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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 147 · 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 the first 9 terms of the AP 2, 7, 12, …? (a) 198 (b) 203 (c) 42 (d) 396
  2. 2.What is the 18th term of the AP 13, 19, 25, 31, …? (a) 108 (b) 115 (c) 102 (d) 121
  3. 3.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 15 (b) 16 (c) 5 (d) 30
  4. 4.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 85 (b) 26 (c) 160 (d) 80
  5. 5.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 29 (b) 30 (c) 31 (d) 39
  6. 6.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 108 (b) 19 (c) 198 (d) 99
  7. 7.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 40 (b) 48 (c) 39 (d) 38
  8. 8.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 256 (c) 31 (d) 136
  9. 9.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2888 (c) 2850 (d) 2926
  10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  11. 11.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 21 (b) 18 (c) 17 (d) 16
  12. 12.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 748 (b) 407 (c) 64 (d) 374
  13. 13.What is the 18th term of the AP 13, 17, 21, 25, …? (a) 68 (b) 85 (c) 72 (d) 81
  14. 14.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 20 (b) 24 (c) 21 (d) 19
  15. 15.What is the 18th term of the AP 2, 11, 20, 29, …? (a) 153 (b) 155 (c) 164 (d) 162
  16. 16.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 7 (b) 5 (c) 4 (d) 6
  17. 17.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 17 (b) 264 (c) 133 (d) 132
  18. 18.What is the 10th term of the AP 4, 10, 16, 22, …? (a) 64 (b) 58 (c) 54 (d) 60
  19. 19.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 666 (c) 630 (d) 1332
  20. 20.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1953 (c) 1891 (d) 3906
  21. 21.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 23 (b) 144 (c) 156 (d) 288
  22. 22.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 182 (b) 161 (c) 41 (d) 322
  23. 23.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 1596 (c) 3306 (d) 1654
  24. 24.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 720 (b) 390 (c) 63 (d) 360
  25. 25.What is the 19th term of the AP 18, 23, 28, 33, …? (a) 90 (b) 95 (c) 113 (d) 108
  26. 26.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 406 (d) 812
  27. 27.What is the sum of all the whole numbers from 1 to 44? (a) 968 (b) 1980 (c) 946 (d) 990
  28. 28.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 72 (c) 16 (d) 80
  29. 29.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 248 (b) 124 (c) 26 (d) 136
  30. 30.What is the 29th term of the AP 15, 17, 19, 21, …? (a) 73 (b) 58 (c) 71 (d) 56
  31. 31.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 57 (b) 704 (c) 352 (d) 357
  32. 32.What is the 25th term of the AP 14, 22, 30, 38, …? (a) 214 (b) 192 (c) 200 (d) 206
  33. 33.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 6162 (c) 3042 (d) 3081
  34. 34.What is the 31st term of the AP 14, 20, 26, 32, …? (a) 194 (b) 200 (c) 180 (d) 186
  35. 35.What is the 12th term of the AP 2, 6, 10, 14, …? (a) 44 (b) 46 (c) 48 (d) 50
  36. 36.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 105 (c) 240 (d) 120
  37. 37.What is the 26th term of the AP 15, 21, 27, 33, …? (a) 156 (b) 171 (c) 150 (d) 165
  38. 38.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 77 (b) 78 (c) 154 (d) 14
  39. 39.Which term of the AP 4, 6, 8, 10, … is 76? (a) 39th (b) 36th (c) 38th (d) 37th
  40. 40.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 55 (c) 67 (d) 66

Answer key

  1. 198
  2. 115
  3. 15
  4. 80
  5. 30
  6. 99
  7. 39
  8. 256
  9. 2926
  10. 441
  11. 17
  12. 374
  13. 81
  14. 20
  15. 155
  16. 5
  17. 132
  18. 58
  19. 666
  20. 1953
  21. 144
  22. 161
  23. 1653
  24. 360
  25. 108
  26. 784
  27. 990
  28. 72
  29. 124
  30. 71
  31. 352
  32. 206
  33. 3081
  34. 194
  35. 46
  36. 120
  37. 165
  38. 77
  39. 37th
  40. 66

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