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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 166 · 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.Which term of the AP 14, 18, 22, 26, … is 138? (a) 31st (b) 32nd (c) 34th (d) 33rd
  2. 2.Which term of the AP 17, 26, 35, 44, … is 107? (a) 12th (b) 10th (c) 11th (d) 13th
  3. 3.Which term of the AP 14, 23, 32, 41, … is 95? (a) 12th (b) 10th (c) 9th (d) 11th
  4. 4.What is the missing term in the AP 9, 16, ?, 30, 37? (a) 22 (b) 30 (c) 23 (d) 24
  5. 5.What is the 25th term of the AP 8, 11, 14, 17, …? (a) 83 (b) 80 (c) 72 (d) 75
  6. 6.What is the 17th term of the AP 4, 6, 8, 10, …? (a) 36 (b) 38 (c) 32 (d) 34
  7. 7.What is the 23rd term of the AP 3, 12, 21, 30, …? (a) 201 (b) 210 (c) 207 (d) 198
  8. 8.What is the 22nd term of the AP 3, 5, 7, 9, …? (a) 44 (b) 47 (c) 45 (d) 42
  9. 9.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 3042 (c) 6162 (d) 3081
  10. 10.What is the 26th term of the AP 16, 20, 24, 28, …? (a) 104 (b) 100 (c) 116 (d) 120
  11. 11.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 31 (c) 114 (d) 192
  12. 12.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 580 (b) 56 (c) 290 (d) 320
  13. 13.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 33 (b) 38 (c) 32 (d) 31
  14. 14.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 492 (b) 264 (c) 246 (d) 37
  15. 15.What is the 36th term of the AP 2, 6, 10, 14, …? (a) 146 (b) 144 (c) 142 (d) 140
  16. 16.Which term of the AP 10, 16, 22, 28, … is 196? (a) 33rd (b) 31st (c) 34th (d) 32nd
  17. 17.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  18. 18.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 441 (d) 462
  19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 400 (d) 39
  20. 20.What is the 13th term of the AP 12, 17, 22, 27, …? (a) 77 (b) 65 (c) 72 (d) 60
  21. 21.Which term of the AP 15, 18, 21, 24, … is 108? (a) 36th (b) 31st (c) 33rd (d) 32nd
  22. 22.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
  23. 23.Which term of the AP 20, 27, 34, 41, … is 272? (a) 36th (b) 38th (c) 37th (d) 39th
  24. 24.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 342 (b) 189 (c) 171 (d) 35
  25. 25.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 276 (d) 529
  26. 26.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 3422 (c) 1711 (d) 1653
  27. 27.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 130 (b) 25 (c) 80 (d) 65
  28. 28.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 109 (b) 16 (c) 216 (d) 108
  29. 29.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 182 (b) 91 (c) 25 (d) 105
  30. 30.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  31. 31.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 98 (b) 10 (c) 50 (d) 49
  32. 32.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 256 (d) 136
  33. 33.What is the 35th term of the AP 5, 12, 19, 26, …? (a) 243 (b) 245 (c) 250 (d) 238
  34. 34.What is the 19th term of the AP 9, 16, 23, 30, …? (a) 135 (b) 133 (c) 142 (d) 126
  35. 35.What is the 30th term of the AP 6, 11, 16, 21, …? (a) 151 (b) 156 (c) 145 (d) 150
  36. 36.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 266 (b) 37 (c) 133 (d) 154
  37. 37.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 3782 (c) 1830 (d) 1892
  38. 38.What is the 30th term of the AP 12, 20, 28, 36, …? (a) 240 (b) 232 (c) 252 (d) 244
  39. 39.What is the 23rd term of the AP 12, 19, 26, 33, …? (a) 154 (b) 173 (c) 161 (d) 166
  40. 40.Which term of the AP 11, 18, 25, 32, … is 193? (a) 28th (b) 29th (c) 26th (d) 27th

Answer key

  1. 32nd
  2. 11th
  3. 10th
  4. 23
  5. 80
  6. 36
  7. 201
  8. 45
  9. 3081
  10. 116
  11. 96
  12. 290
  13. 32
  14. 246
  15. 142
  16. 32nd
  17. 361
  18. 441
  19. 400
  20. 72
  21. 32nd
  22. 841
  23. 37th
  24. 171
  25. 529
  26. 1711
  27. 65
  28. 108
  29. 91
  30. 729
  31. 49
  32. 256
  33. 243
  34. 135
  35. 151
  36. 133
  37. 1891
  38. 244
  39. 166
  40. 27th

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