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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 177 · 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 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  2. 2.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 184 (b) 104 (c) 92 (d) 22
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 231 (d) 441
  4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 784 (d) 406
  5. 5.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 75 (b) 21 (c) 78 (d) 150
  6. 6.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 858 (b) 69 (c) 429 (d) 462
  7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 110 (d) 55
  8. 8.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 25 (b) 23 (c) 26 (d) 24
  9. 9.What is the 35th term of the AP 15, 19, 23, 27, …? (a) 155 (b) 151 (c) 136 (d) 140
  10. 10.What is the 25th term of the AP 3, 9, 15, 21, …? (a) 150 (b) 153 (c) 144 (d) 147
  11. 11.What is the 35th term of the AP 9, 12, 15, 18, …? (a) 111 (b) 114 (c) 105 (d) 102
  12. 12.What is the 22nd term of the AP 19, 25, 31, 37, …? (a) 151 (b) 145 (c) 132 (d) 126
  13. 13.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 324 (b) 19 (c) 168 (d) 162
  14. 14.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  15. 15.What is the 30th term of the AP 13, 20, 27, 34, …? (a) 203 (b) 216 (c) 210 (d) 223
  16. 16.Which term of the AP 3, 10, 17, 24, … is 199? (a) 30th (b) 31st (c) 28th (d) 29th
  17. 17.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 300 (d) 47
  18. 18.What is the 26th term of the AP 17, 21, 25, 29, …? (a) 121 (b) 117 (c) 100 (d) 104
  19. 19.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 20 (b) 22 (c) 21 (d) 29
  20. 20.What is the 10th term of the AP 19, 21, 23, 25, …? (a) 39 (b) 18 (c) 20 (d) 37
  21. 21.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 374 (c) 27 (d) 187
  22. 22.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 13 (b) 11 (c) 10 (d) 9
  23. 23.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 16 (b) 12 (c) 11 (d) 10
  24. 24.Which term of the AP 16, 18, 20, 22, … is 78? (a) 39th (b) 32nd (c) 31st (d) 33rd
  25. 25.Which term of the AP 9, 11, 13, 15, … is 33? (a) 15th (b) 12th (c) 14th (d) 13th
  26. 26.What is the 24th term of the AP 8, 14, 20, 26, …? (a) 138 (b) 146 (c) 144 (d) 152
  27. 27.Which term of the AP 18, 22, 26, 30, … is 166? (a) 38th (b) 40th (c) 37th (d) 39th
  28. 28.What is the 38th term of the AP 14, 22, 30, 38, …? (a) 318 (b) 296 (c) 304 (d) 310
  29. 29.What is the 35th term of the AP 9, 18, 27, 36, …? (a) 324 (b) 316 (c) 306 (d) 315
  30. 30.What is the 12th term of the AP 17, 24, 31, 38, …? (a) 101 (b) 94 (c) 84 (d) 77
  31. 31.What is the 15th term of the AP 9, 12, 15, 18, …? (a) 42 (b) 54 (c) 51 (d) 45
  32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  33. 33.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 98 (c) 105 (d) 210
  34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 253 (d) 43
  35. 35.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 25 (b) 27 (c) 33 (d) 26
  36. 36.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 10 (b) 12 (c) 13 (d) 11
  37. 37.What is the 27th term of the AP 5, 13, 21, 29, …? (a) 208 (b) 221 (c) 216 (d) 213
  38. 38.Which term of the AP 12, 14, 16, 18, … is 82? (a) 41st (b) 35th (c) 36th (d) 37th
  39. 39.What is the 28th term of the AP 2, 5, 8, 11, …? (a) 81 (b) 84 (c) 83 (d) 86
  40. 40.Which term of the AP 12, 15, 18, 21, … is 51? (a) 17th (b) 14th (c) 13th (d) 15th

Answer key

  1. 256
  2. 92
  3. 441
  4. 784
  5. 75
  6. 429
  7. 100
  8. 24
  9. 151
  10. 147
  11. 111
  12. 145
  13. 162
  14. 25
  15. 216
  16. 29th
  17. 576
  18. 117
  19. 21
  20. 37
  21. 187
  22. 10
  23. 11
  24. 32nd
  25. 13th
  26. 146
  27. 38th
  28. 310
  29. 315
  30. 94
  31. 51
  32. 144
  33. 105
  34. 484
  35. 26
  36. 11
  37. 213
  38. 36th
  39. 83
  40. 14th

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