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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 472 · 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 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 300 (d) 47
  2. 2.What is the 25th term of the AP 20, 22, 24, 26, …? (a) 68 (b) 50 (c) 70 (d) 48
  3. 3.What is the 25th term of the AP 10, 13, 16, 19, …? (a) 75 (b) 82 (c) 85 (d) 72
  4. 4.What is the 40th term of the AP 12, 18, 24, 30, …? (a) 234 (b) 252 (c) 240 (d) 246
  5. 5.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 25 (b) 330 (c) 176 (d) 165
  6. 6.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 120 (b) 65 (c) 16 (d) 60
  7. 7.Which term of the AP 14, 18, 22, 26, … is 170? (a) 42nd (b) 40th (c) 41st (d) 39th
  8. 8.What is the 28th term of the AP 14, 19, 24, 29, …? (a) 154 (b) 135 (c) 140 (d) 149
  9. 9.What is the missing term in the AP 20, 24, 28, ?, 36? (a) 36 (b) 32 (c) 31 (d) 33
  10. 10.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 20 (b) 17 (c) 19 (d) 18
  11. 11.What is the 37th term of the AP 12, 14, 16, 18, …? (a) 86 (b) 72 (c) 84 (d) 74
  12. 12.What is the sum of all the whole numbers from 1 to 87? (a) 7656 (b) 3741 (c) 3829 (d) 3828
  13. 13.What is the 38th term of the AP 2, 4, 6, 8, …? (a) 78 (b) 74 (c) 77 (d) 76
  14. 14.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 30 (d) 25
  15. 15.What is the 34th term of the AP 19, 25, 31, 37, …? (a) 204 (b) 198 (c) 217 (d) 223
  16. 16.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 148 (b) 36 (c) 296 (d) 168
  17. 17.Which term of the AP 9, 15, 21, 27, … is 129? (a) 20th (b) 21st (c) 22nd (d) 23rd
  18. 18.Which term of the AP 11, 17, 23, 29, … is 233? (a) 37th (b) 40th (c) 38th (d) 39th
  19. 19.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3655 (c) 7482 (d) 3741
  20. 20.What is the 11th term of the AP 2, 7, 12, 17, …? (a) 50 (b) 52 (c) 57 (d) 55
  21. 21.Which term of the AP 20, 28, 36, 44, … is 164? (a) 20th (b) 21st (c) 18th (d) 19th
  22. 22.What is the 32nd term of the AP 2, 7, 12, 17, …? (a) 155 (b) 162 (c) 160 (d) 157
  23. 23.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 12 (b) 11 (c) 16 (d) 10
  24. 24.What is the 10th term of the AP 8, 13, 18, 23, …? (a) 45 (b) 53 (c) 50 (d) 58
  25. 25.Which term of the AP 15, 18, 21, 24, … is 69? (a) 18th (b) 23rd (c) 20th (d) 19th
  26. 26.What is the 36th term of the AP 20, 26, 32, 38, …? (a) 216 (b) 210 (c) 236 (d) 230
  27. 27.What is the 39th term of the AP 12, 17, 22, 27, …? (a) 195 (b) 207 (c) 190 (d) 202
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 57 (d) 435
  29. 29.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 7 (b) 5 (c) 8 (d) 6
  30. 30.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
  31. 31.What is the 37th term of the AP 17, 26, 35, 44, …? (a) 333 (b) 341 (c) 350 (d) 324
  32. 32.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
  33. 33.What is the 38th term of the AP 6, 14, 22, 30, …? (a) 304 (b) 310 (c) 296 (d) 302
  34. 34.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 25 (b) 75 (c) 150 (d) 80
  35. 35.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 286 (b) 143 (c) 18 (d) 144
  36. 36.What is the 24th term of the AP 8, 14, 20, 26, …? (a) 138 (b) 144 (c) 146 (d) 152
  37. 37.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 7 (b) 6 (c) 5 (d) 10
  38. 38.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 22 (b) 135 (c) 252 (d) 126
  39. 39.What is the 21st term of the AP 4, 7, 10, 13, …? (a) 64 (b) 63 (c) 60 (d) 67
  40. 40.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 34 (b) 198 (c) 396 (d) 201

Answer key

  1. 576
  2. 68
  3. 82
  4. 246
  5. 165
  6. 60
  7. 40th
  8. 149
  9. 32
  10. 18
  11. 84
  12. 3828
  13. 76
  14. 25
  15. 217
  16. 148
  17. 21st
  18. 38th
  19. 3741
  20. 52
  21. 19th
  22. 157
  23. 11
  24. 53
  25. 19th
  26. 230
  27. 202
  28. 841
  29. 6
  30. 784
  31. 341
  32. 441
  33. 302
  34. 75
  35. 143
  36. 146
  37. 6
  38. 126
  39. 64
  40. 198

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