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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 207 · 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.Which term of the AP 2, 10, 18, 26, … is 234? (a) 32nd (b) 30th (c) 29th (d) 31st
  2. 2.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 16 (b) 22 (c) 17 (d) 15
  3. 3.Which term of the AP 6, 13, 20, 27, … is 69? (a) 9th (b) 11th (c) 12th (d) 10th
  4. 4.What is the 18th term of the AP 10, 18, 26, 34, …? (a) 154 (b) 136 (c) 144 (d) 146
  5. 5.What is the 25th term of the AP 18, 21, 24, 27, …? (a) 75 (b) 72 (c) 93 (d) 90
  6. 6.What is the 11th term of the AP 6, 12, 18, 24, …? (a) 60 (b) 72 (c) 67 (d) 66
  7. 7.What is the 12th term of the AP 10, 12, 14, 16, …? (a) 24 (b) 32 (c) 22 (d) 34
  8. 8.Which term of the AP 6, 15, 24, 33, … is 177? (a) 22nd (b) 19th (c) 20th (d) 21st
  9. 9.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 630 (c) 1260 (d) 595
  10. 10.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 14 (b) 108 (c) 60 (d) 54
  11. 11.What is the 24th term of the AP 12, 14, 16, 18, …? (a) 60 (b) 48 (c) 46 (d) 58
  12. 12.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 47 (b) 270 (c) 245 (d) 490
  13. 13.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 19 (b) 17 (c) 24 (d) 18
  14. 14.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 80 (b) 40 (c) 12 (d) 45
  15. 15.What is the missing term in the AP 20, 29, 38, ?, 56? (a) 48 (b) 56 (c) 47 (d) 46
  16. 16.Which term of the AP 7, 14, 21, 28, … is 105? (a) 14th (b) 16th (c) 15th (d) 17th
  17. 17.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 19 (b) 18 (c) 26 (d) 20
  18. 18.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 84 (b) 168 (c) 88 (d) 14
  19. 19.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 351 (c) 379 (d) 378
  20. 20.What is the 18th term of the AP 10, 13, 16, 19, …? (a) 51 (b) 64 (c) 61 (d) 54
  21. 21.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4753 (c) 9702 (d) 4851
  22. 22.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 56 (b) 315 (c) 576 (d) 288
  23. 23.What is the sum of all the whole numbers from 1 to 77? (a) 2926 (b) 3004 (c) 6006 (d) 3003
  24. 24.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
  25. 25.Which term of the AP 20, 29, 38, 47, … is 326? (a) 34th (b) 37th (c) 36th (d) 35th
  26. 26.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 26 (b) 108 (c) 192 (d) 96
  27. 27.What is the 35th term of the AP 12, 16, 20, 24, …? (a) 140 (b) 148 (c) 136 (d) 152
  28. 28.What is the 31st term of the AP 10, 12, 14, 16, …? (a) 60 (b) 72 (c) 70 (d) 62
  29. 29.What is the 30th term of the AP 3, 7, 11, 15, …? (a) 119 (b) 116 (c) 120 (d) 123
  30. 30.What is the 11th term of the AP 6, 15, 24, 33, …? (a) 96 (b) 90 (c) 105 (d) 99
  31. 31.Which term of the AP 17, 23, 29, 35, … is 71? (a) 11th (b) 10th (c) 9th (d) 12th
  32. 32.What is the 24th term of the AP 12, 16, 20, 24, …? (a) 92 (b) 96 (c) 108 (d) 104
  33. 33.What is the 12th term of the AP 1, 8, 15, 22, …? (a) 77 (b) 84 (c) 85 (d) 78
  34. 34.What is the 22nd term of the AP 2, 11, 20, 29, …? (a) 189 (b) 198 (c) 200 (d) 191
  35. 35.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 261 (b) 522 (c) 49 (d) 266
  36. 36.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 33 (b) 306 (c) 153 (d) 171
  37. 37.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 25 (d) 169
  38. 38.What is the 16th term of the AP 9, 18, 27, 36, …? (a) 144 (b) 153 (c) 145 (d) 135
  39. 39.What is the 26th term of the AP 13, 16, 19, 22, …? (a) 91 (b) 88 (c) 78 (d) 75
  40. 40.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1225 (c) 1176 (d) 1226

Answer key

  1. 30th
  2. 16
  3. 10th
  4. 146
  5. 90
  6. 66
  7. 32
  8. 20th
  9. 630
  10. 54
  11. 58
  12. 245
  13. 18
  14. 40
  15. 47
  16. 15th
  17. 19
  18. 84
  19. 378
  20. 61
  21. 4851
  22. 288
  23. 3003
  24. 729
  25. 35th
  26. 96
  27. 148
  28. 70
  29. 119
  30. 96
  31. 10th
  32. 104
  33. 78
  34. 191
  35. 261
  36. 153
  37. 169
  38. 144
  39. 88
  40. 1225

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