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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 652 · 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 6 terms of the AP 8, 10, 12, …? (a) 156 (b) 18 (c) 84 (d) 78
  2. 2.What is the 28th term of the AP 13, 17, 21, 25, …? (a) 125 (b) 112 (c) 121 (d) 108
  3. 3.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 5852 (c) 2926 (d) 2850
  4. 4.Which term of the AP 3, 7, 11, 15, … is 71? (a) 19th (b) 17th (c) 18th (d) 20th
  5. 5.Which term of the AP 3, 6, 9, 12, … is 99? (a) 35th (b) 33rd (c) 32nd (d) 34th
  6. 6.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 722 (c) 1482 (d) 741
  7. 7.What is the 28th term of the AP 7, 10, 13, 16, …? (a) 81 (b) 91 (c) 84 (d) 88
  8. 8.What is the 27th term of the AP 16, 24, 32, 40, …? (a) 216 (b) 232 (c) 208 (d) 224
  9. 9.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 1081 (c) 1129 (d) 2256
  10. 10.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 50 (c) 110 (d) 55
  11. 11.What is the 24th term of the AP 16, 20, 24, 28, …? (a) 92 (b) 108 (c) 96 (d) 112
  12. 12.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 23 (b) 19 (c) 18 (d) 17
  13. 13.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 4830 (c) 2415 (d) 2416
  14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  15. 15.What is the 25th term of the AP 1, 5, 9, 13, …? (a) 100 (b) 101 (c) 97 (d) 96
  16. 16.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 25 (b) 306 (c) 162 (d) 153
  17. 17.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 1122 (c) 528 (d) 561
  18. 18.What is the 22nd term of the AP 16, 19, 22, 25, …? (a) 79 (b) 63 (c) 82 (d) 66
  19. 19.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 174 (b) 27 (c) 87 (d) 102
  20. 20.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 326 (c) 300 (d) 325
  21. 21.Which term of the AP 16, 19, 22, 25, … is 79? (a) 21st (b) 23rd (c) 22nd (d) 24th
  22. 22.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 135 (c) 22 (d) 126
  23. 23.What is the 14th term of the AP 10, 16, 22, 28, …? (a) 94 (b) 84 (c) 88 (d) 78
  24. 24.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 78 (b) 72 (c) 17 (d) 144
  25. 25.What is the 12th term of the AP 16, 18, 20, 22, …? (a) 40 (b) 22 (c) 38 (d) 24
  26. 26.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 28 (c) 108 (d) 93
  27. 27.Which term of the AP 9, 13, 17, 21, … is 57? (a) 15th (b) 14th (c) 13th (d) 12th
  28. 28.What is the 31st term of the AP 17, 19, 21, 23, …? (a) 77 (b) 60 (c) 79 (d) 62
  29. 29.What is the 22nd term of the AP 1, 5, 9, 13, …? (a) 89 (b) 84 (c) 88 (d) 85
  30. 30.What is the 17th term of the AP 4, 7, 10, 13, …? (a) 52 (b) 48 (c) 55 (d) 51
  31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 406 (d) 55
  32. 32.What is the 35th term of the AP 17, 22, 27, 32, …? (a) 192 (b) 187 (c) 175 (d) 170
  33. 33.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 9312 (c) 4608 (d) 4560
  34. 34.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 8 (b) 6 (c) 9 (d) 7
  35. 35.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 600 (b) 330 (c) 300 (d) 57
  36. 36.Which term of the AP 7, 9, 11, 13, … is 27? (a) 11th (b) 12th (c) 13th (d) 10th
  37. 37.What is the 24th term of the AP 14, 19, 24, 29, …? (a) 134 (b) 129 (c) 115 (d) 120
  38. 38.What is the 26th term of the AP 1, 5, 9, 13, …? (a) 104 (b) 101 (c) 100 (d) 105
  39. 39.What is the 15th term of the AP 17, 21, 25, 29, …? (a) 56 (b) 73 (c) 60 (d) 77
  40. 40.Which term of the AP 5, 9, 13, 17, … is 145? (a) 37th (b) 35th (c) 38th (d) 36th

Answer key

  1. 78
  2. 121
  3. 2926
  4. 18th
  5. 33rd
  6. 741
  7. 88
  8. 224
  9. 1128
  10. 55
  11. 108
  12. 18
  13. 2415
  14. 729
  15. 97
  16. 153
  17. 561
  18. 79
  19. 87
  20. 325
  21. 22nd
  22. 126
  23. 88
  24. 72
  25. 38
  26. 93
  27. 13th
  28. 77
  29. 85
  30. 52
  31. 784
  32. 187
  33. 4656
  34. 7
  35. 300
  36. 11th
  37. 129
  38. 101
  39. 73
  40. 36th

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