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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 566 · 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 36th term of the AP 15, 23, 31, 39, …? (a) 295 (b) 303 (c) 280 (d) 288
  2. 2.What is the 37th term of the AP 11, 15, 19, 23, …? (a) 155 (b) 159 (c) 148 (d) 144
  3. 3.What is the 40th term of the AP 9, 18, 27, 36, …? (a) 369 (b) 351 (c) 360 (d) 361
  4. 4.What is the missing term in the AP 16, 20, ?, 28, 32? (a) 23 (b) 28 (c) 24 (d) 25
  5. 5.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 210 (b) 114 (c) 25 (d) 105
  6. 6.What is the 26th term of the AP 16, 23, 30, 37, …? (a) 182 (b) 198 (c) 191 (d) 175
  7. 7.What is the 11th term of the AP 19, 22, 25, 28, …? (a) 30 (b) 33 (c) 52 (d) 49
  8. 8.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 396 (b) 216 (c) 198 (d) 38
  9. 9.What is the 29th term of the AP 14, 16, 18, 20, …? (a) 72 (b) 70 (c) 58 (d) 56
  10. 10.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 154 (b) 308 (c) 40 (d) 175
  11. 11.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 31 (b) 222 (c) 111 (d) 126
  12. 12.What is the 27th term of the AP 14, 17, 20, 23, …? (a) 81 (b) 95 (c) 92 (d) 78
  13. 13.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 204 (b) 27 (c) 192 (d) 384
  14. 14.What is the 11th term of the AP 7, 13, 19, 25, …? (a) 60 (b) 66 (c) 67 (d) 73
  15. 15.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 41 (b) 231 (c) 462 (d) 253
  16. 16.Which term of the AP 5, 8, 11, 14, … is 29? (a) 9th (b) 10th (c) 11th (d) 8th
  17. 17.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 396 (b) 66 (c) 792 (d) 429
  18. 18.What is the missing term in the AP 15, 17, ?, 21, 23? (a) 20 (b) 18 (c) 19 (d) 21
  19. 19.Which term of the AP 8, 13, 18, 23, … is 108? (a) 21st (b) 23rd (c) 22nd (d) 20th
  20. 20.What is the 36th term of the AP 4, 8, 12, 16, …? (a) 140 (b) 144 (c) 145 (d) 148
  21. 21.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 41 (d) 441
  22. 22.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 496 (c) 992 (d) 465
  23. 23.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 200 (b) 220 (c) 38 (d) 400
  24. 24.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 54 (c) 7 (d) 27
  25. 25.Which term of the AP 14, 21, 28, 35, … is 112? (a) 16th (b) 15th (c) 17th (d) 14th
  26. 26.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 947 (c) 1892 (d) 946
  27. 27.What is the 29th term of the AP 11, 16, 21, 26, …? (a) 145 (b) 156 (c) 151 (d) 140
  28. 28.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1891 (c) 3906 (d) 1953
  29. 29.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2278 (c) 2346 (d) 2312
  30. 30.What is the 28th term of the AP 7, 9, 11, 13, …? (a) 56 (b) 54 (c) 61 (d) 63
  31. 31.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 69 (b) 858 (c) 462 (d) 429
  32. 32.What is the 40th term of the AP 6, 8, 10, 12, …? (a) 78 (b) 84 (c) 86 (d) 80
  33. 33.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 4802 (c) 9702 (d) 4753
  34. 34.Which term of the AP 19, 23, 27, 31, … is 171? (a) 41st (b) 38th (c) 40th (d) 39th
  35. 35.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 144 (b) 286 (c) 143 (d) 18
  36. 36.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 153 (d) 33
  37. 37.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  38. 38.Which term of the AP 11, 14, 17, 20, … is 104? (a) 33rd (b) 31st (c) 34th (d) 32nd
  39. 39.What is the 28th term of the AP 7, 11, 15, 19, …? (a) 108 (b) 112 (c) 119 (d) 115
  40. 40.Which term of the AP 18, 24, 30, 36, … is 138? (a) 23rd (b) 20th (c) 21st (d) 22nd

Answer key

  1. 295
  2. 155
  3. 360
  4. 24
  5. 105
  6. 191
  7. 49
  8. 198
  9. 70
  10. 154
  11. 111
  12. 92
  13. 192
  14. 67
  15. 231
  16. 9th
  17. 396
  18. 19
  19. 21st
  20. 144
  21. 441
  22. 496
  23. 200
  24. 27
  25. 15th
  26. 946
  27. 151
  28. 1953
  29. 2346
  30. 61
  31. 429
  32. 84
  33. 4851
  34. 39th
  35. 143
  36. 289
  37. 64
  38. 32nd
  39. 115
  40. 21st

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