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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 488 · 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 missing term in the AP 5, 14, 23, ?, 41? (a) 33 (b) 31 (c) 32 (d) 41
  2. 2.What is the 22nd term of the AP 11, 18, 25, 32, …? (a) 165 (b) 147 (c) 154 (d) 158
  3. 3.What is the 20th term of the AP 18, 20, 22, 24, …? (a) 38 (b) 58 (c) 56 (d) 40
  4. 4.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 436 (c) 870 (d) 435
  5. 5.What is the 37th term of the AP 7, 13, 19, 25, …? (a) 223 (b) 216 (c) 222 (d) 229
  6. 6.What is the 15th term of the AP 6, 9, 12, 15, …? (a) 42 (b) 51 (c) 45 (d) 48
  7. 7.What is the 27th term of the AP 9, 13, 17, 21, …? (a) 108 (b) 113 (c) 104 (d) 117
  8. 8.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 78 (b) 15 (c) 75 (d) 150
  9. 9.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 41 (d) 462
  10. 10.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 22 (b) 27 (c) 20 (d) 21
  11. 11.What is the 35th term of the AP 1, 4, 7, 10, …? (a) 105 (b) 103 (c) 106 (d) 102
  12. 12.What is the 23rd term of the AP 11, 20, 29, 38, …? (a) 218 (b) 198 (c) 209 (d) 207
  13. 13.What is the 39th term of the AP 14, 22, 30, 38, …? (a) 318 (b) 304 (c) 326 (d) 312
  14. 14.What is the 31st term of the AP 9, 16, 23, 30, …? (a) 226 (b) 217 (c) 210 (d) 219
  15. 15.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4560 (c) 4561 (d) 4465
  16. 16.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 109 (b) 216 (c) 16 (d) 108
  17. 17.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 722 (c) 1482 (d) 741
  18. 18.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 6162 (c) 3042 (d) 3081
  19. 19.What is the 18th term of the AP 6, 11, 16, 21, …? (a) 91 (b) 96 (c) 85 (d) 90
  20. 20.What is the 27th term of the AP 17, 21, 25, 29, …? (a) 104 (b) 108 (c) 121 (d) 125
  21. 21.Which term of the AP 9, 16, 23, 30, … is 135? (a) 18th (b) 21st (c) 20th (d) 19th
  22. 22.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2080 (c) 2145 (d) 2146
  23. 23.What is the 17th term of the AP 1, 7, 13, 19, …? (a) 102 (b) 103 (c) 96 (d) 97
  24. 24.What is the 14th term of the AP 12, 20, 28, 36, …? (a) 124 (b) 112 (c) 116 (d) 104
  25. 25.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 66 (b) 8 (c) 36 (d) 33
  26. 26.What is the 12th term of the AP 13, 20, 27, 34, …? (a) 84 (b) 97 (c) 77 (d) 90
  27. 27.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2850 (c) 2926 (d) 5852
  28. 28.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 903 (c) 882 (d) 1806
  29. 29.What is the 13th term of the AP 20, 22, 24, 26, …? (a) 26 (b) 46 (c) 44 (d) 24
  30. 30.What is the 17th term of the AP 4, 10, 16, 22, …? (a) 100 (b) 102 (c) 106 (d) 96
  31. 31.What is the 24th term of the AP 12, 15, 18, 21, …? (a) 81 (b) 69 (c) 72 (d) 84
  32. 32.What is the 32nd term of the AP 10, 15, 20, 25, …? (a) 155 (b) 165 (c) 160 (d) 170
  33. 33.What is the 10th term of the AP 20, 24, 28, 32, …? (a) 56 (b) 60 (c) 40 (d) 36
  34. 34.What is the 39th term of the AP 17, 20, 23, 26, …? (a) 134 (b) 131 (c) 114 (d) 117
  35. 35.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 120 (b) 29 (c) 240 (d) 136
  36. 36.What is the 11th term of the AP 16, 23, 30, 37, …? (a) 93 (b) 70 (c) 77 (d) 86
  37. 37.What is the 37th term of the AP 12, 19, 26, 33, …? (a) 264 (b) 252 (c) 259 (d) 271
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 400 (d) 39
  39. 39.Which term of the AP 18, 21, 24, 27, … is 72? (a) 24th (b) 19th (c) 20th (d) 18th
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 11 (d) 21

Answer key

  1. 32
  2. 158
  3. 56
  4. 435
  5. 223
  6. 48
  7. 113
  8. 75
  9. 441
  10. 21
  11. 103
  12. 209
  13. 318
  14. 219
  15. 4560
  16. 108
  17. 741
  18. 3081
  19. 91
  20. 121
  21. 19th
  22. 2145
  23. 97
  24. 116
  25. 33
  26. 90
  27. 2926
  28. 903
  29. 44
  30. 100
  31. 81
  32. 165
  33. 56
  34. 131
  35. 120
  36. 86
  37. 264
  38. 400
  39. 19th
  40. 36

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