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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 725 · 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 6, 12, 18, 24, … is 168? (a) 27th (b) 29th (c) 28th (d) 30th
  2. 2.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 224 (b) 119 (c) 112 (d) 22
  3. 3.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 17 (b) 16 (c) 22 (d) 18
  4. 4.What is the 22nd term of the AP 6, 11, 16, 21, …? (a) 116 (b) 105 (c) 110 (d) 111
  5. 5.Which term of the AP 16, 23, 30, 37, … is 226? (a) 33rd (b) 32nd (c) 30th (d) 31st
  6. 6.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 30 (b) 27 (c) 28 (d) 26
  7. 7.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 121 (d) 132
  8. 8.What is the 25th term of the AP 15, 22, 29, 36, …? (a) 175 (b) 183 (c) 168 (d) 190
  9. 9.What is the 32nd term of the AP 16, 23, 30, 37, …? (a) 233 (b) 217 (c) 224 (d) 240
  10. 10.What is the 39th term of the AP 19, 22, 25, 28, …? (a) 117 (b) 136 (c) 133 (d) 114
  11. 11.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 741 (c) 1482 (d) 722
  12. 12.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 135 (c) 22 (d) 126
  13. 13.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 19 (d) 100
  14. 14.What is the sum of all the whole numbers from 1 to 58? (a) 1711 (b) 1682 (c) 3422 (d) 1653
  15. 15.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 152 (b) 36 (c) 294 (d) 147
  16. 16.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 270 (b) 144 (c) 135 (d) 23
  17. 17.What is the 12th term of the AP 11, 20, 29, 38, …? (a) 119 (b) 108 (c) 99 (d) 110
  18. 18.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 176 (b) 34 (c) 160 (d) 320
  19. 19.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  20. 20.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 168 (b) 304 (c) 33 (d) 152
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 169 (c) 25 (d) 91
  22. 22.What is the 34th term of the AP 19, 22, 25, 28, …? (a) 121 (b) 99 (c) 118 (d) 102
  23. 23.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 379 (b) 59 (c) 374 (d) 748
  24. 24.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 396 (b) 198 (c) 34 (d) 201
  25. 25.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 108 (c) 198 (d) 19
  26. 26.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4465 (c) 4418 (d) 4371
  27. 27.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 173 (b) 168 (c) 336 (d) 39
  28. 28.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 61 (b) 402 (c) 804 (d) 432
  29. 29.What is the sum of all the whole numbers from 1 to 79? (a) 6320 (b) 3161 (c) 3160 (d) 3081
  30. 30.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 350 (b) 640 (c) 59 (d) 320
  31. 31.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4186 (c) 4095 (d) 8372
  32. 32.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 11 (b) 17 (c) 10 (d) 9
  33. 33.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 812 (d) 55
  34. 34.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2211 (c) 2178 (d) 2145
  35. 35.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 18 (b) 16 (c) 17 (d) 19
  36. 36.What is the 23rd term of the AP 11, 16, 21, 26, …? (a) 126 (b) 121 (c) 110 (d) 115
  37. 37.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  38. 38.What is the 35th term of the AP 20, 26, 32, 38, …? (a) 230 (b) 210 (c) 224 (d) 204
  39. 39.What is the 11th term of the AP 8, 14, 20, 26, …? (a) 66 (b) 68 (c) 74 (d) 60
  40. 40.What is the 16th term of the AP 9, 11, 13, 15, …? (a) 41 (b) 30 (c) 39 (d) 32

Answer key

  1. 28th
  2. 112
  3. 17
  4. 111
  5. 31st
  6. 27
  7. 121
  8. 183
  9. 233
  10. 133
  11. 741
  12. 126
  13. 100
  14. 1711
  15. 147
  16. 135
  17. 110
  18. 160
  19. 81
  20. 152
  21. 169
  22. 118
  23. 374
  24. 198
  25. 99
  26. 4465
  27. 168
  28. 402
  29. 3160
  30. 320
  31. 4186
  32. 10
  33. 784
  34. 2211
  35. 17
  36. 121
  37. 441
  38. 224
  39. 68
  40. 39

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