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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 549 · 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 23rd term of the AP 3, 5, 7, 9, …? (a) 49 (b) 44 (c) 46 (d) 47
  2. 2.Which term of the AP 1, 8, 15, 22, … is 71? (a) 10th (b) 13th (c) 11th (d) 12th
  3. 3.What is the 26th term of the AP 16, 23, 30, 37, …? (a) 191 (b) 198 (c) 182 (d) 175
  4. 4.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 540 (c) 504 (d) 1008
  5. 5.What is the 18th term of the AP 15, 17, 19, 21, …? (a) 34 (b) 49 (c) 36 (d) 51
  6. 6.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 58 (b) 726 (c) 363 (d) 368
  7. 7.What is the 27th term of the AP 12, 16, 20, 24, …? (a) 104 (b) 120 (c) 116 (d) 108
  8. 8.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2628 (c) 2556 (d) 2592
  9. 9.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 28 (d) 13
  10. 10.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 35 (b) 36 (c) 9 (d) 70
  11. 11.What is the 35th term of the AP 6, 13, 20, 27, …? (a) 238 (b) 245 (c) 251 (d) 244
  12. 12.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3828 (c) 7656 (d) 3829
  13. 13.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 435 (c) 436 (d) 406
  14. 14.What is the 19th term of the AP 8, 14, 20, 26, …? (a) 108 (b) 116 (c) 122 (d) 114
  15. 15.What is the 24th term of the AP 5, 12, 19, 26, …? (a) 166 (b) 173 (c) 168 (d) 161
  16. 16.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 300 (b) 560 (c) 280 (d) 46
  17. 17.Which term of the AP 6, 13, 20, 27, … is 132? (a) 18th (b) 20th (c) 21st (d) 19th
  18. 18.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 12 (b) 11 (c) 10 (d) 14
  19. 19.What is the 18th term of the AP 1, 6, 11, 16, …? (a) 85 (b) 86 (c) 91 (d) 90
  20. 20.What is the 12th term of the AP 3, 8, 13, 18, …? (a) 60 (b) 63 (c) 55 (d) 58
  21. 21.What is the 38th term of the AP 1, 5, 9, 13, …? (a) 152 (b) 149 (c) 153 (d) 148
  22. 22.What is the 40th term of the AP 9, 11, 13, 15, …? (a) 87 (b) 78 (c) 89 (d) 80
  23. 23.What is the 12th term of the AP 15, 21, 27, 33, …? (a) 87 (b) 72 (c) 81 (d) 66
  24. 24.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 260 (b) 240 (c) 480 (d) 42
  25. 25.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 5 (b) 6 (c) 8 (d) 7
  26. 26.Which term of the AP 16, 18, 20, 22, … is 50? (a) 19th (b) 25th (c) 17th (d) 18th
  27. 27.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 20 (b) 75 (c) 150 (d) 84
  28. 28.Which term of the AP 14, 22, 30, 38, … is 70? (a) 10th (b) 8th (c) 9th (d) 7th
  29. 29.Which term of the AP 13, 19, 25, 31, … is 103? (a) 15th (b) 18th (c) 17th (d) 16th
  30. 30.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 231 (d) 41
  31. 31.What is the 38th term of the AP 11, 14, 17, 20, …? (a) 114 (b) 122 (c) 125 (d) 111
  32. 32.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 26 (b) 32 (c) 25 (d) 27
  33. 33.What is the 12th term of the AP 4, 8, 12, 16, …? (a) 44 (b) 48 (c) 52 (d) 49
  34. 34.Which term of the AP 1, 7, 13, 19, … is 175? (a) 29th (b) 30th (c) 31st (d) 32nd
  35. 35.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 351 (d) 51
  36. 36.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 572 (c) 286 (d) 51
  37. 37.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 27 (b) 138 (c) 135 (d) 270
  38. 38.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 83 (b) 22 (c) 160 (d) 80
  39. 39.Which term of the AP 2, 8, 14, 20, … is 74? (a) 12th (b) 13th (c) 14th (d) 15th
  40. 40.What is the 15th term of the AP 17, 22, 27, 32, …? (a) 87 (b) 92 (c) 75 (d) 70

Answer key

  1. 47
  2. 11th
  3. 191
  4. 504
  5. 49
  6. 363
  7. 116
  8. 2628
  9. 49
  10. 35
  11. 244
  12. 3828
  13. 435
  14. 116
  15. 166
  16. 280
  17. 19th
  18. 11
  19. 86
  20. 58
  21. 149
  22. 87
  23. 81
  24. 240
  25. 6
  26. 18th
  27. 75
  28. 8th
  29. 16th
  30. 441
  31. 122
  32. 26
  33. 48
  34. 30th
  35. 676
  36. 286
  37. 135
  38. 80
  39. 13th
  40. 87

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