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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 701 · 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 1, 3, ?, 7, 9? (a) 6 (b) 7 (c) 4 (d) 5
  2. 2.What is the 40th term of the AP 16, 23, 30, 37, …? (a) 289 (b) 273 (c) 296 (d) 280
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  4. 4.What is the 26th term of the AP 7, 15, 23, 31, …? (a) 215 (b) 208 (c) 207 (d) 200
  5. 5.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 208 (b) 104 (c) 20 (d) 112
  6. 6.What is the 17th term of the AP 10, 15, 20, 25, …? (a) 95 (b) 90 (c) 85 (d) 80
  7. 7.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 280 (b) 260 (c) 520 (d) 44
  8. 8.Which term of the AP 1, 10, 19, 28, … is 73? (a) 11th (b) 10th (c) 9th (d) 8th
  9. 9.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 66 (b) 72 (c) 132 (d) 16
  10. 10.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 153 (b) 288 (c) 24 (d) 144
  11. 11.Which term of the AP 13, 20, 27, 34, … is 62? (a) 9th (b) 7th (c) 8th (d) 10th
  12. 12.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 2070 (d) 1035
  13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 378 (d) 756
  15. 15.What is the 20th term of the AP 10, 16, 22, 28, …? (a) 130 (b) 114 (c) 120 (d) 124
  16. 16.Which term of the AP 3, 8, 13, 18, … is 123? (a) 25th (b) 27th (c) 24th (d) 26th
  17. 17.What is the 26th term of the AP 6, 12, 18, 24, …? (a) 150 (b) 156 (c) 162 (d) 157
  18. 18.What is the sum of all the whole numbers from 1 to 69? (a) 2416 (b) 2415 (c) 4830 (d) 2346
  19. 19.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 418 (b) 451 (c) 836 (d) 68
  20. 20.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 165 (b) 24 (c) 308 (d) 154
  21. 21.What is the 31st term of the AP 14, 18, 22, 26, …? (a) 124 (b) 138 (c) 134 (d) 120
  22. 22.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 240 (b) 440 (c) 220 (d) 45
  23. 23.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 71 (b) 492 (c) 456 (d) 912
  24. 24.Which term of the AP 14, 17, 20, 23, … is 98? (a) 28th (b) 30th (c) 31st (d) 29th
  25. 25.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 444 (b) 35 (c) 240 (d) 222
  26. 26.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 34 (b) 36 (c) 35 (d) 44
  27. 27.What is the 29th term of the AP 2, 10, 18, 26, …? (a) 224 (b) 226 (c) 234 (d) 232
  28. 28.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 70 (b) 140 (c) 20 (d) 73
  29. 29.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 10 (b) 8 (c) 6 (d) 7
  30. 30.What is the 10th term of the AP 10, 12, 14, 16, …? (a) 20 (b) 18 (c) 28 (d) 30
  31. 31.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 153 (d) 306
  32. 32.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 552 (d) 276
  33. 33.What is the 12th term of the AP 19, 24, 29, 34, …? (a) 74 (b) 55 (c) 79 (d) 60
  34. 34.What is the 34th term of the AP 8, 15, 22, 29, …? (a) 231 (b) 238 (c) 246 (d) 239
  35. 35.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 351 (c) 702 (d) 51
  36. 36.What is the missing term in the AP 4, 8, ?, 16, 20? (a) 13 (b) 12 (c) 11 (d) 16
  37. 37.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 300 (b) 57 (c) 600 (d) 330
  38. 38.What is the 34th term of the AP 3, 12, 21, 30, …? (a) 297 (b) 309 (c) 300 (d) 306
  39. 39.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 374 (b) 190 (c) 32 (d) 187
  40. 40.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 56 (b) 98 (c) 49 (d) 13

Answer key

  1. 5
  2. 289
  3. 441
  4. 207
  5. 104
  6. 90
  7. 260
  8. 9th
  9. 66
  10. 144
  11. 8th
  12. 1035
  13. 121
  14. 729
  15. 124
  16. 25th
  17. 156
  18. 2415
  19. 418
  20. 154
  21. 134
  22. 220
  23. 456
  24. 29th
  25. 222
  26. 35
  27. 226
  28. 70
  29. 7
  30. 28
  31. 289
  32. 529
  33. 74
  34. 239
  35. 676
  36. 12
  37. 300
  38. 300
  39. 187
  40. 49

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