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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 599 · 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 3, 12, 21, ?, 39? (a) 29 (b) 39 (c) 31 (d) 30
  2. 2.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 470 (c) 260 (d) 235
  3. 3.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 279 (b) 52 (c) 504 (d) 252
  4. 4.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 275 (b) 50 (c) 550 (d) 300
  5. 5.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 81 (c) 96 (d) 162
  6. 6.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 207 (b) 414 (c) 43 (d) 212
  7. 7.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 133 (b) 37 (c) 266 (d) 154
  8. 8.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 7 (b) 14 (c) 9 (d) 8
  9. 9.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 756 (d) 378
  10. 10.What is the 20th term of the AP 10, 19, 28, 37, …? (a) 171 (b) 180 (c) 181 (d) 190
  11. 11.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 110 (b) 55 (c) 60 (d) 15
  12. 12.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 230 (b) 16 (c) 115 (d) 120
  13. 13.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 243 (b) 486 (c) 270 (d) 51
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 406 (d) 812
  15. 15.Which term of the AP 6, 12, 18, 24, … is 84? (a) 14th (b) 16th (c) 13th (d) 15th
  16. 16.What is the 24th term of the AP 2, 6, 10, 14, …? (a) 98 (b) 94 (c) 92 (d) 96
  17. 17.Which term of the AP 13, 16, 19, 22, … is 43? (a) 13th (b) 12th (c) 11th (d) 10th
  18. 18.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 9 (b) 78 (c) 39 (d) 42
  19. 19.What is the 14th term of the AP 12, 16, 20, 24, …? (a) 52 (b) 64 (c) 56 (d) 68
  20. 20.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 2256 (c) 1081 (d) 1129
  21. 21.What is the 32nd term of the AP 6, 13, 20, 27, …? (a) 223 (b) 224 (c) 230 (d) 217
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  23. 23.What is the 27th term of the AP 18, 21, 24, 27, …? (a) 96 (b) 81 (c) 99 (d) 78
  24. 24.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 9 (c) 15 (d) 30
  25. 25.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 406 (d) 812
  26. 26.What is the missing term in the AP 11, ?, 23, 29, 35? (a) 23 (b) 18 (c) 16 (d) 17
  27. 27.What is the missing term in the AP 19, 23, ?, 31, 35? (a) 27 (b) 31 (c) 28 (d) 26
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 28 (d) 13
  29. 29.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 130 (c) 65 (d) 70
  30. 30.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 69 (b) 138 (c) 14 (d) 72
  31. 31.Which term of the AP 4, 9, 14, 19, … is 164? (a) 34th (b) 35th (c) 32nd (d) 33rd
  32. 32.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1378 (c) 1326 (d) 1352
  33. 33.What is the 28th term of the AP 18, 21, 24, 27, …? (a) 99 (b) 84 (c) 81 (d) 102
  34. 34.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  35. 35.What is the 23rd term of the AP 4, 13, 22, 31, …? (a) 211 (b) 202 (c) 198 (d) 207
  36. 36.What is the 14th term of the AP 4, 6, 8, 10, …? (a) 26 (b) 30 (c) 28 (d) 32
  37. 37.What is the 11th term of the AP 14, 16, 18, 20, …? (a) 22 (b) 34 (c) 36 (d) 20
  38. 38.Which term of the AP 2, 7, 12, 17, … is 92? (a) 18th (b) 20th (c) 21st (d) 19th
  39. 39.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3872 (c) 3828 (d) 3916
  40. 40.What is the 23rd term of the AP 17, 26, 35, 44, …? (a) 198 (b) 215 (c) 207 (d) 224

Answer key

  1. 30
  2. 235
  3. 252
  4. 275
  5. 81
  6. 207
  7. 133
  8. 8
  9. 729
  10. 181
  11. 55
  12. 115
  13. 243
  14. 784
  15. 14th
  16. 94
  17. 11th
  18. 39
  19. 64
  20. 1128
  21. 223
  22. 144
  23. 96
  24. 25
  25. 406
  26. 17
  27. 27
  28. 49
  29. 65
  30. 69
  31. 33rd
  32. 1378
  33. 99
  34. 529
  35. 202
  36. 30
  37. 34
  38. 19th
  39. 3916
  40. 215

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