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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 554 · 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 18th term of the AP 2, 4, 6, 8, …? (a) 36 (b) 38 (c) 34 (d) 37
  2. 2.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 360 (b) 720 (c) 52 (d) 384
  3. 3.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  4. 4.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 1482 (c) 722 (d) 741
  5. 5.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 900 (c) 59 (d) 930
  6. 6.What is the 21st term of the AP 17, 19, 21, 23, …? (a) 57 (b) 40 (c) 59 (d) 42
  7. 7.What is the 35th term of the AP 2, 7, 12, 17, …? (a) 175 (b) 170 (c) 172 (d) 177
  8. 8.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 256 (d) 272
  9. 9.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 289 (d) 306
  10. 10.What is the 38th term of the AP 2, 5, 8, 11, …? (a) 114 (b) 113 (c) 111 (d) 116
  11. 11.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 1722 (c) 861 (d) 862
  12. 12.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 250 (b) 125 (c) 130 (d) 17
  13. 13.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 992 (c) 496 (d) 465
  14. 14.What is the 17th term of the AP 9, 17, 25, 33, …? (a) 136 (b) 145 (c) 128 (d) 137
  15. 15.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 120 (c) 105 (d) 240
  16. 16.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 450 (c) 435 (d) 465
  17. 17.What is the 36th term of the AP 11, 19, 27, 35, …? (a) 280 (b) 299 (c) 291 (d) 288
  18. 18.What is the 20th term of the AP 17, 21, 25, 29, …? (a) 93 (b) 97 (c) 76 (d) 80
  19. 19.What is the 23rd term of the AP 18, 25, 32, 39, …? (a) 161 (b) 172 (c) 179 (d) 154
  20. 20.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 432 (b) 44 (c) 221 (d) 216
  21. 21.What is the 38th term of the AP 20, 29, 38, 47, …? (a) 333 (b) 362 (c) 342 (d) 353
  22. 22.What is the 19th term of the AP 2, 9, 16, 23, …? (a) 128 (b) 135 (c) 133 (d) 126
  23. 23.What is the 35th term of the AP 7, 13, 19, 25, …? (a) 210 (b) 217 (c) 204 (d) 211
  24. 24.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 8372 (c) 4187 (d) 4186
  25. 25.What is the 15th term of the AP 13, 15, 17, 19, …? (a) 30 (b) 28 (c) 41 (d) 43
  26. 26.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 42 (b) 203 (c) 396 (d) 198
  27. 27.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 105 (b) 30 (c) 100 (d) 200
  28. 28.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 660 (b) 335 (c) 55 (d) 330
  29. 29.Which term of the AP 1, 7, 13, 19, … is 157? (a) 29th (b) 27th (c) 28th (d) 26th
  30. 30.What is the 19th term of the AP 3, 10, 17, 24, …? (a) 136 (b) 126 (c) 129 (d) 133
  31. 31.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 4802 (c) 4851 (d) 9702
  32. 32.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 9 (d) 25
  33. 33.What is the 10th term of the AP 16, 20, 24, 28, …? (a) 52 (b) 40 (c) 56 (d) 36
  34. 34.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 540 (b) 270 (c) 54 (d) 297
  35. 35.What is the 37th term of the AP 11, 13, 15, 17, …? (a) 83 (b) 72 (c) 74 (d) 85
  36. 36.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 1260 (c) 630 (d) 595
  37. 37.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 104 (b) 22 (c) 92 (d) 184
  38. 38.What is the 13th term of the AP 19, 26, 33, 40, …? (a) 103 (b) 84 (c) 110 (d) 91
  39. 39.Which term of the AP 3, 8, 13, 18, … is 38? (a) 9th (b) 10th (c) 8th (d) 7th
  40. 40.Which term of the AP 11, 18, 25, 32, … is 109? (a) 14th (b) 16th (c) 17th (d) 15th

Answer key

  1. 36
  2. 360
  3. 121
  4. 741
  5. 900
  6. 57
  7. 172
  8. 256
  9. 289
  10. 113
  11. 861
  12. 125
  13. 496
  14. 137
  15. 120
  16. 465
  17. 291
  18. 93
  19. 172
  20. 216
  21. 353
  22. 128
  23. 211
  24. 4186
  25. 41
  26. 198
  27. 100
  28. 330
  29. 27th
  30. 129
  31. 4851
  32. 25
  33. 52
  34. 270
  35. 83
  36. 630
  37. 92
  38. 103
  39. 8th
  40. 15th

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