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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 418 · 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.Which term of the AP 17, 20, 23, 26, … is 119? (a) 34th (b) 35th (c) 36th (d) 37th
  2. 2.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 231 (c) 210 (d) 462
  3. 3.Which term of the AP 8, 17, 26, 35, … is 242? (a) 28th (b) 29th (c) 26th (d) 27th
  4. 4.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 2450 (c) 1226 (d) 1225
  5. 5.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 153 (c) 162 (d) 342
  6. 6.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 16 (b) 25 (c) 17 (d) 15
  7. 7.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 16 (b) 15 (c) 5 (d) 30
  8. 8.Which term of the AP 19, 28, 37, 46, … is 109? (a) 13th (b) 12th (c) 11th (d) 10th
  9. 9.What is the 35th term of the AP 1, 4, 7, 10, …? (a) 106 (b) 102 (c) 103 (d) 105
  10. 10.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 406 (c) 55 (d) 812
  11. 11.Which term of the AP 6, 13, 20, 27, … is 83? (a) 13th (b) 14th (c) 11th (d) 12th
  12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  13. 13.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 34 (b) 35 (c) 44 (d) 36
  14. 14.What is the 20th term of the AP 4, 13, 22, 31, …? (a) 171 (b) 175 (c) 180 (d) 184
  15. 15.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 379 (c) 351 (d) 756
  16. 16.What is the 16th term of the AP 2, 7, 12, 17, …? (a) 75 (b) 80 (c) 82 (d) 77
  17. 17.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 21 (b) 27 (c) 19 (d) 20
  18. 18.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 19 (b) 90 (c) 168 (d) 84
  19. 19.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 23 (d) 78
  20. 20.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 25 (b) 50 (c) 30 (d) 9
  21. 21.Which term of the AP 4, 8, 12, 16, … is 88? (a) 24th (b) 21st (c) 22nd (d) 23rd
  22. 22.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 59 (d) 900
  23. 23.What is the 20th term of the AP 6, 11, 16, 21, …? (a) 106 (b) 101 (c) 95 (d) 100
  24. 24.What is the 17th term of the AP 20, 28, 36, 44, …? (a) 136 (b) 156 (c) 148 (d) 128
  25. 25.What is the 36th term of the AP 11, 18, 25, 32, …? (a) 252 (b) 245 (c) 256 (d) 263
  26. 26.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 154 (c) 306 (d) 136
  27. 27.What is the 17th term of the AP 17, 21, 25, 29, …? (a) 85 (b) 81 (c) 64 (d) 68
  28. 28.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 25 (b) 176 (c) 165 (d) 330
  29. 29.What is the 19th term of the AP 19, 24, 29, 34, …? (a) 114 (b) 90 (c) 109 (d) 95
  30. 30.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 23 (b) 154 (c) 143 (d) 286
  31. 31.Which term of the AP 8, 17, 26, 35, … is 161? (a) 17th (b) 19th (c) 18th (d) 20th
  32. 32.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 70 (b) 75 (c) 24 (d) 140
  33. 33.What is the 12th term of the AP 4, 12, 20, 28, …? (a) 92 (b) 96 (c) 100 (d) 88
  34. 34.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 10 (c) 104 (d) 52
  35. 35.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 26 (b) 23 (c) 21 (d) 22
  36. 36.What is the 28th term of the AP 18, 26, 34, 42, …? (a) 242 (b) 224 (c) 234 (d) 216
  37. 37.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 19 (b) 55 (c) 110 (d) 65
  38. 38.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 338 (c) 702 (d) 351
  39. 39.Which term of the AP 18, 21, 24, 27, … is 60? (a) 15th (b) 20th (c) 14th (d) 16th
  40. 40.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 9120 (c) 4561 (d) 4560

Answer key

  1. 35th
  2. 231
  3. 27th
  4. 1225
  5. 171
  6. 16
  7. 15
  8. 11th
  9. 103
  10. 784
  11. 12th
  12. 81
  13. 35
  14. 175
  15. 378
  16. 77
  17. 20
  18. 84
  19. 144
  20. 25
  21. 22nd
  22. 900
  23. 101
  24. 148
  25. 256
  26. 153
  27. 81
  28. 165
  29. 109
  30. 143
  31. 18th
  32. 70
  33. 92
  34. 52
  35. 22
  36. 234
  37. 55
  38. 351
  39. 15th
  40. 4560

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