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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 883 · 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 15, ?, 29, 36, 43? (a) 22 (b) 29 (c) 21 (d) 23
  2. 2.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 36 (b) 144 (c) 126 (d) 252
  3. 3.Which term of the AP 4, 8, 12, 16, … is 160? (a) 39th (b) 41st (c) 40th (d) 42nd
  4. 4.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 42 (b) 264 (c) 242 (d) 484
  5. 5.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 238 (b) 133 (c) 119 (d) 29
  6. 6.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 756 (d) 53
  7. 7.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 57 (d) 435
  8. 8.What is the 11th term of the AP 20, 22, 24, 26, …? (a) 42 (b) 22 (c) 20 (d) 40
  9. 9.What is the 14th term of the AP 6, 9, 12, 15, …? (a) 42 (b) 39 (c) 45 (d) 48
  10. 10.What is the missing term in the AP 3, 10, 17, ?, 31? (a) 25 (b) 24 (c) 31 (d) 23
  11. 11.Which term of the AP 10, 14, 18, 22, … is 138? (a) 34th (b) 32nd (c) 33rd (d) 35th
  12. 12.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 650 (c) 325 (d) 326
  13. 13.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 252 (b) 36 (c) 234 (d) 468
  14. 14.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 84 (b) 15 (c) 85 (d) 168
  15. 15.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 36 (d) 15
  16. 16.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 176 (b) 187 (c) 26 (d) 352
  17. 17.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  18. 18.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 18 (b) 19 (c) 20 (d) 27
  19. 19.Which term of the AP 5, 8, 11, 14, … is 56? (a) 19th (b) 18th (c) 20th (d) 17th
  20. 20.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4753 (c) 9506 (d) 4656
  21. 21.Which term of the AP 5, 10, 15, 20, … is 40? (a) 8th (b) 9th (c) 10th (d) 7th
  22. 22.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 112 (b) 224 (c) 25 (d) 115
  23. 23.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 94 (c) 22 (d) 91
  24. 24.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 17 (c) 117 (d) 118
  25. 25.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 9702 (c) 4753 (d) 4851
  26. 26.What is the 22nd term of the AP 18, 26, 34, 42, …? (a) 186 (b) 194 (c) 168 (d) 176
  27. 27.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 66 (c) 67 (d) 132
  28. 28.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2926 (c) 2888 (d) 2850
  29. 29.What is the 36th term of the AP 15, 21, 27, 33, …? (a) 216 (b) 231 (c) 225 (d) 210
  30. 30.What is the 37th term of the AP 1, 3, 5, 7, …? (a) 75 (b) 72 (c) 73 (d) 74
  31. 31.What is the 12th term of the AP 19, 22, 25, 28, …? (a) 52 (b) 55 (c) 33 (d) 36
  32. 32.What is the 21st term of the AP 13, 15, 17, 19, …? (a) 53 (b) 42 (c) 40 (d) 55
  33. 33.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 78 (b) 18 (c) 156 (d) 84
  34. 34.What is the 10th term of the AP 9, 12, 15, 18, …? (a) 27 (b) 36 (c) 39 (d) 30
  35. 35.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 625 (d) 49
  36. 36.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 13 (b) 18 (c) 12 (d) 14
  37. 37.What is the 17th term of the AP 19, 21, 23, 25, …? (a) 32 (b) 51 (c) 34 (d) 53
  38. 38.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 22 (b) 14 (c) 15 (d) 16
  39. 39.Which term of the AP 9, 17, 25, 33, … is 161? (a) 20th (b) 21st (c) 22nd (d) 19th
  40. 40.What is the 15th term of the AP 7, 13, 19, 25, …? (a) 84 (b) 97 (c) 91 (d) 90

Answer key

  1. 22
  2. 126
  3. 40th
  4. 242
  5. 119
  6. 729
  7. 841
  8. 40
  9. 45
  10. 24
  11. 33rd
  12. 325
  13. 234
  14. 84
  15. 64
  16. 176
  17. 324
  18. 19
  19. 18th
  20. 4753
  21. 8th
  22. 112
  23. 91
  24. 117
  25. 4851
  26. 186
  27. 66
  28. 2926
  29. 225
  30. 73
  31. 52
  32. 53
  33. 78
  34. 36
  35. 625
  36. 13
  37. 51
  38. 15
  39. 20th
  40. 91

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