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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 828 · 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 10, 12, 14, ?, 18? (a) 17 (b) 15 (c) 16 (d) 18
  2. 2.Which term of the AP 9, 15, 21, 27, … is 147? (a) 26th (b) 24th (c) 23rd (d) 25th
  3. 3.What is the 14th term of the AP 18, 23, 28, 33, …? (a) 88 (b) 83 (c) 65 (d) 70
  4. 4.What is the 18th term of the AP 16, 21, 26, 31, …? (a) 101 (b) 90 (c) 85 (d) 106
  5. 5.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 45 (c) 17 (d) 90
  6. 6.What is the 17th term of the AP 1, 3, 5, 7, …? (a) 34 (b) 32 (c) 33 (d) 35
  7. 7.What is the 16th term of the AP 12, 14, 16, 18, …? (a) 32 (b) 44 (c) 42 (d) 30
  8. 8.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 506 (d) 484
  9. 9.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 576 (d) 600
  10. 10.Which term of the AP 19, 24, 29, 34, … is 154? (a) 28th (b) 29th (c) 30th (d) 27th
  11. 11.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 85 (b) 26 (c) 70 (d) 140
  12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 81 (d) 45
  13. 13.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 88 (b) 9 (c) 48 (d) 44
  14. 14.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 396 (b) 63 (c) 363 (d) 726
  15. 15.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 10 (b) 17 (c) 11 (d) 9
  16. 16.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 25 (b) 27 (c) 24 (d) 23
  17. 17.What is the 15th term of the AP 4, 6, 8, 10, …? (a) 32 (b) 34 (c) 30 (d) 28
  18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  19. 19.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 20 (b) 19 (c) 21 (d) 22
  20. 20.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 29 (b) 170 (c) 85 (d) 100
  21. 21.Which term of the AP 13, 22, 31, 40, … is 121? (a) 12th (b) 15th (c) 14th (d) 13th
  22. 22.What is the 34th term of the AP 13, 21, 29, 37, …? (a) 277 (b) 285 (c) 272 (d) 264
  23. 23.What is the missing term in the AP 9, 18, ?, 36, 45? (a) 26 (b) 27 (c) 28 (d) 36
  24. 24.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 512 (c) 496 (d) 528
  25. 25.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 37 (d) 361
  26. 26.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 2256 (c) 1129 (d) 1081
  27. 27.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 203 (b) 44 (c) 182 (d) 364
  28. 28.Which term of the AP 8, 11, 14, 17, … is 29? (a) 10th (b) 8th (c) 9th (d) 7th
  29. 29.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
  30. 30.What is the 25th term of the AP 18, 23, 28, 33, …? (a) 120 (b) 143 (c) 125 (d) 138
  31. 31.What is the missing term in the AP 8, 13, 18, ?, 28? (a) 22 (b) 28 (c) 23 (d) 24
  32. 32.Which term of the AP 16, 24, 32, 40, … is 248? (a) 29th (b) 32nd (c) 31st (d) 30th
  33. 33.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 876 (b) 468 (c) 64 (d) 438
  34. 34.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 183 (b) 180 (c) 32 (d) 360
  35. 35.What is the 37th term of the AP 15, 17, 19, 21, …? (a) 72 (b) 89 (c) 87 (d) 74
  36. 36.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1653 (c) 1654 (d) 1596
  37. 37.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 72 (d) 64
  38. 38.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 464 (b) 256 (c) 50 (d) 232
  39. 39.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 19 (b) 15 (c) 14 (d) 16
  40. 40.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 10100 (c) 5000 (d) 5050

Answer key

  1. 16
  2. 24th
  3. 83
  4. 101
  5. 45
  6. 33
  7. 42
  8. 484
  9. 576
  10. 28th
  11. 70
  12. 81
  13. 44
  14. 363
  15. 10
  16. 24
  17. 32
  18. 289
  19. 20
  20. 85
  21. 13th
  22. 277
  23. 27
  24. 528
  25. 361
  26. 1128
  27. 182
  28. 8th
  29. 144
  30. 138
  31. 23
  32. 30th
  33. 438
  34. 180
  35. 87
  36. 1653
  37. 64
  38. 232
  39. 15
  40. 5050

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