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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 941 · 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 all the whole numbers from 1 to 58? (a) 3422 (b) 1682 (c) 1653 (d) 1711
  2. 2.Which term of the AP 15, 23, 31, 39, … is 231? (a) 29th (b) 30th (c) 27th (d) 28th
  3. 3.Which term of the AP 17, 26, 35, 44, … is 152? (a) 17th (b) 18th (c) 15th (d) 16th
  4. 4.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 105 (c) 120 (d) 121
  5. 5.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 42 (b) 24 (c) 6 (d) 21
  6. 6.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 60 (b) 50 (c) 100 (d) 18
  7. 7.What is the 10th term of the AP 20, 22, 24, 26, …? (a) 40 (b) 18 (c) 20 (d) 38
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 110 (d) 55
  9. 9.What is the missing term in the AP 12, 15, ?, 21, 24? (a) 17 (b) 19 (c) 21 (d) 18
  10. 10.What is the 37th term of the AP 4, 7, 10, 13, …? (a) 112 (b) 115 (c) 111 (d) 108
  11. 11.What is the 20th term of the AP 1, 10, 19, 28, …? (a) 180 (b) 172 (c) 181 (d) 171
  12. 12.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 190 (c) 380 (d) 171
  13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 53 (d) 729
  14. 14.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 16 (b) 17 (c) 15 (d) 22
  15. 15.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 1176 (c) 2352 (d) 1128
  16. 16.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 154 (c) 153 (d) 306
  17. 17.What is the 39th term of the AP 3, 7, 11, 15, …? (a) 159 (b) 152 (c) 156 (d) 155
  18. 18.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 31 (b) 272 (c) 136 (d) 152
  19. 19.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 19 (b) 168 (c) 324 (d) 162
  20. 20.Which term of the AP 4, 9, 14, 19, … is 69? (a) 15th (b) 13th (c) 14th (d) 16th
  21. 21.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 81 (d) 17
  22. 22.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 32 (b) 26 (c) 27 (d) 25
  23. 23.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 903 (c) 882 (d) 861
  24. 24.What is the 35th term of the AP 19, 21, 23, 25, …? (a) 89 (b) 68 (c) 87 (d) 70
  25. 25.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 78 (c) 66 (d) 156
  26. 26.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 392 (d) 406
  27. 27.What is the 10th term of the AP 17, 25, 33, 41, …? (a) 97 (b) 80 (c) 89 (d) 72
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 56 (d) 28
  29. 29.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  30. 30.What is the 13th term of the AP 8, 14, 20, 26, …? (a) 86 (b) 80 (c) 72 (d) 78
  31. 31.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 625 (d) 325
  32. 32.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 114 (b) 204 (c) 27 (d) 102
  33. 33.What is the 11th term of the AP 15, 19, 23, 27, …? (a) 59 (b) 40 (c) 55 (d) 44
  34. 34.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 232 (c) 210 (d) 462
  35. 35.What is the 10th term of the AP 4, 13, 22, 31, …? (a) 81 (b) 85 (c) 94 (d) 90
  36. 36.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 4186 (c) 8556 (d) 4278
  37. 37.What is the 20th term of the AP 15, 21, 27, 33, …? (a) 135 (b) 120 (c) 129 (d) 114
  38. 38.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 300 (b) 47 (c) 600 (d) 324
  39. 39.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 36 (b) 66 (c) 8 (d) 33
  40. 40.What is the 10th term of the AP 15, 19, 23, 27, …? (a) 40 (b) 36 (c) 55 (d) 51

Answer key

  1. 1711
  2. 28th
  3. 16th
  4. 120
  5. 21
  6. 50
  7. 38
  8. 100
  9. 18
  10. 112
  11. 172
  12. 190
  13. 729
  14. 16
  15. 1176
  16. 153
  17. 155
  18. 136
  19. 162
  20. 14th
  21. 81
  22. 26
  23. 903
  24. 87
  25. 78
  26. 406
  27. 89
  28. 49
  29. 324
  30. 80
  31. 625
  32. 102
  33. 55
  34. 231
  35. 85
  36. 4278
  37. 129
  38. 300
  39. 33
  40. 51

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