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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 843 · 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, ?, 18, 22, 26? (a) 18 (b) 13 (c) 14 (d) 15
  2. 2.What is the 17th term of the AP 15, 20, 25, 30, …? (a) 80 (b) 85 (c) 95 (d) 100
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 462 (d) 441
  4. 4.What is the 12th term of the AP 7, 16, 25, 34, …? (a) 106 (b) 115 (c) 108 (d) 99
  5. 5.What is the 23rd term of the AP 19, 24, 29, 34, …? (a) 129 (b) 115 (c) 110 (d) 134
  6. 6.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3403 (c) 3487 (d) 3486
  7. 7.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 54 (b) 27 (c) 30 (d) 7
  8. 8.What is the 15th term of the AP 7, 10, 13, 16, …? (a) 45 (b) 52 (c) 49 (d) 42
  9. 9.What is the 32nd term of the AP 16, 19, 22, 25, …? (a) 109 (b) 112 (c) 93 (d) 96
  10. 10.What is the 22nd term of the AP 4, 6, 8, 10, …? (a) 46 (b) 44 (c) 42 (d) 48
  11. 11.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 330 (b) 48 (c) 308 (d) 616
  12. 12.What is the 38th term of the AP 20, 25, 30, 35, …? (a) 210 (b) 185 (c) 190 (d) 205
  13. 13.What is the 17th term of the AP 5, 8, 11, 14, …? (a) 53 (b) 48 (c) 51 (d) 56
  14. 14.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 165 (b) 330 (c) 166 (d) 20
  15. 15.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 406 (d) 812
  16. 16.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 200 (b) 368 (c) 184 (d) 37
  17. 17.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
  18. 18.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 506 (b) 256 (c) 253 (d) 38
  19. 19.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  20. 20.What is the missing term in the AP 17, 22, 27, ?, 37? (a) 31 (b) 33 (c) 37 (d) 32
  21. 21.What is the 40th term of the AP 2, 4, 6, 8, …? (a) 81 (b) 80 (c) 78 (d) 82
  22. 22.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 138 (b) 78 (c) 69 (d) 19
  23. 23.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 528 (c) 1056 (d) 496
  24. 24.Which term of the AP 3, 5, 7, 9, … is 59? (a) 30th (b) 31st (c) 29th (d) 28th
  25. 25.What is the 20th term of the AP 19, 26, 33, 40, …? (a) 140 (b) 152 (c) 133 (d) 159
  26. 26.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 34 (b) 37 (c) 30 (d) 27
  27. 27.Which term of the AP 6, 10, 14, 18, … is 78? (a) 19th (b) 21st (c) 20th (d) 18th
  28. 28.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 91 (c) 92 (d) 182
  29. 29.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1327 (c) 1275 (d) 1326
  30. 30.Which term of the AP 7, 9, 11, 13, … is 33? (a) 14th (b) 13th (c) 15th (d) 16th
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  32. 32.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 39 (d) 210
  33. 33.What is the 26th term of the AP 6, 9, 12, 15, …? (a) 78 (b) 75 (c) 81 (d) 84
  34. 34.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 630 (c) 648 (d) 666
  35. 35.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 17 (b) 12 (c) 13 (d) 11
  36. 36.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 160 (b) 85 (c) 80 (d) 26
  37. 37.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 16 (b) 92 (c) 182 (d) 91
  38. 38.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 8 (b) 7 (c) 6 (d) 9
  39. 39.Which term of the AP 12, 17, 22, 27, … is 197? (a) 38th (b) 39th (c) 40th (d) 37th
  40. 40.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 15 (b) 19 (c) 14 (d) 16

Answer key

  1. 14
  2. 95
  3. 441
  4. 106
  5. 129
  6. 3486
  7. 27
  8. 49
  9. 109
  10. 46
  11. 308
  12. 205
  13. 53
  14. 165
  15. 784
  16. 184
  17. 81
  18. 253
  19. 529
  20. 32
  21. 80
  22. 69
  23. 528
  24. 29th
  25. 152
  26. 34
  27. 19th
  28. 91
  29. 1326
  30. 14th
  31. 64
  32. 400
  33. 81
  34. 666
  35. 12
  36. 80
  37. 91
  38. 7
  39. 38th
  40. 15

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