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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 601 · 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 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 114 (c) 12 (d) 60
  2. 2.What is the 20th term of the AP 2, 5, 8, 11, …? (a) 62 (b) 59 (c) 57 (d) 60
  3. 3.What is the 12th term of the AP 16, 21, 26, 31, …? (a) 55 (b) 60 (c) 76 (d) 71
  4. 4.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 91 (b) 92 (c) 16 (d) 182
  5. 5.What is the 39th term of the AP 14, 20, 26, 32, …? (a) 228 (b) 234 (c) 248 (d) 242
  6. 6.What is the 17th term of the AP 8, 16, 24, 32, …? (a) 128 (b) 137 (c) 144 (d) 136
  7. 7.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 812 (c) 406 (d) 378
  8. 8.What is the 28th term of the AP 1, 4, 7, 10, …? (a) 81 (b) 84 (c) 82 (d) 85
  9. 9.What is the missing term in the AP 7, 12, 17, ?, 27? (a) 22 (b) 21 (c) 23 (d) 27
  10. 10.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 23 (b) 22 (c) 21 (d) 28
  11. 11.What is the missing term in the AP 15, ?, 21, 24, 27? (a) 19 (b) 21 (c) 18 (d) 17
  12. 12.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 40 (b) 6 (c) 20 (d) 21
  13. 13.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 496 (b) 52 (c) 272 (d) 248
  14. 14.What is the 24th term of the AP 8, 10, 12, 14, …? (a) 56 (b) 48 (c) 54 (d) 46
  15. 15.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 400 (b) 200 (c) 220 (d) 38
  16. 16.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 132 (b) 66 (c) 16 (d) 72
  17. 17.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 90 (b) 48 (c) 45 (d) 10
  18. 18.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 12 (b) 11 (c) 13 (d) 18
  19. 19.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 32 (b) 190 (c) 187 (d) 374
  20. 20.What is the 15th term of the AP 14, 21, 28, 35, …? (a) 105 (b) 98 (c) 112 (d) 119
  21. 21.What is the missing term in the AP 20, 23, 26, ?, 32? (a) 28 (b) 32 (c) 30 (d) 29
  22. 22.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 4 (b) 2 (c) 5 (d) 3
  23. 23.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 204 (b) 208 (c) 198 (d) 202
  24. 24.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 4032 (c) 2016 (d) 2017
  25. 25.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 7832 (c) 3872 (d) 3916
  26. 26.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 756 (c) 351 (d) 378
  27. 27.Which term of the AP 5, 9, 13, 17, … is 137? (a) 36th (b) 33rd (c) 34th (d) 35th
  28. 28.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 59 (b) 374 (c) 379 (d) 748
  29. 29.Which term of the AP 8, 17, 26, 35, … is 224? (a) 25th (b) 24th (c) 26th (d) 27th
  30. 30.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 9 (b) 8 (c) 10 (d) 13
  31. 31.Which term of the AP 6, 12, 18, 24, … is 198? (a) 35th (b) 32nd (c) 34th (d) 33rd
  32. 32.Which term of the AP 6, 10, 14, 18, … is 154? (a) 39th (b) 37th (c) 38th (d) 40th
  33. 33.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 276 (d) 552
  34. 34.Which term of the AP 10, 12, 14, 16, … is 72? (a) 31st (b) 36th (c) 32nd (d) 33rd
  35. 35.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4851 (c) 4950 (d) 9900
  36. 36.What is the missing term in the AP 11, 20, ?, 38, 47? (a) 30 (b) 38 (c) 29 (d) 28
  37. 37.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 19 (b) 10 (c) 11 (d) 9
  38. 38.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 25 (b) 336 (c) 168 (d) 180
  39. 39.What is the missing term in the AP 7, ?, 23, 31, 39? (a) 16 (b) 23 (c) 14 (d) 15
  40. 40.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 11 (b) 7 (c) 9 (d) 8

Answer key

  1. 57
  2. 59
  3. 71
  4. 91
  5. 242
  6. 136
  7. 406
  8. 82
  9. 22
  10. 22
  11. 18
  12. 20
  13. 248
  14. 54
  15. 200
  16. 66
  17. 45
  18. 12
  19. 187
  20. 112
  21. 29
  22. 3
  23. 202
  24. 2016
  25. 3916
  26. 378
  27. 34th
  28. 374
  29. 25th
  30. 9
  31. 33rd
  32. 38th
  33. 529
  34. 32nd
  35. 4950
  36. 29
  37. 10
  38. 168
  39. 15
  40. 8

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