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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 770 · 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 9 terms of the AP 10, 15, 20, …? (a) 275 (b) 270 (c) 50 (d) 540
  2. 2.What is the 12th term of the AP 3, 8, 13, 18, …? (a) 58 (b) 60 (c) 55 (d) 63
  3. 3.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 266 (b) 28 (c) 133 (d) 136
  4. 4.What is the 24th term of the AP 6, 8, 10, 12, …? (a) 48 (b) 46 (c) 52 (d) 54
  5. 5.Which term of the AP 2, 9, 16, 23, … is 65? (a) 12th (b) 11th (c) 9th (d) 10th
  6. 6.What is the 35th term of the AP 9, 14, 19, 24, …? (a) 175 (b) 179 (c) 170 (d) 184
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 15 (d) 36
  8. 8.What is the 28th term of the AP 9, 11, 13, 15, …? (a) 65 (b) 63 (c) 56 (d) 54
  9. 9.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 90 (d) 45
  10. 10.What is the 30th term of the AP 15, 17, 19, 21, …? (a) 58 (b) 73 (c) 75 (d) 60
  11. 11.What is the 14th term of the AP 16, 24, 32, 40, …? (a) 128 (b) 104 (c) 120 (d) 112
  12. 12.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 138 (b) 19 (c) 69 (d) 78
  13. 13.What is the 11th term of the AP 2, 9, 16, 23, …? (a) 72 (b) 70 (c) 77 (d) 79
  14. 14.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 70 (b) 140 (c) 20 (d) 73
  15. 15.What is the 12th term of the AP 13, 20, 27, 34, …? (a) 77 (b) 97 (c) 84 (d) 90
  16. 16.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 220 (b) 200 (c) 400 (d) 38
  17. 17.What is the 39th term of the AP 9, 13, 17, 21, …? (a) 152 (b) 165 (c) 156 (d) 161
  18. 18.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  19. 19.What is the 13th term of the AP 15, 20, 25, 30, …? (a) 60 (b) 65 (c) 75 (d) 80
  20. 20.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 198 (b) 38 (c) 396 (d) 216
  21. 21.Which term of the AP 7, 10, 13, 16, … is 28? (a) 10th (b) 8th (c) 7th (d) 9th
  22. 22.Which term of the AP 2, 6, 10, 14, … is 38? (a) 11th (b) 9th (c) 10th (d) 12th
  23. 23.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 48 (b) 336 (c) 624 (d) 312
  24. 24.What is the 13th term of the AP 7, 12, 17, 22, …? (a) 72 (b) 67 (c) 65 (d) 60
  25. 25.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 33 (d) 289
  26. 26.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 22 (b) 119 (c) 224 (d) 112
  27. 27.What is the 11th term of the AP 2, 11, 20, 29, …? (a) 99 (b) 101 (c) 92 (d) 90
  28. 28.What is the 38th term of the AP 15, 21, 27, 33, …? (a) 228 (b) 222 (c) 237 (d) 243
  29. 29.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 9 (b) 8 (c) 7 (d) 6
  30. 30.What is the 27th term of the AP 3, 6, 9, 12, …? (a) 84 (b) 82 (c) 78 (d) 81
  31. 31.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 18 (b) 14 (c) 15 (d) 16
  32. 32.What is the 14th term of the AP 5, 11, 17, 23, …? (a) 84 (b) 83 (c) 89 (d) 78
  33. 33.What is the 12th term of the AP 13, 17, 21, 25, …? (a) 57 (b) 61 (c) 48 (d) 44
  34. 34.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 78 (c) 12 (d) 77
  35. 35.What is the 28th term of the AP 15, 18, 21, 24, …? (a) 99 (b) 84 (c) 81 (d) 96
  36. 36.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1891 (c) 3906 (d) 1953
  37. 37.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 115 (b) 112 (c) 25 (d) 224
  38. 38.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 722 (c) 741 (d) 703
  39. 39.What is the 26th term of the AP 20, 23, 26, 29, …? (a) 98 (b) 75 (c) 78 (d) 95
  40. 40.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 468 (b) 36 (c) 252 (d) 234

Answer key

  1. 270
  2. 58
  3. 133
  4. 52
  5. 10th
  6. 179
  7. 64
  8. 63
  9. 81
  10. 73
  11. 120
  12. 69
  13. 72
  14. 70
  15. 90
  16. 200
  17. 161
  18. 100
  19. 75
  20. 198
  21. 8th
  22. 10th
  23. 312
  24. 67
  25. 289
  26. 112
  27. 92
  28. 237
  29. 7
  30. 81
  31. 15
  32. 83
  33. 57
  34. 77
  35. 96
  36. 1953
  37. 112
  38. 741
  39. 95
  40. 234

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