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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 338 · 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 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 16 (c) 72 (d) 80
  2. 2.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 154 (b) 14 (c) 77 (d) 78
  3. 3.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 26 (b) 24 (c) 34 (d) 25
  4. 4.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 200 (b) 104 (c) 100 (d) 16
  5. 5.What is the 34th term of the AP 12, 15, 18, 21, …? (a) 111 (b) 99 (c) 102 (d) 114
  6. 6.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 60 (b) 31 (c) 8 (d) 30
  7. 7.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 360 (b) 720 (c) 384 (d) 52
  8. 8.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 30 (b) 60 (c) 10 (d) 35
  9. 9.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 26 (b) 360 (c) 180 (d) 192
  10. 10.What is the 36th term of the AP 6, 13, 20, 27, …? (a) 258 (b) 245 (c) 251 (d) 252
  11. 11.What is the 23rd term of the AP 11, 19, 27, 35, …? (a) 184 (b) 187 (c) 176 (d) 195
  12. 12.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 26 (b) 24 (c) 30 (d) 25
  13. 13.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 726 (c) 58 (d) 363
  14. 14.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 31 (b) 240 (c) 252 (d) 480
  15. 15.What is the 18th term of the AP 5, 9, 13, 17, …? (a) 73 (b) 72 (c) 68 (d) 77
  16. 16.What is the 38th term of the AP 1, 6, 11, 16, …? (a) 191 (b) 185 (c) 186 (d) 190
  17. 17.What is the 40th term of the AP 18, 23, 28, 33, …? (a) 195 (b) 213 (c) 218 (d) 200
  18. 18.What is the 24th term of the AP 13, 16, 19, 22, …? (a) 85 (b) 82 (c) 69 (d) 72
  19. 19.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 36 (b) 44 (c) 35 (d) 34
  20. 20.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 108 (b) 33 (c) 216 (d) 126
  21. 21.What is the missing term in the AP 11, ?, 29, 38, 47? (a) 19 (b) 21 (c) 29 (d) 20
  22. 22.Which term of the AP 19, 25, 31, 37, … is 67? (a) 8th (b) 11th (c) 10th (d) 9th
  23. 23.What is the 39th term of the AP 14, 18, 22, 26, …? (a) 170 (b) 166 (c) 152 (d) 156
  24. 24.What is the 22nd term of the AP 20, 26, 32, 38, …? (a) 132 (b) 126 (c) 146 (d) 152
  25. 25.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 40 (b) 180 (c) 175 (d) 350
  26. 26.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 306 (b) 333 (c) 612 (d) 58
  27. 27.What is the 30th term of the AP 7, 10, 13, 16, …? (a) 87 (b) 97 (c) 94 (d) 90
  28. 28.What is the 36th term of the AP 6, 11, 16, 21, …? (a) 180 (b) 175 (c) 181 (d) 186
  29. 29.Which term of the AP 11, 13, 15, 17, … is 47? (a) 21st (b) 20th (c) 18th (d) 19th
  30. 30.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 21 (b) 242 (c) 121 (d) 132
  31. 31.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  32. 32.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 135 (b) 18 (c) 270 (d) 140
  33. 33.What is the 16th term of the AP 8, 11, 14, 17, …? (a) 53 (b) 48 (c) 45 (d) 56
  34. 34.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 379 (b) 374 (c) 59 (d) 748
  35. 35.What is the 15th term of the AP 11, 17, 23, 29, …? (a) 101 (b) 84 (c) 90 (d) 95
  36. 36.Which term of the AP 8, 10, 12, 14, … is 34? (a) 13th (b) 17th (c) 14th (d) 15th
  37. 37.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 8 (b) 36 (c) 35 (d) 70
  38. 38.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 372 (b) 396 (c) 53 (d) 744
  39. 39.What is the 21st term of the AP 8, 12, 16, 20, …? (a) 84 (b) 92 (c) 88 (d) 80
  40. 40.What is the 20th term of the AP 19, 26, 33, 40, …? (a) 133 (b) 159 (c) 152 (d) 140

Answer key

  1. 72
  2. 77
  3. 25
  4. 100
  5. 111
  6. 30
  7. 360
  8. 30
  9. 180
  10. 251
  11. 187
  12. 25
  13. 363
  14. 240
  15. 73
  16. 186
  17. 213
  18. 82
  19. 35
  20. 108
  21. 20
  22. 9th
  23. 166
  24. 146
  25. 175
  26. 306
  27. 94
  28. 181
  29. 19th
  30. 121
  31. 441
  32. 135
  33. 53
  34. 374
  35. 95
  36. 14th
  37. 35
  38. 372
  39. 88
  40. 152

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