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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 988 · 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 17th term of the AP 2, 5, 8, 11, …? (a) 53 (b) 51 (c) 48 (d) 50
  2. 2.What is the sum of all the whole numbers from 1 to 73? (a) 2701 (b) 2628 (c) 5402 (d) 2702
  3. 3.What is the 24th term of the AP 2, 5, 8, 11, …? (a) 72 (b) 69 (c) 71 (d) 74
  4. 4.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 66 (b) 114 (c) 57 (d) 17
  5. 5.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 4095 (c) 4050 (d) 8190
  6. 6.What is the 18th term of the AP 4, 10, 16, 22, …? (a) 112 (b) 102 (c) 106 (d) 108
  7. 7.Which term of the AP 1, 8, 15, 22, … is 267? (a) 40th (b) 41st (c) 39th (d) 38th
  8. 8.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 3486 (c) 6972 (d) 3487
  9. 9.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 70 (c) 35 (d) 8
  10. 10.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 729 (d) 756
  11. 11.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 29 (b) 148 (c) 296 (d) 160
  12. 12.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 14 (b) 10 (c) 11 (d) 12
  13. 13.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 4556 (c) 2279 (d) 2211
  14. 14.What is the 15th term of the AP 9, 12, 15, 18, …? (a) 51 (b) 45 (c) 54 (d) 42
  15. 15.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 131 (b) 33 (c) 252 (d) 126
  16. 16.Which term of the AP 19, 21, 23, 25, … is 65? (a) 24th (b) 23rd (c) 25th (d) 26th
  17. 17.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 100 (b) 99 (c) 14 (d) 198
  18. 18.What is the 20th term of the AP 17, 24, 31, 38, …? (a) 157 (b) 140 (c) 133 (d) 150
  19. 19.Which term of the AP 15, 19, 23, 27, … is 127? (a) 28th (b) 30th (c) 31st (d) 29th
  20. 20.Which term of the AP 1, 10, 19, 28, … is 217? (a) 24th (b) 27th (c) 26th (d) 25th
  21. 21.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 120 (c) 240 (d) 105
  22. 22.What is the 35th term of the AP 10, 13, 16, 19, …? (a) 115 (b) 102 (c) 105 (d) 112
  23. 23.What is the 32nd term of the AP 17, 20, 23, 26, …? (a) 113 (b) 110 (c) 93 (d) 96
  24. 24.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 10 (b) 11 (c) 9 (d) 13
  25. 25.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 216 (c) 112 (d) 108
  26. 26.What is the 18th term of the AP 5, 13, 21, 29, …? (a) 149 (b) 144 (c) 141 (d) 136
  27. 27.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  28. 28.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 77 (b) 17 (c) 84 (d) 154
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 105 (c) 27 (d) 196
  30. 30.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 31 (c) 192 (d) 114
  31. 31.Which term of the AP 3, 12, 21, 30, … is 165? (a) 21st (b) 18th (c) 20th (d) 19th
  32. 32.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 100 (b) 18 (c) 50 (d) 60
  33. 33.What is the 37th term of the AP 11, 13, 15, 17, …? (a) 83 (b) 85 (c) 72 (d) 74
  34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 59 (d) 465
  35. 35.What is the 40th term of the AP 5, 7, 9, 11, …? (a) 80 (b) 78 (c) 85 (d) 83
  36. 36.What is the sum of all the whole numbers from 1 to 21? (a) 462 (b) 231 (c) 232 (d) 210
  37. 37.What is the missing term in the AP 12, 19, ?, 33, 40? (a) 27 (b) 25 (c) 26 (d) 33
  38. 38.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 440 (b) 220 (c) 240 (d) 45
  39. 39.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 126 (b) 27 (c) 129 (d) 252
  40. 40.What is the 10th term of the AP 18, 27, 36, 45, …? (a) 81 (b) 90 (c) 108 (d) 99

Answer key

  1. 50
  2. 2701
  3. 71
  4. 57
  5. 4095
  6. 106
  7. 39th
  8. 3486
  9. 35
  10. 729
  11. 148
  12. 11
  13. 2278
  14. 51
  15. 126
  16. 24th
  17. 99
  18. 150
  19. 29th
  20. 25th
  21. 120
  22. 112
  23. 110
  24. 10
  25. 108
  26. 141
  27. 441
  28. 77
  29. 196
  30. 96
  31. 19th
  32. 50
  33. 83
  34. 900
  35. 83
  36. 231
  37. 26
  38. 220
  39. 126
  40. 99

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