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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 428 · 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 79? (a) 3081 (b) 3160 (c) 3161 (d) 6320
  2. 2.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 55 (d) 784
  3. 3.What is the 38th term of the AP 2, 11, 20, 29, …? (a) 344 (b) 342 (c) 333 (d) 335
  4. 4.What is the 20th term of the AP 3, 7, 11, 15, …? (a) 79 (b) 83 (c) 76 (d) 80
  5. 5.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 207 (b) 378 (c) 189 (d) 37
  6. 6.What is the missing term in the AP 20, 25, 30, ?, 40? (a) 34 (b) 36 (c) 40 (d) 35
  7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 28 (d) 13
  8. 8.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 31 (b) 30 (c) 36 (d) 29
  9. 9.What is the 18th term of the AP 16, 25, 34, 43, …? (a) 162 (b) 178 (c) 169 (d) 153
  10. 10.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 306 (c) 136 (d) 153
  11. 11.What is the 24th term of the AP 16, 20, 24, 28, …? (a) 112 (b) 92 (c) 108 (d) 96
  12. 12.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 15 (b) 24 (c) 17 (d) 16
  13. 13.What is the missing term in the AP 9, 15, ?, 27, 33? (a) 21 (b) 20 (c) 22 (d) 27
  14. 14.What is the 36th term of the AP 5, 13, 21, 29, …? (a) 288 (b) 293 (c) 280 (d) 285
  15. 15.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3321 (c) 6806 (d) 3362
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 90 (d) 45
  17. 17.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 30 (b) 31 (c) 34 (d) 29
  18. 18.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 108 (b) 216 (c) 120 (d) 28
  19. 19.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 161 (b) 38 (c) 322 (d) 166
  20. 20.What is the 29th term of the AP 9, 14, 19, 24, …? (a) 140 (b) 145 (c) 149 (d) 154
  21. 21.Which term of the AP 13, 18, 23, 28, … is 203? (a) 40th (b) 39th (c) 41st (d) 38th
  22. 22.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 132 (c) 264 (d) 150
  23. 23.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 98 (b) 91 (c) 19 (d) 182
  24. 24.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5000 (c) 10100 (d) 5050
  25. 25.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 50 (b) 98 (c) 49 (d) 10
  26. 26.What is the 26th term of the AP 19, 25, 31, 37, …? (a) 169 (b) 156 (c) 150 (d) 175
  27. 27.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 117 (b) 112 (c) 224 (d) 31
  28. 28.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 6 (b) 7 (c) 10 (d) 8
  29. 29.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 72 (c) 66 (d) 156
  30. 30.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 17 (b) 15 (c) 16 (d) 14
  31. 31.What is the 35th term of the AP 5, 7, 9, 11, …? (a) 70 (b) 68 (c) 73 (d) 75
  32. 32.What is the 10th term of the AP 5, 12, 19, 26, …? (a) 75 (b) 63 (c) 70 (d) 68
  33. 33.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 4186 (c) 8372 (d) 4187
  34. 34.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 1653 (c) 3422 (d) 1711
  35. 35.What is the 26th term of the AP 12, 15, 18, 21, …? (a) 90 (b) 78 (c) 87 (d) 75
  36. 36.What is the 11th term of the AP 9, 15, 21, 27, …? (a) 75 (b) 60 (c) 66 (d) 69
  37. 37.Which term of the AP 17, 25, 33, 41, … is 225? (a) 27th (b) 26th (c) 28th (d) 29th
  38. 38.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 3306 (c) 1654 (d) 1596
  39. 39.What is the 35th term of the AP 14, 20, 26, 32, …? (a) 204 (b) 210 (c) 218 (d) 224
  40. 40.What is the 22nd term of the AP 19, 21, 23, 25, …? (a) 63 (b) 42 (c) 44 (d) 61

Answer key

  1. 3160
  2. 784
  3. 335
  4. 79
  5. 189
  6. 35
  7. 49
  8. 30
  9. 169
  10. 153
  11. 108
  12. 16
  13. 21
  14. 285
  15. 3403
  16. 81
  17. 30
  18. 108
  19. 161
  20. 149
  21. 39th
  22. 132
  23. 91
  24. 5050
  25. 49
  26. 169
  27. 112
  28. 7
  29. 78
  30. 15
  31. 73
  32. 68
  33. 4186
  34. 1711
  35. 87
  36. 69
  37. 27th
  38. 1653
  39. 218
  40. 61

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