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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 895 · 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 15th term of the AP 8, 13, 18, 23, …? (a) 70 (b) 75 (c) 78 (d) 83
  2. 2.What is the 22nd term of the AP 13, 20, 27, 34, …? (a) 154 (b) 160 (c) 167 (d) 147
  3. 3.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 756 (d) 53
  4. 4.What is the 19th term of the AP 10, 14, 18, 22, …? (a) 86 (b) 76 (c) 72 (d) 82
  5. 5.What is the 21st term of the AP 5, 7, 9, 11, …? (a) 42 (b) 47 (c) 40 (d) 45
  6. 6.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 135 (b) 23 (c) 270 (d) 144
  7. 7.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 325 (d) 49
  8. 8.What is the missing term in the AP 19, 28, ?, 46, 55? (a) 38 (b) 36 (c) 46 (d) 37
  9. 9.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 153 (d) 306
  10. 10.Which term of the AP 12, 21, 30, 39, … is 183? (a) 19th (b) 20th (c) 22nd (d) 21st
  11. 11.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  12. 12.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 130 (b) 17 (c) 65 (d) 70
  13. 13.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 252 (b) 126 (c) 127 (d) 18
  14. 14.What is the 30th term of the AP 8, 10, 12, 14, …? (a) 68 (b) 60 (c) 58 (d) 66
  15. 15.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4560 (c) 9312 (d) 4608
  16. 16.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 504 (b) 936 (c) 468 (d) 72
  17. 17.Which term of the AP 7, 14, 21, 28, … is 266? (a) 39th (b) 40th (c) 38th (d) 37th
  18. 18.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2592 (c) 2556 (d) 2628
  19. 19.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1596 (c) 1540 (d) 3192
  20. 20.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 10 (b) 9 (c) 7 (d) 8
  21. 21.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 117 (b) 120 (c) 25 (d) 234
  22. 22.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 25 (b) 22 (c) 24 (d) 23
  23. 23.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 23 (c) 150 (d) 75
  24. 24.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 260 (b) 22 (c) 140 (d) 130
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 56 (d) 13
  26. 26.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 90 (b) 75 (c) 150 (d) 27
  27. 27.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 21 (b) 26 (c) 22 (d) 23
  28. 28.What is the 34th term of the AP 11, 20, 29, 38, …? (a) 306 (b) 317 (c) 297 (d) 308
  29. 29.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 93 (c) 28 (d) 108
  30. 30.Which term of the AP 20, 24, 28, 32, … is 140? (a) 35th (b) 32nd (c) 31st (d) 30th
  31. 31.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 41 (b) 462 (c) 231 (d) 253
  32. 32.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 24 (b) 70 (c) 75 (d) 140
  33. 33.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 34 (b) 212 (c) 418 (d) 209
  34. 34.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 702 (d) 351
  35. 35.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 594 (b) 57 (c) 324 (d) 297
  36. 36.What is the 13th term of the AP 1, 4, 7, 10, …? (a) 37 (b) 40 (c) 36 (d) 39
  37. 37.What is the 24th term of the AP 9, 11, 13, 15, …? (a) 57 (b) 46 (c) 48 (d) 55
  38. 38.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 7656 (c) 3828 (d) 3741
  39. 39.What is the 14th term of the AP 12, 19, 26, 33, …? (a) 91 (b) 103 (c) 110 (d) 98
  40. 40.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 26 (c) 108 (d) 192

Answer key

  1. 78
  2. 160
  3. 729
  4. 82
  5. 45
  6. 135
  7. 625
  8. 37
  9. 289
  10. 20th
  11. 256
  12. 65
  13. 126
  14. 66
  15. 4656
  16. 468
  17. 38th
  18. 2628
  19. 1596
  20. 8
  21. 117
  22. 23
  23. 75
  24. 130
  25. 49
  26. 75
  27. 22
  28. 308
  29. 93
  30. 31st
  31. 231
  32. 70
  33. 209
  34. 351
  35. 297
  36. 37
  37. 55
  38. 3828
  39. 103
  40. 96

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