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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 195 · 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 missing term in the AP 17, ?, 23, 26, 29? (a) 21 (b) 23 (c) 20 (d) 19
  2. 2.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 70 (b) 23 (c) 130 (d) 65
  3. 3.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 414 (b) 207 (c) 39 (d) 225
  4. 4.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 85 (b) 170 (c) 29 (d) 100
  5. 5.Which term of the AP 8, 10, 12, 14, … is 62? (a) 31st (b) 28th (c) 29th (d) 27th
  6. 6.What is the 36th term of the AP 12, 14, 16, 18, …? (a) 72 (b) 84 (c) 70 (d) 82
  7. 7.What is the 34th term of the AP 13, 15, 17, 19, …? (a) 68 (b) 79 (c) 81 (d) 66
  8. 8.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 15 (b) 220 (c) 111 (d) 110
  9. 9.What is the 40th term of the AP 7, 16, 25, 34, …? (a) 351 (b) 367 (c) 360 (d) 358
  10. 10.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 21 (b) 20 (c) 24 (d) 22
  11. 11.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 1830 (c) 1891 (d) 3782
  12. 12.What is the 35th term of the AP 6, 13, 20, 27, …? (a) 245 (b) 251 (c) 244 (d) 238
  13. 13.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 32 (b) 26 (c) 28 (d) 27
  14. 14.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 34 (b) 210 (c) 420 (d) 228
  15. 15.What is the 37th term of the AP 2, 8, 14, 20, …? (a) 216 (b) 222 (c) 218 (d) 224
  16. 16.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 130 (c) 21 (d) 240
  17. 17.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 25 (b) 336 (c) 180 (d) 168
  18. 18.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 162 (b) 324 (c) 168 (d) 19
  19. 19.What is the 18th term of the AP 9, 17, 25, 33, …? (a) 153 (b) 136 (c) 145 (d) 144
  20. 20.What is the 35th term of the AP 1, 4, 7, 10, …? (a) 106 (b) 105 (c) 103 (d) 102
  21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 253 (d) 43
  22. 22.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 136 (b) 256 (c) 23 (d) 128
  23. 23.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3403 (c) 3487 (d) 3486
  24. 24.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 30 (b) 144 (c) 256 (d) 128
  25. 25.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 330 (b) 165 (c) 30 (d) 180
  26. 26.What is the 23rd term of the AP 12, 19, 26, 33, …? (a) 161 (b) 154 (c) 166 (d) 173
  27. 27.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 18 (b) 75 (c) 70 (d) 140
  28. 28.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 54 (b) 408 (c) 768 (d) 384
  29. 29.What is the missing term in the AP 15, ?, 19, 21, 23? (a) 16 (b) 19 (c) 18 (d) 17
  30. 30.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 70 (b) 130 (c) 65 (d) 17
  31. 31.What is the 13th term of the AP 14, 23, 32, 41, …? (a) 117 (b) 108 (c) 131 (d) 122
  32. 32.What is the 21st term of the AP 16, 19, 22, 25, …? (a) 60 (b) 63 (c) 76 (d) 79
  33. 33.What is the 36th term of the AP 11, 13, 15, 17, …? (a) 83 (b) 72 (c) 81 (d) 70
  34. 34.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 36 (d) 64
  35. 35.What is the 19th term of the AP 15, 17, 19, 21, …? (a) 36 (b) 51 (c) 38 (d) 53
  36. 36.What is the 26th term of the AP 13, 16, 19, 22, …? (a) 91 (b) 75 (c) 78 (d) 88
  37. 37.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 288 (b) 144 (c) 162 (d) 39
  38. 38.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 26 (b) 24 (c) 25 (d) 32
  39. 39.What is the 34th term of the AP 8, 14, 20, 26, …? (a) 198 (b) 204 (c) 212 (d) 206
  40. 40.What is the 21st term of the AP 18, 22, 26, 30, …? (a) 84 (b) 98 (c) 80 (d) 102

Answer key

  1. 20
  2. 65
  3. 207
  4. 85
  5. 28th
  6. 82
  7. 79
  8. 110
  9. 358
  10. 21
  11. 1891
  12. 244
  13. 27
  14. 210
  15. 218
  16. 120
  17. 168
  18. 162
  19. 145
  20. 103
  21. 484
  22. 128
  23. 3486
  24. 128
  25. 165
  26. 166
  27. 70
  28. 384
  29. 17
  30. 65
  31. 122
  32. 76
  33. 81
  34. 64
  35. 51
  36. 88
  37. 144
  38. 25
  39. 206
  40. 98

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