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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 474 · 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 11 terms of the AP 1, 2, 3, …? (a) 66 (b) 132 (c) 11 (d) 67
  2. 2.What is the 20th term of the AP 2, 4, 6, 8, …? (a) 42 (b) 40 (c) 38 (d) 41
  3. 3.What is the 24th term of the AP 5, 7, 9, 11, …? (a) 46 (b) 48 (c) 53 (d) 51
  4. 4.What is the 23rd term of the AP 6, 8, 10, 12, …? (a) 50 (b) 46 (c) 44 (d) 52
  5. 5.What is the 35th term of the AP 5, 10, 15, 20, …? (a) 170 (b) 180 (c) 175 (d) 176
  6. 6.Which term of the AP 1, 9, 17, 25, … is 161? (a) 23rd (b) 20th (c) 21st (d) 22nd
  7. 7.Which term of the AP 19, 26, 33, 40, … is 257? (a) 34th (b) 35th (c) 36th (d) 37th
  8. 8.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1596 (c) 3192 (d) 1540
  9. 9.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 576 (b) 56 (c) 288 (d) 315
  10. 10.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 1260 (c) 630 (d) 631
  11. 11.What is the missing term in the AP 17, 25, 33, ?, 49? (a) 49 (b) 40 (c) 41 (d) 42
  12. 12.What is the missing term in the AP 16, 19, 22, ?, 28? (a) 26 (b) 25 (c) 28 (d) 24
  13. 13.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4465 (c) 4418 (d) 4371
  14. 14.What is the 22nd term of the AP 2, 5, 8, 11, …? (a) 65 (b) 68 (c) 66 (d) 63
  15. 15.What is the 35th term of the AP 5, 9, 13, 17, …? (a) 140 (b) 141 (c) 145 (d) 136
  16. 16.What is the 26th term of the AP 16, 19, 22, 25, …? (a) 75 (b) 91 (c) 94 (d) 78
  17. 17.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 440 (b) 40 (c) 220 (d) 240
  18. 18.What is the 31st term of the AP 20, 27, 34, 41, …? (a) 210 (b) 230 (c) 237 (d) 217
  19. 19.Which term of the AP 2, 4, 6, 8, … is 38? (a) 20th (b) 21st (c) 18th (d) 19th
  20. 20.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 418 (b) 451 (c) 836 (d) 68
  21. 21.Which term of the AP 1, 6, 11, 16, … is 191? (a) 39th (b) 40th (c) 38th (d) 41st
  22. 22.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  23. 23.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 232 (b) 208 (c) 47 (d) 416
  24. 24.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 14 (b) 13 (c) 12 (d) 16
  25. 25.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 65 (b) 385 (c) 418 (d) 770
  26. 26.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 43 (b) 200 (c) 176 (d) 352
  27. 27.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 38 (b) 37 (c) 36 (d) 46
  28. 28.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 65 (b) 23 (c) 130 (d) 70
  29. 29.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 2162 (c) 1081 (d) 1058
  30. 30.What is the missing term in the AP 8, ?, 14, 17, 20? (a) 12 (b) 10 (c) 14 (d) 11
  31. 31.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 1953 (c) 2017 (d) 4032
  32. 32.What is the 38th term of the AP 16, 22, 28, 34, …? (a) 222 (b) 244 (c) 238 (d) 228
  33. 33.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 105 (c) 240 (d) 120
  34. 34.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 11 (b) 10 (c) 9 (d) 8
  35. 35.What is the 38th term of the AP 17, 19, 21, 23, …? (a) 93 (b) 91 (c) 76 (d) 74
  36. 36.Which term of the AP 7, 11, 15, 19, … is 111? (a) 28th (b) 29th (c) 26th (d) 27th
  37. 37.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 15 (b) 5 (c) 16 (d) 30
  38. 38.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 24 (b) 216 (c) 120 (d) 108
  39. 39.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 6642 (c) 3322 (d) 3240
  40. 40.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 169 (c) 182 (d) 25

Answer key

  1. 66
  2. 40
  3. 51
  4. 50
  5. 175
  6. 21st
  7. 35th
  8. 1596
  9. 288
  10. 630
  11. 41
  12. 25
  13. 4465
  14. 65
  15. 141
  16. 91
  17. 220
  18. 230
  19. 19th
  20. 418
  21. 39th
  22. 100
  23. 208
  24. 13
  25. 385
  26. 176
  27. 37
  28. 65
  29. 1081
  30. 11
  31. 2016
  32. 238
  33. 120
  34. 9
  35. 91
  36. 27th
  37. 15
  38. 108
  39. 3321
  40. 169

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