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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 265 · 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 27th term of the AP 6, 8, 10, 12, …? (a) 60 (b) 52 (c) 54 (d) 58
  2. 2.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 38 (b) 164 (c) 184 (d) 328
  3. 3.What is the 33rd term of the AP 13, 18, 23, 28, …? (a) 160 (b) 178 (c) 165 (d) 173
  4. 4.Which term of the AP 7, 13, 19, 25, … is 109? (a) 17th (b) 18th (c) 20th (d) 19th
  5. 5.Which term of the AP 3, 5, 7, 9, … is 73? (a) 37th (b) 38th (c) 36th (d) 35th
  6. 6.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 29 (b) 310 (c) 170 (d) 155
  7. 7.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 85 (c) 140 (d) 70
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  9. 9.What is the 38th term of the AP 4, 13, 22, 31, …? (a) 342 (b) 337 (c) 333 (d) 346
  10. 10.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 630 (c) 648 (d) 666
  11. 11.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 132 (b) 143 (c) 264 (d) 22
  12. 12.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 73 (c) 12 (d) 72
  13. 13.Which term of the AP 9, 15, 21, 27, … is 147? (a) 23rd (b) 26th (c) 24th (d) 25th
  14. 14.Which term of the AP 5, 11, 17, 23, … is 107? (a) 18th (b) 17th (c) 20th (d) 19th
  15. 15.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 27 (b) 29 (c) 28 (d) 36
  16. 16.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 16 (b) 252 (c) 126 (d) 132
  17. 17.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 120 (c) 136 (d) 128
  18. 18.What is the 15th term of the AP 6, 13, 20, 27, …? (a) 104 (b) 111 (c) 98 (d) 105
  19. 19.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 396 (b) 34 (c) 198 (d) 201
  20. 20.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  21. 21.What is the 21st term of the AP 9, 12, 15, 18, …? (a) 69 (b) 72 (c) 63 (d) 60
  22. 22.Which term of the AP 2, 5, 8, 11, … is 74? (a) 27th (b) 24th (c) 25th (d) 26th
  23. 23.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 17 (c) 144 (d) 138
  24. 24.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 81 (b) 82 (c) 162 (d) 13
  25. 25.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 26 (c) 192 (d) 108
  26. 26.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  27. 27.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 11 (b) 16 (c) 10 (d) 12
  28. 28.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 504 (b) 257 (c) 48 (d) 252
  29. 29.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 21 (b) 132 (c) 242 (d) 121
  30. 30.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 6 (b) 12 (c) 7 (d) 8
  31. 31.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300
  32. 32.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 3828 (d) 7832
  33. 33.What is the 28th term of the AP 13, 21, 29, 37, …? (a) 237 (b) 216 (c) 229 (d) 224
  34. 34.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 50 (c) 55 (d) 110
  35. 35.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 600 (b) 300 (c) 57 (d) 330
  36. 36.What is the 15th term of the AP 8, 17, 26, 35, …? (a) 135 (b) 143 (c) 134 (d) 126
  37. 37.Which term of the AP 16, 25, 34, 43, … is 133? (a) 13th (b) 15th (c) 16th (d) 14th
  38. 38.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 90 (b) 85 (c) 170 (d) 13
  39. 39.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 19 (b) 20 (c) 28 (d) 21
  40. 40.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 17 (c) 70 (d) 130

Answer key

  1. 58
  2. 164
  3. 173
  4. 18th
  5. 36th
  6. 155
  7. 70
  8. 81
  9. 337
  10. 666
  11. 132
  12. 72
  13. 24th
  14. 18th
  15. 28
  16. 126
  17. 136
  18. 104
  19. 198
  20. 361
  21. 69
  22. 25th
  23. 138
  24. 81
  25. 96
  26. 289
  27. 11
  28. 252
  29. 121
  30. 7
  31. 576
  32. 3916
  33. 229
  34. 55
  35. 300
  36. 134
  37. 14th
  38. 85
  39. 20
  40. 65

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