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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 704 · 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 18th term of the AP 11, 17, 23, 29, …? (a) 113 (b) 102 (c) 119 (d) 108
  2. 2.What is the 25th term of the AP 15, 24, 33, 42, …? (a) 225 (b) 240 (c) 216 (d) 231
  3. 3.Which term of the AP 11, 14, 17, 20, … is 92? (a) 27th (b) 29th (c) 28th (d) 30th
  4. 4.What is the 35th term of the AP 1, 7, 13, 19, …? (a) 205 (b) 204 (c) 210 (d) 211
  5. 5.What is the 29th term of the AP 5, 7, 9, 11, …? (a) 63 (b) 56 (c) 61 (d) 58
  6. 6.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 114 (b) 228 (c) 34 (d) 132
  7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 441 (d) 462
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 17 (d) 45
  9. 9.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 252 (b) 126 (c) 30 (d) 140
  10. 10.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4754 (c) 4753 (d) 9506
  11. 11.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 9702 (c) 4851 (d) 4802
  12. 12.What is the 31st term of the AP 4, 13, 22, 31, …? (a) 270 (b) 279 (c) 274 (d) 283
  13. 13.What is the 22nd term of the AP 14, 17, 20, 23, …? (a) 66 (b) 77 (c) 80 (d) 63
  14. 14.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 136 (d) 31
  15. 15.What is the 23rd term of the AP 8, 16, 24, 32, …? (a) 176 (b) 192 (c) 184 (d) 185
  16. 16.Which term of the AP 10, 19, 28, 37, … is 145? (a) 17th (b) 18th (c) 16th (d) 15th
  17. 17.What is the 20th term of the AP 6, 12, 18, 24, …? (a) 121 (b) 126 (c) 114 (d) 120
  18. 18.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 13 (b) 16 (c) 15 (d) 14
  19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 625 (d) 49
  20. 20.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  21. 21.What is the 35th term of the AP 3, 9, 15, 21, …? (a) 210 (b) 204 (c) 207 (d) 213
  22. 22.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 43 (b) 36 (c) 35 (d) 34
  23. 23.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 132 (b) 21 (c) 242 (d) 121
  24. 24.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 504 (c) 264 (d) 252
  25. 25.Which term of the AP 11, 17, 23, 29, … is 119? (a) 20th (b) 21st (c) 18th (d) 19th
  26. 26.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 272 (c) 120 (d) 136
  27. 27.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 23 (b) 20 (c) 19 (d) 21
  28. 28.What is the 30th term of the AP 9, 18, 27, 36, …? (a) 271 (b) 261 (c) 279 (d) 270
  29. 29.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 120 (c) 204 (d) 102
  30. 30.What is the sum of all the whole numbers from 1 to 39? (a) 1560 (b) 780 (c) 781 (d) 741
  31. 31.What is the 11th term of the AP 15, 22, 29, 36, …? (a) 92 (b) 77 (c) 70 (d) 85
  32. 32.What is the 36th term of the AP 16, 22, 28, 34, …? (a) 216 (b) 210 (c) 226 (d) 232
  33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 78 (c) 156 (d) 23
  34. 34.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 50 (b) 12 (c) 100 (d) 51
  35. 35.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 290 (b) 580 (c) 320 (d) 56
  36. 36.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 30 (b) 28 (c) 38 (d) 29
  37. 37.What is the 37th term of the AP 18, 25, 32, 39, …? (a) 277 (b) 252 (c) 270 (d) 259
  38. 38.What is the 17th term of the AP 5, 8, 11, 14, …? (a) 48 (b) 51 (c) 56 (d) 53
  39. 39.What is the 16th term of the AP 11, 13, 15, 17, …? (a) 43 (b) 30 (c) 41 (d) 32
  40. 40.What is the 32nd term of the AP 13, 22, 31, 40, …? (a) 279 (b) 288 (c) 292 (d) 301

Answer key

  1. 113
  2. 231
  3. 28th
  4. 205
  5. 61
  6. 114
  7. 441
  8. 81
  9. 126
  10. 4753
  11. 4851
  12. 274
  13. 77
  14. 256
  15. 184
  16. 16th
  17. 120
  18. 14
  19. 625
  20. 169
  21. 207
  22. 35
  23. 121
  24. 252
  25. 19th
  26. 136
  27. 20
  28. 270
  29. 102
  30. 780
  31. 85
  32. 226
  33. 144
  34. 50
  35. 290
  36. 29
  37. 270
  38. 53
  39. 41
  40. 292

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