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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 313 · 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 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 13 (c) 50 (d) 45
  2. 2.What is the 11th term of the AP 20, 28, 36, 44, …? (a) 100 (b) 108 (c) 80 (d) 88
  3. 3.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 11 (b) 10 (c) 9 (d) 14
  4. 4.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 368 (b) 44 (c) 208 (d) 184
  5. 5.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 2450 (c) 1226 (d) 1176
  6. 6.What is the 39th term of the AP 6, 10, 14, 18, …? (a) 156 (b) 162 (c) 158 (d) 152
  7. 7.What is the 35th term of the AP 17, 25, 33, 41, …? (a) 280 (b) 272 (c) 297 (d) 289
  8. 8.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 37 (b) 36 (c) 46 (d) 38
  9. 9.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 105 (c) 120 (d) 240
  10. 10.Which term of the AP 14, 21, 28, 35, … is 119? (a) 15th (b) 16th (c) 17th (d) 18th
  11. 11.What is the 17th term of the AP 6, 11, 16, 21, …? (a) 91 (b) 80 (c) 86 (d) 85
  12. 12.What is the 20th term of the AP 20, 29, 38, 47, …? (a) 180 (b) 171 (c) 200 (d) 191
  13. 13.What is the 19th term of the AP 14, 17, 20, 23, …? (a) 54 (b) 57 (c) 71 (d) 68
  14. 14.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 55 (b) 110 (c) 60 (d) 10
  15. 15.What is the 20th term of the AP 11, 20, 29, 38, …? (a) 182 (b) 191 (c) 171 (d) 180
  16. 16.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 78 (d) 156
  17. 17.What is the 12th term of the AP 7, 13, 19, 25, …? (a) 66 (b) 72 (c) 79 (d) 73
  18. 18.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 216 (b) 120 (c) 108 (d) 28
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 25 (d) 9
  20. 20.What is the missing term in the AP 16, 21, 26, ?, 36? (a) 31 (b) 30 (c) 32 (d) 36
  21. 21.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 4802 (c) 4753 (d) 9702
  22. 22.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2346 (c) 2415 (d) 2416
  23. 23.Which term of the AP 2, 9, 16, 23, … is 65? (a) 11th (b) 9th (c) 12th (d) 10th
  24. 24.Which term of the AP 6, 15, 24, 33, … is 285? (a) 34th (b) 31st (c) 33rd (d) 32nd
  25. 25.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 27 (b) 21 (c) 20 (d) 22
  26. 26.What is the 33rd term of the AP 19, 27, 35, 43, …? (a) 256 (b) 283 (c) 275 (d) 264
  27. 27.Which term of the AP 12, 15, 18, 21, … is 75? (a) 25th (b) 21st (c) 22nd (d) 23rd
  28. 28.What is the 24th term of the AP 10, 18, 26, 34, …? (a) 192 (b) 184 (c) 194 (d) 202
  29. 29.What is the 11th term of the AP 4, 13, 22, 31, …? (a) 90 (b) 103 (c) 99 (d) 94
  30. 30.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 231 (c) 462 (d) 41
  31. 31.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 2775 (c) 2738 (d) 5550
  32. 32.What is the 17th term of the AP 14, 16, 18, 20, …? (a) 32 (b) 34 (c) 48 (d) 46
  33. 33.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1275 (c) 1326 (d) 1327
  34. 34.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 10 (b) 8 (c) 9 (d) 15
  35. 35.What is the 10th term of the AP 15, 21, 27, 33, …? (a) 60 (b) 75 (c) 54 (d) 69
  36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  37. 37.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 10 (b) 104 (c) 56 (d) 52
  38. 38.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 122 (b) 238 (c) 119 (d) 26
  39. 39.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 14 (b) 13 (c) 12 (d) 22
  40. 40.What is the 24th term of the AP 16, 22, 28, 34, …? (a) 138 (b) 144 (c) 160 (d) 154

Answer key

  1. 45
  2. 100
  3. 10
  4. 184
  5. 1225
  6. 158
  7. 289
  8. 37
  9. 120
  10. 16th
  11. 86
  12. 191
  13. 68
  14. 55
  15. 182
  16. 78
  17. 73
  18. 108
  19. 25
  20. 31
  21. 4851
  22. 2415
  23. 10th
  24. 32nd
  25. 21
  26. 275
  27. 22nd
  28. 194
  29. 94
  30. 441
  31. 2775
  32. 46
  33. 1326
  34. 9
  35. 69
  36. 144
  37. 52
  38. 119
  39. 13
  40. 154

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