 19, …? (a) 144 (b) 138 (c) 139 (d) 145
  11. 11.Which term of the AP 14, 17, 20, 23, … is 65? (a) 19th (b) 18th (c) 17th (d) 20th
  12. 12.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 92 (d) 91
  13. 13.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 105 (c) 196 (d) 27
  14. 14.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 468 (b) 46 (c) 234 (d) 239
  15. 15.Which term of the AP 2, 4, 6, 8, … is 76? (a) 37th (b) 39th (c) 38th (d) 40th
  16. 16.What is the 19th term of the AP 4, 9, 14, 19, …? (a) 95 (b) 99 (c) 90 (d) 94
  17. 17.Which term of the AP 7, 16, 25, 34, … is 205? (a) 24th (b) 22nd (c) 25th (d) 23rd
  18. 18.What is the 39th term of the AP 3, 5, 7, 9, …? (a) 78 (b) 76 (c) 81 (d) 79
  19. 19.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 253 (b) 231 (c) 41 (d) 462
  20. 20.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 858 (b) 429 (c) 69 (d) 462
  21. 21.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 26 (b) 23 (c) 22 (d) 24
  22. 22.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 100 (b) 50 (c) 60 (d) 18
  23. 23.What is the 32nd term of the AP 20, 26, 32, 38, …? (a) 186 (b) 212 (c) 192 (d) 206
  24. 24.What is the 12th term of the AP 9, 15, 21, 27, …? (a) 72 (b) 81 (c) 66 (d) 75
  25. 25.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3403 (c) 3321 (d) 6806
  26. 26.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 25 (b) 34 (c) 26 (d) 24
  27. 27.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 625 (d) 49
  28. 28.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 406 (c) 870 (d) 435
  29. 29.What is the missing term in the AP 7, 13, 19, ?, 31? (a) 31 (b) 25 (c) 24 (d) 26
  30. 30.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 702 (c) 338 (d) 325
  31. 31.Which term of the AP 6, 8, 10, 12, … is 68? (a) 34th (b) 32nd (c) 33rd (d) 31st
  32. 32.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 3422 (c) 1711 (d) 1682
  33. 33.What is the 18th term of the AP 16, 25, 34, 43, …? (a) 178 (b) 162 (c) 153 (d) 169
  34. 34.Which term of the AP 17, 24, 31, 38, … is 87? (a) 10th (b) 13th (c) 12th (d) 11th
  35. 35.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 29 (b) 22 (c) 21 (d) 20
  36. 36.What is the 26th term of the AP 20, 23, 26, 29, …? (a) 98 (b) 95 (c) 75 (d) 78
  37. 37.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 21 (b) 65 (c) 75 (d) 130
  38. 38.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 171 (c) 162 (d) 342
  39. 39.What is the 16th term of the AP 3, 5, 7, 9, …? (a) 33 (b) 32 (c) 35 (d) 30
  40. 40.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 120 (b) 216 (c) 108 (d) 24

Answer key

  1. 113
  2. 34th
  3. 105
  4. 147
  5. 4950
  6. 99
  7. 79
  8. 192
  9. 529
  10. 139
  11. 18th
  12. 91
  13. 196
  14. 234
  15. 38th
  16. 94
  17. 23rd
  18. 79
  19. 231
  20. 429
  21. 23
  22. 50
  23. 206
  24. 75
  25. 3403
  26. 25
  27. 625
  28. 435
  29. 25
  30. 351
  31. 32nd
  32. 1711
  33. 169
  34. 11th
  35. 21
  36. 95
  37. 65
  38. 171
  39. 33
  40. 108

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