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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 389 · 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 6, 11, ?, 21, 26? (a) 16 (b) 17 (c) 15 (d) 21
  2. 2.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 126 (c) 22 (d) 135
  3. 3.What is the 12th term of the AP 9, 17, 25, 33, …? (a) 88 (b) 97 (c) 96 (d) 105
  4. 4.Which term of the AP 13, 21, 29, 37, … is 317? (a) 40th (b) 38th (c) 39th (d) 41st
  5. 5.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 264 (b) 252 (c) 504 (d) 32
  6. 6.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 3540 (c) 1711 (d) 1771
  7. 7.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 23 (b) 24 (c) 22 (d) 25
  8. 8.What is the 28th term of the AP 8, 11, 14, 17, …? (a) 92 (b) 81 (c) 84 (d) 89
  9. 9.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 26 (b) 18 (c) 17 (d) 19
  10. 10.Which term of the AP 15, 17, 19, 21, … is 77? (a) 34th (b) 33rd (c) 32nd (d) 31st
  11. 11.What is the 28th term of the AP 6, 13, 20, 27, …? (a) 195 (b) 196 (c) 202 (d) 189
  12. 12.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 270 (b) 135 (c) 138 (d) 27
  13. 13.What is the 29th term of the AP 17, 23, 29, 35, …? (a) 168 (b) 185 (c) 191 (d) 174
  14. 14.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 435 (c) 870 (d) 406
  15. 15.What is the missing term in the AP 1, 10, ?, 28, 37? (a) 19 (b) 28 (c) 18 (d) 20
  16. 16.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 13 (b) 48 (c) 54 (d) 96
  17. 17.What is the 40th term of the AP 10, 18, 26, 34, …? (a) 312 (b) 330 (c) 320 (d) 322
  18. 18.Which term of the AP 20, 28, 36, 44, … is 260? (a) 32nd (b) 33rd (c) 30th (d) 31st
  19. 19.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 112 (b) 208 (c) 104 (d) 20
  20. 20.What is the missing term in the AP 1, 9, ?, 25, 33? (a) 18 (b) 16 (c) 17 (d) 25
  21. 21.Which term of the AP 9, 13, 17, 21, … is 109? (a) 28th (b) 27th (c) 25th (d) 26th
  22. 22.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 256 (d) 136
  23. 23.What is the 25th term of the AP 9, 11, 13, 15, …? (a) 50 (b) 57 (c) 59 (d) 48
  24. 24.What is the 10th term of the AP 3, 7, 11, 15, …? (a) 43 (b) 40 (c) 36 (d) 39
  25. 25.What is the 13th term of the AP 7, 15, 23, 31, …? (a) 111 (b) 104 (c) 96 (d) 103
  26. 26.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 10 (b) 9 (c) 12 (d) 11
  27. 27.What is the 36th term of the AP 1, 3, 5, 7, …? (a) 71 (b) 73 (c) 70 (d) 72
  28. 28.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 115 (b) 32 (c) 200 (d) 100
  29. 29.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4753 (c) 9702 (d) 4851
  30. 30.What is the missing term in the AP 20, 27, ?, 41, 48? (a) 33 (b) 35 (c) 34 (d) 41
  31. 31.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 132 (b) 34 (c) 114 (d) 228
  32. 32.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 552 (d) 276
  33. 33.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 1540 (c) 1568 (d) 3192
  34. 34.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 201 (b) 198 (c) 396 (d) 33
  35. 35.Which term of the AP 5, 8, 11, 14, … is 110? (a) 36th (b) 38th (c) 37th (d) 35th
  36. 36.What is the missing term in the AP 19, 27, 35, ?, 51? (a) 43 (b) 42 (c) 51 (d) 44
  37. 37.What is the 29th term of the AP 5, 7, 9, 11, …? (a) 61 (b) 58 (c) 63 (d) 56
  38. 38.What is the 11th term of the AP 16, 23, 30, 37, …? (a) 86 (b) 70 (c) 77 (d) 93
  39. 39.What is the 19th term of the AP 7, 13, 19, 25, …? (a) 121 (b) 115 (c) 114 (d) 108
  40. 40.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 260 (b) 140 (c) 130 (d) 22

Answer key

  1. 16
  2. 126
  3. 97
  4. 39th
  5. 252
  6. 1770
  7. 23
  8. 89
  9. 18
  10. 32nd
  11. 195
  12. 135
  13. 185
  14. 435
  15. 19
  16. 48
  17. 322
  18. 31st
  19. 104
  20. 17
  21. 26th
  22. 256
  23. 57
  24. 39
  25. 103
  26. 10
  27. 71
  28. 100
  29. 4851
  30. 34
  31. 114
  32. 529
  33. 1596
  34. 198
  35. 36th
  36. 43
  37. 61
  38. 86
  39. 115
  40. 130

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