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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 849 · 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 34th term of the AP 13, 20, 27, 34, …? (a) 251 (b) 244 (c) 231 (d) 238
  2. 2.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 22 (b) 20 (c) 28 (d) 21
  3. 3.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 351 (d) 702
  4. 4.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 496 (c) 497 (d) 992
  5. 5.What is the 21st term of the AP 3, 8, 13, 18, …? (a) 108 (b) 103 (c) 100 (d) 105
  6. 6.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 15 (b) 110 (c) 111 (d) 220
  7. 7.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 153 (b) 171 (c) 33 (d) 306
  8. 8.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 160 (b) 83 (c) 80 (d) 22
  9. 9.What is the sum of all the whole numbers from 1 to 89? (a) 4006 (b) 8010 (c) 3916 (d) 4005
  10. 10.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 27 (b) 138 (c) 270 (d) 135
  11. 11.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 78 (c) 156 (d) 72
  12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  13. 13.Which term of the AP 6, 9, 12, 15, … is 84? (a) 28th (b) 26th (c) 29th (d) 27th
  14. 14.What is the 22nd term of the AP 2, 4, 6, 8, …? (a) 42 (b) 45 (c) 44 (d) 46
  15. 15.What is the 30th term of the AP 20, 23, 26, 29, …? (a) 110 (b) 87 (c) 90 (d) 107
  16. 16.What is the 13th term of the AP 20, 24, 28, 32, …? (a) 52 (b) 68 (c) 48 (d) 72
  17. 17.Which term of the AP 7, 10, 13, 16, … is 73? (a) 22nd (b) 23rd (c) 24th (d) 25th
  18. 18.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 744 (b) 396 (c) 372 (d) 53
  19. 19.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 20 (b) 26 (c) 21 (d) 22
  20. 20.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 3906 (c) 1891 (d) 1922
  21. 21.Which term of the AP 6, 10, 14, 18, … is 70? (a) 19th (b) 16th (c) 18th (d) 17th
  22. 22.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 14 (b) 16 (c) 15 (d) 17
  23. 23.What is the 31st term of the AP 17, 22, 27, 32, …? (a) 167 (b) 155 (c) 172 (d) 150
  24. 24.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 29 (d) 120
  25. 25.Which term of the AP 19, 21, 23, 25, … is 33? (a) 10th (b) 7th (c) 9th (d) 8th
  26. 26.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 39 (b) 49 (c) 41 (d) 40
  27. 27.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 406 (c) 784 (d) 55
  28. 28.Which term of the AP 17, 20, 23, 26, … is 107? (a) 30th (b) 33rd (c) 31st (d) 32nd
  29. 29.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 10 (b) 9 (c) 8 (d) 16
  30. 30.What is the 14th term of the AP 1, 3, 5, 7, …? (a) 27 (b) 26 (c) 29 (d) 28
  31. 31.Which term of the AP 13, 18, 23, 28, … is 93? (a) 19th (b) 16th (c) 18th (d) 17th
  32. 32.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 208 (b) 376 (c) 188 (d) 41
  33. 33.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 192 (b) 216 (c) 384 (d) 45
  34. 34.What is the 26th term of the AP 4, 6, 8, 10, …? (a) 50 (b) 52 (c) 54 (d) 56
  35. 35.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 504 (b) 468 (c) 72 (d) 936
  36. 36.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 98 (b) 49 (c) 13 (d) 56
  37. 37.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 60 (b) 14 (c) 54 (d) 108
  38. 38.What is the 16th term of the AP 7, 14, 21, 28, …? (a) 105 (b) 113 (c) 112 (d) 119
  39. 39.What is the 20th term of the AP 17, 22, 27, 32, …? (a) 95 (b) 100 (c) 112 (d) 117
  40. 40.Which term of the AP 2, 8, 14, 20, … is 98? (a) 17th (b) 19th (c) 16th (d) 18th

Answer key

  1. 244
  2. 21
  3. 351
  4. 496
  5. 103
  6. 110
  7. 153
  8. 80
  9. 4005
  10. 135
  11. 78
  12. 36
  13. 27th
  14. 44
  15. 107
  16. 68
  17. 23rd
  18. 372
  19. 21
  20. 1953
  21. 17th
  22. 15
  23. 167
  24. 225
  25. 8th
  26. 40
  27. 784
  28. 31st
  29. 9
  30. 27
  31. 17th
  32. 188
  33. 192
  34. 54
  35. 468
  36. 49
  37. 54
  38. 112
  39. 112
  40. 17th

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