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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 685 · 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 1, 8, 15, ?, 29? (a) 23 (b) 21 (c) 29 (d) 22
  2. 2.What is the 10th term of the AP 18, 25, 32, 39, …? (a) 81 (b) 63 (c) 88 (d) 70
  3. 3.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 480 (b) 888 (c) 444 (d) 70
  4. 4.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  5. 5.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 729 (d) 756
  6. 6.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 13 (b) 11 (c) 10 (d) 9
  7. 7.What is the 26th term of the AP 11, 14, 17, 20, …? (a) 78 (b) 86 (c) 75 (d) 89
  8. 8.Which term of the AP 18, 23, 28, 33, … is 108? (a) 21st (b) 19th (c) 20th (d) 18th
  9. 9.What is the 11th term of the AP 4, 11, 18, 25, …? (a) 70 (b) 74 (c) 81 (d) 77
  10. 10.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
  11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 45 (d) 90
  12. 12.What is the 38th term of the AP 9, 11, 13, 15, …? (a) 76 (b) 83 (c) 74 (d) 85
  13. 13.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 21 (d) 11
  14. 14.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 49 (d) 625
  15. 15.What is the 39th term of the AP 4, 10, 16, 22, …? (a) 232 (b) 234 (c) 228 (d) 238
  16. 16.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 30 (b) 28 (c) 29 (d) 38
  17. 17.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4095 (c) 4186 (d) 4187
  18. 18.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 156 (b) 38 (c) 138 (d) 276
  19. 19.What is the 32nd term of the AP 15, 20, 25, 30, …? (a) 175 (b) 170 (c) 155 (d) 160
  20. 20.Which term of the AP 3, 12, 21, 30, … is 210? (a) 23rd (b) 26th (c) 24th (d) 25th
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  22. 22.What is the 20th term of the AP 16, 20, 24, 28, …? (a) 92 (b) 80 (c) 76 (d) 96
  23. 23.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 7310 (c) 3655 (d) 3656
  24. 24.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 460 (b) 41 (c) 250 (d) 230
  25. 25.What is the missing term in the AP 20, 24, 28, ?, 36? (a) 31 (b) 32 (c) 33 (d) 36
  26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 256 (d) 272
  27. 27.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3828 (d) 3916
  28. 28.What is the 33rd term of the AP 9, 17, 25, 33, …? (a) 256 (b) 264 (c) 273 (d) 265
  29. 29.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 17 (b) 13 (c) 12 (d) 14
  30. 30.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 112 (b) 63 (c) 14 (d) 56
  31. 31.What is the 26th term of the AP 7, 11, 15, 19, …? (a) 111 (b) 104 (c) 100 (d) 107
  32. 32.What is the 13th term of the AP 8, 12, 16, 20, …? (a) 60 (b) 48 (c) 56 (d) 52
  33. 33.What is the 29th term of the AP 20, 23, 26, 29, …? (a) 104 (b) 87 (c) 107 (d) 84
  34. 34.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 10 (c) 90 (d) 45
  35. 35.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 1654 (c) 3306 (d) 1596
  36. 36.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 84 (b) 156 (c) 12 (d) 78
  37. 37.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 676 (d) 351
  38. 38.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 270 (c) 250 (d) 43
  39. 39.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 57 (c) 870 (d) 435
  40. 40.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28

Answer key

  1. 22
  2. 81
  3. 444
  4. 576
  5. 729
  6. 10
  7. 86
  8. 19th
  9. 74
  10. 400
  11. 81
  12. 83
  13. 36
  14. 625
  15. 232
  16. 29
  17. 4186
  18. 138
  19. 170
  20. 24th
  21. 121
  22. 92
  23. 3655
  24. 230
  25. 32
  26. 256
  27. 3916
  28. 265
  29. 13
  30. 56
  31. 107
  32. 56
  33. 104
  34. 45
  35. 1653
  36. 78
  37. 676
  38. 250
  39. 841
  40. 49

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