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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 286 · 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 the first 6 terms of the AP 4, 6, 8, …? (a) 108 (b) 54 (c) 60 (d) 14
  2. 2.What is the 10th term of the AP 7, 12, 17, 22, …? (a) 52 (b) 57 (c) 50 (d) 45
  3. 3.What is the 35th term of the AP 15, 17, 19, 21, …? (a) 85 (b) 68 (c) 83 (d) 70
  4. 4.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 28 (b) 186 (c) 108 (d) 93
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  6. 6.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 704 (b) 357 (c) 352 (d) 57
  7. 7.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 49 (c) 325 (d) 650
  8. 8.Which term of the AP 17, 20, 23, 26, … is 131? (a) 38th (b) 41st (c) 40th (d) 39th
  9. 9.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 438 (b) 468 (c) 876 (d) 64
  10. 10.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 16 (c) 80 (d) 72
  11. 11.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1800 (c) 1770 (d) 1830
  12. 12.What is the 29th term of the AP 5, 8, 11, 14, …? (a) 84 (b) 89 (c) 87 (d) 92
  13. 13.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 29 (b) 26 (c) 25 (d) 27
  14. 14.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 2346 (c) 2312 (d) 4692
  15. 15.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 232 (c) 462 (d) 231
  16. 16.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 264 (b) 480 (c) 240 (d) 51
  17. 17.Which term of the AP 9, 15, 21, 27, … is 63? (a) 11th (b) 12th (c) 9th (d) 10th
  18. 18.What is the missing term in the AP 2, 9, 16, ?, 30? (a) 24 (b) 22 (c) 30 (d) 23
  19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 33 (d) 153
  20. 20.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 300 (b) 18 (c) 156 (d) 150
  21. 21.What is the 15th term of the AP 14, 17, 20, 23, …? (a) 56 (b) 45 (c) 42 (d) 59
  22. 22.What is the 13th term of the AP 20, 27, 34, 41, …? (a) 91 (b) 84 (c) 111 (d) 104
  23. 23.What is the 16th term of the AP 7, 16, 25, 34, …? (a) 144 (b) 135 (c) 151 (d) 142
  24. 24.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 17 (b) 19 (c) 18 (d) 22
  25. 25.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 120 (c) 105 (d) 121
  26. 26.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 19 (b) 20 (c) 17 (d) 18
  27. 27.What is the 20th term of the AP 20, 24, 28, 32, …? (a) 76 (b) 100 (c) 96 (d) 80
  28. 28.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 4560 (c) 9120 (d) 4465
  29. 29.Which term of the AP 2, 11, 20, 29, … is 263? (a) 29th (b) 32nd (c) 30th (d) 31st
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 17 (d) 45
  31. 31.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1225 (c) 1275 (d) 1250
  32. 32.Which term of the AP 5, 14, 23, 32, … is 329? (a) 39th (b) 38th (c) 37th (d) 36th
  33. 33.Which term of the AP 5, 7, 9, 11, … is 33? (a) 16th (b) 14th (c) 17th (d) 15th
  34. 34.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 17 (b) 16 (c) 19 (d) 15
  35. 35.What is the 17th term of the AP 10, 17, 24, 31, …? (a) 122 (b) 129 (c) 119 (d) 112
  36. 36.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 156 (b) 176 (c) 37 (d) 312
  37. 37.What is the 39th term of the AP 2, 4, 6, 8, …? (a) 76 (b) 78 (c) 79 (d) 80
  38. 38.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 30 (b) 26 (c) 28 (d) 29
  39. 39.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1771 (c) 3540 (d) 1770
  40. 40.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2080 (c) 2146 (d) 2145

Answer key

  1. 54
  2. 52
  3. 83
  4. 93
  5. 100
  6. 352
  7. 625
  8. 39th
  9. 438
  10. 72
  11. 1830
  12. 89
  13. 26
  14. 2346
  15. 231
  16. 240
  17. 10th
  18. 23
  19. 289
  20. 150
  21. 56
  22. 104
  23. 142
  24. 18
  25. 120
  26. 18
  27. 96
  28. 4560
  29. 30th
  30. 81
  31. 1275
  32. 37th
  33. 15th
  34. 16
  35. 122
  36. 156
  37. 78
  38. 28
  39. 1770
  40. 2145

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