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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 477 · 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 sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1540 (c) 3080 (d) 1541
  2. 2.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 136 (b) 72 (c) 68 (d) 12
  3. 3.Which term of the AP 4, 13, 22, 31, … is 310? (a) 36th (b) 37th (c) 34th (d) 35th
  4. 4.What is the 29th term of the AP 17, 19, 21, 23, …? (a) 75 (b) 73 (c) 56 (d) 58
  5. 5.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 169 (d) 25
  6. 6.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1275 (c) 1326 (d) 1327
  7. 7.What is the 16th term of the AP 7, 14, 21, 28, …? (a) 113 (b) 105 (c) 112 (d) 119
  8. 8.What is the 10th term of the AP 19, 25, 31, 37, …? (a) 73 (b) 60 (c) 54 (d) 79
  9. 9.Which term of the AP 18, 22, 26, 30, … is 142? (a) 31st (b) 34th (c) 32nd (d) 33rd
  10. 10.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 5852 (c) 2926 (d) 2850
  11. 11.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 2256 (c) 1081 (d) 1128
  12. 12.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 194 (b) 378 (c) 41 (d) 189
  13. 13.What is the missing term in the AP 10, 16, 22, ?, 34? (a) 34 (b) 28 (c) 29 (d) 27
  14. 14.What is the sum of all the whole numbers from 1 to 90? (a) 8190 (b) 4095 (c) 4050 (d) 4005
  15. 15.What is the 14th term of the AP 5, 14, 23, 32, …? (a) 131 (b) 117 (c) 126 (d) 122
  16. 16.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 180 (b) 26 (c) 170 (d) 340
  17. 17.What is the missing term in the AP 13, ?, 21, 25, 29? (a) 16 (b) 21 (c) 18 (d) 17
  18. 18.What is the 36th term of the AP 18, 27, 36, 45, …? (a) 333 (b) 342 (c) 324 (d) 315
  19. 19.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 168 (b) 14 (c) 84 (d) 88
  20. 20.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 3 (b) 4 (c) 5 (d) 2
  21. 21.What is the 13th term of the AP 16, 18, 20, 22, …? (a) 40 (b) 42 (c) 26 (d) 24
  22. 22.What is the 22nd term of the AP 18, 23, 28, 33, …? (a) 123 (b) 128 (c) 110 (d) 105
  23. 23.What is the 11th term of the AP 10, 14, 18, 22, …? (a) 50 (b) 40 (c) 54 (d) 44
  24. 24.What is the 31st term of the AP 5, 12, 19, 26, …? (a) 210 (b) 215 (c) 217 (d) 222
  25. 25.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 300 (c) 276 (d) 600
  26. 26.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 81 (d) 45
  27. 27.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 192 (b) 180 (c) 26 (d) 360
  28. 28.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 26 (b) 25 (c) 28 (d) 24
  29. 29.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  30. 30.What is the 27th term of the AP 16, 20, 24, 28, …? (a) 108 (b) 120 (c) 124 (d) 104
  31. 31.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 5402 (c) 2701 (d) 2702
  32. 32.Which term of the AP 7, 14, 21, 28, … is 280? (a) 40th (b) 39th (c) 41st (d) 42nd
  33. 33.Which term of the AP 20, 25, 30, 35, … is 55? (a) 7th (b) 9th (c) 8th (d) 11th
  34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 13 (d) 49
  35. 35.What is the 25th term of the AP 15, 18, 21, 24, …? (a) 75 (b) 90 (c) 87 (d) 72
  36. 36.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 9 (b) 14 (c) 10 (d) 8
  37. 37.What is the 27th term of the AP 2, 5, 8, 11, …? (a) 78 (b) 83 (c) 80 (d) 81
  38. 38.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 138 (b) 19 (c) 78 (d) 69
  39. 39.Which term of the AP 6, 13, 20, 27, … is 55? (a) 7th (b) 9th (c) 10th (d) 8th
  40. 40.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 182 (c) 92 (d) 78

Answer key

  1. 1540
  2. 68
  3. 35th
  4. 73
  5. 169
  6. 1326
  7. 112
  8. 73
  9. 32nd
  10. 2926
  11. 1128
  12. 189
  13. 28
  14. 4095
  15. 122
  16. 170
  17. 17
  18. 333
  19. 84
  20. 3
  21. 40
  22. 123
  23. 50
  24. 215
  25. 300
  26. 81
  27. 180
  28. 25
  29. 784
  30. 120
  31. 2701
  32. 40th
  33. 8th
  34. 49
  35. 87
  36. 9
  37. 80
  38. 69
  39. 8th
  40. 91

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