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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 192 · 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 33rd term of the AP 17, 24, 31, 38, …? (a) 248 (b) 231 (c) 224 (d) 241
  2. 2.What is the 35th term of the AP 12, 20, 28, 36, …? (a) 284 (b) 280 (c) 272 (d) 292
  3. 3.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1378 (c) 1432 (d) 1431
  4. 4.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 407 (b) 748 (c) 374 (d) 64
  5. 5.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 51 (b) 486 (c) 243 (d) 270
  6. 6.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 194 (b) 41 (c) 378 (d) 189
  7. 7.Which term of the AP 2, 5, 8, 11, … is 32? (a) 13th (b) 12th (c) 10th (d) 11th
  8. 8.Which term of the AP 6, 13, 20, 27, … is 90? (a) 12th (b) 15th (c) 13th (d) 14th
  9. 9.What is the 24th term of the AP 15, 18, 21, 24, …? (a) 69 (b) 87 (c) 84 (d) 72
  10. 10.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 60 (c) 55 (d) 10
  11. 11.What is the 27th term of the AP 20, 22, 24, 26, …? (a) 72 (b) 74 (c) 54 (d) 52
  12. 12.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 3487 (c) 6972 (d) 3486
  13. 13.What is the 29th term of the AP 13, 16, 19, 22, …? (a) 84 (b) 87 (c) 97 (d) 100
  14. 14.Which term of the AP 20, 24, 28, 32, … is 68? (a) 12th (b) 17th (c) 13th (d) 14th
  15. 15.What is the 11th term of the AP 14, 18, 22, 26, …? (a) 58 (b) 54 (c) 44 (d) 40
  16. 16.Which term of the AP 15, 20, 25, 30, … is 75? (a) 14th (b) 15th (c) 12th (d) 13th
  17. 17.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 9 (b) 8 (c) 10 (d) 12
  18. 18.Which term of the AP 8, 13, 18, 23, … is 88? (a) 16th (b) 18th (c) 17th (d) 19th
  19. 19.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 30 (b) 37 (c) 27 (d) 34
  20. 20.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 4 (b) 2 (c) 5 (d) 3
  21. 21.Which term of the AP 19, 23, 27, 31, … is 163? (a) 37th (b) 38th (c) 39th (d) 36th
  22. 22.What is the 23rd term of the AP 6, 11, 16, 21, …? (a) 116 (b) 121 (c) 110 (d) 115
  23. 23.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 104 (b) 96 (c) 19 (d) 192
  24. 24.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 231 (d) 41
  25. 25.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1711 (c) 1770 (d) 3540
  26. 26.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 379 (b) 59 (c) 374 (d) 748
  27. 27.What is the 12th term of the AP 13, 16, 19, 22, …? (a) 49 (b) 46 (c) 36 (d) 33
  28. 28.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 1891 (c) 3906 (d) 1922
  29. 29.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 96 (c) 114 (d) 192
  30. 30.What is the 40th term of the AP 14, 18, 22, 26, …? (a) 156 (b) 174 (c) 160 (d) 170
  31. 31.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 26 (b) 20 (c) 22 (d) 21
  32. 32.Which term of the AP 15, 23, 31, 39, … is 223? (a) 28th (b) 26th (c) 29th (d) 27th
  33. 33.What is the 37th term of the AP 18, 27, 36, 45, …? (a) 324 (b) 342 (c) 333 (d) 351
  34. 34.What is the 30th term of the AP 7, 12, 17, 22, …? (a) 145 (b) 157 (c) 150 (d) 152
  35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  36. 36.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 204 (b) 120 (c) 32 (d) 102
  37. 37.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 203 (c) 198 (d) 42
  38. 38.What is the 18th term of the AP 17, 19, 21, 23, …? (a) 53 (b) 34 (c) 51 (d) 36
  39. 39.What is the 23rd term of the AP 14, 20, 26, 32, …? (a) 152 (b) 138 (c) 132 (d) 146
  40. 40.What is the missing term in the AP 2, 10, ?, 26, 34? (a) 26 (b) 18 (c) 17 (d) 19

Answer key

  1. 241
  2. 284
  3. 1431
  4. 374
  5. 243
  6. 189
  7. 11th
  8. 13th
  9. 84
  10. 55
  11. 72
  12. 3486
  13. 97
  14. 13th
  15. 54
  16. 13th
  17. 9
  18. 17th
  19. 34
  20. 3
  21. 37th
  22. 116
  23. 96
  24. 441
  25. 1770
  26. 374
  27. 46
  28. 1953
  29. 96
  30. 170
  31. 21
  32. 27th
  33. 342
  34. 152
  35. 289
  36. 102
  37. 198
  38. 51
  39. 146
  40. 18

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