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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 661 · 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 5, 8, 11, 14, … is 47? (a) 16th (b) 15th (c) 17th (d) 14th
  2. 2.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 33 (d) 153
  3. 3.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 34 (b) 138 (c) 266 (d) 133
  4. 4.What is the 10th term of the AP 9, 12, 15, 18, …? (a) 30 (b) 39 (c) 27 (d) 36
  5. 5.What is the 32nd term of the AP 17, 26, 35, 44, …? (a) 288 (b) 296 (c) 305 (d) 279
  6. 6.What is the missing term in the AP 19, 23, ?, 31, 35? (a) 27 (b) 31 (c) 26 (d) 28
  7. 7.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 882 (c) 903 (d) 1806
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 51 (d) 351
  9. 9.What is the 17th term of the AP 16, 22, 28, 34, …? (a) 102 (b) 118 (c) 96 (d) 112
  10. 10.Which term of the AP 15, 17, 19, 21, … is 89? (a) 39th (b) 40th (c) 37th (d) 38th
  11. 11.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 20 (b) 18 (c) 27 (d) 19
  12. 12.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 208 (b) 188 (c) 41 (d) 376
  13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  14. 14.What is the 14th term of the AP 15, 21, 27, 33, …? (a) 78 (b) 99 (c) 84 (d) 93
  15. 15.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 8 (b) 9 (c) 12 (d) 10
  16. 16.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 111 (b) 15 (c) 110 (d) 220
  17. 17.What is the 38th term of the AP 12, 14, 16, 18, …? (a) 88 (b) 86 (c) 76 (d) 74
  18. 18.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 11 (c) 45 (d) 46
  19. 19.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 21 (d) 36
  20. 20.Which term of the AP 17, 26, 35, 44, … is 80? (a) 10th (b) 9th (c) 8th (d) 7th
  21. 21.What is the 16th term of the AP 1, 9, 17, 25, …? (a) 120 (b) 121 (c) 129 (d) 128
  22. 22.What is the 25th term of the AP 20, 23, 26, 29, …? (a) 95 (b) 72 (c) 75 (d) 92
  23. 23.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 4187 (c) 8372 (d) 4095
  24. 24.What is the 18th term of the AP 1, 7, 13, 19, …? (a) 109 (b) 103 (c) 108 (d) 102
  25. 25.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4465 (c) 9120 (d) 4561
  26. 26.What is the 16th term of the AP 15, 17, 19, 21, …? (a) 30 (b) 45 (c) 32 (d) 47
  27. 27.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 110 (b) 210 (c) 15 (d) 105
  28. 28.Which term of the AP 15, 19, 23, 27, … is 47? (a) 11th (b) 10th (c) 8th (d) 9th
  29. 29.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 374 (c) 187 (d) 27
  30. 30.What is the 33rd term of the AP 3, 8, 13, 18, …? (a) 168 (b) 165 (c) 160 (d) 163
  31. 31.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 27 (b) 26 (c) 25 (d) 35
  32. 32.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 9 (b) 14 (c) 10 (d) 11
  33. 33.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 266 (b) 133 (c) 28 (d) 136
  34. 34.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 75 (b) 140 (c) 18 (d) 70
  35. 35.Which term of the AP 17, 22, 27, 32, … is 182? (a) 35th (b) 33rd (c) 34th (d) 36th
  36. 36.Which term of the AP 7, 11, 15, 19, … is 111? (a) 28th (b) 26th (c) 27th (d) 29th
  37. 37.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 25 (b) 26 (c) 33 (d) 24
  38. 38.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 12 (b) 126 (c) 63 (d) 64
  39. 39.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 552 (d) 276
  40. 40.What is the 35th term of the AP 18, 27, 36, 45, …? (a) 324 (b) 306 (c) 315 (d) 333

Answer key

  1. 15th
  2. 289
  3. 133
  4. 36
  5. 296
  6. 27
  7. 903
  8. 676
  9. 112
  10. 38th
  11. 19
  12. 188
  13. 25
  14. 93
  15. 9
  16. 110
  17. 86
  18. 45
  19. 36
  20. 8th
  21. 121
  22. 92
  23. 4186
  24. 103
  25. 4560
  26. 45
  27. 105
  28. 9th
  29. 187
  30. 163
  31. 26
  32. 10
  33. 133
  34. 70
  35. 34th
  36. 27th
  37. 25
  38. 63
  39. 529
  40. 324

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