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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 803 · 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.Which term of the AP 20, 28, 36, 44, … is 324? (a) 39th (b) 40th (c) 41st (d) 38th
  2. 2.What is the 35th term of the AP 19, 28, 37, 46, …? (a) 306 (b) 325 (c) 315 (d) 334
  3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 56 (d) 28
  4. 4.What is the 16th term of the AP 2, 11, 20, 29, …? (a) 135 (b) 146 (c) 144 (d) 137
  5. 5.Which term of the AP 11, 18, 25, 32, … is 88? (a) 11th (b) 12th (c) 14th (d) 13th
  6. 6.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 253 (d) 43
  7. 7.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 11 (b) 6 (c) 8 (d) 7
  8. 8.Which term of the AP 3, 6, 9, 12, … is 39? (a) 12th (b) 14th (c) 15th (d) 13th
  9. 9.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 406 (c) 436 (d) 870
  10. 10.What is the missing term in the AP 16, 22, ?, 34, 40? (a) 27 (b) 34 (c) 28 (d) 29
  11. 11.What is the 13th term of the AP 5, 11, 17, 23, …? (a) 77 (b) 83 (c) 78 (d) 72
  12. 12.What is the 40th term of the AP 4, 12, 20, 28, …? (a) 312 (b) 320 (c) 324 (d) 316
  13. 13.Which term of the AP 15, 18, 21, 24, … is 75? (a) 25th (b) 20th (c) 21st (d) 22nd
  14. 14.What is the 26th term of the AP 2, 9, 16, 23, …? (a) 182 (b) 184 (c) 175 (d) 177
  15. 15.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 36 (b) 450 (c) 225 (d) 240
  16. 16.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 182 (d) 169
  17. 17.What is the 30th term of the AP 9, 11, 13, 15, …? (a) 69 (b) 67 (c) 58 (d) 60
  18. 18.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 65 (b) 11 (c) 130 (d) 70
  19. 19.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 61 (b) 14 (c) 120 (d) 60
  20. 20.Which term of the AP 11, 17, 23, 29, … is 137? (a) 24th (b) 21st (c) 23rd (d) 22nd
  21. 21.Which term of the AP 5, 12, 19, 26, … is 89? (a) 13th (b) 14th (c) 15th (d) 12th
  22. 22.What is the missing term in the AP 19, ?, 25, 28, 31? (a) 21 (b) 22 (c) 25 (d) 23
  23. 23.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 45 (d) 529
  24. 24.Which term of the AP 19, 28, 37, 46, … is 181? (a) 18th (b) 19th (c) 21st (d) 20th
  25. 25.What is the 31st term of the AP 1, 4, 7, 10, …? (a) 94 (b) 90 (c) 91 (d) 93
  26. 26.What is the missing term in the AP 16, 18, 20, ?, 24? (a) 23 (b) 22 (c) 21 (d) 24
  27. 27.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 55 (b) 50 (c) 100 (d) 14
  28. 28.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 363 (b) 726 (c) 58 (d) 368
  29. 29.Which term of the AP 8, 10, 12, 14, … is 34? (a) 15th (b) 13th (c) 17th (d) 14th
  30. 30.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 152 (b) 28 (c) 140 (d) 280
  31. 31.What is the 18th term of the AP 1, 5, 9, 13, …? (a) 73 (b) 68 (c) 72 (d) 69
  32. 32.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4418 (c) 4371 (d) 4465
  33. 33.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 83 (b) 22 (c) 160 (d) 80
  34. 34.What is the 39th term of the AP 5, 8, 11, 14, …? (a) 122 (b) 114 (c) 117 (d) 119
  35. 35.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 102 (b) 204 (c) 114 (d) 27
  36. 36.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 78 (b) 84 (c) 156 (d) 12
  37. 37.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 702 (d) 351
  38. 38.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 1892 (c) 946 (d) 947
  39. 39.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  40. 40.What is the 14th term of the AP 16, 25, 34, 43, …? (a) 117 (b) 142 (c) 133 (d) 126

Answer key

  1. 39th
  2. 325
  3. 49
  4. 137
  5. 12th
  6. 484
  7. 7
  8. 13th
  9. 435
  10. 28
  11. 77
  12. 316
  13. 21st
  14. 177
  15. 225
  16. 169
  17. 67
  18. 65
  19. 60
  20. 22nd
  21. 13th
  22. 22
  23. 529
  24. 19th
  25. 91
  26. 22
  27. 50
  28. 363
  29. 14th
  30. 140
  31. 69
  32. 4465
  33. 80
  34. 119
  35. 102
  36. 78
  37. 676
  38. 946
  39. 100
  40. 133

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