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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 384 · 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 23rd term of the AP 18, 26, 34, 42, …? (a) 202 (b) 194 (c) 184 (d) 176
  2. 2.What is the 32nd term of the AP 16, 24, 32, 40, …? (a) 256 (b) 264 (c) 248 (d) 272
  3. 3.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 160 (b) 95 (c) 28 (d) 80
  4. 4.What is the missing term in the AP 9, 16, 23, ?, 37? (a) 29 (b) 31 (c) 37 (d) 30
  5. 5.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 13 (b) 8 (c) 9 (d) 10
  6. 6.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 50 (c) 26 (d) 25
  7. 7.What is the 40th term of the AP 13, 15, 17, 19, …? (a) 80 (b) 91 (c) 78 (d) 93
  8. 8.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 4830 (c) 2416 (d) 2415
  9. 9.What is the sum of all the whole numbers from 1 to 55? (a) 3080 (b) 1541 (c) 1485 (d) 1540
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 676 (d) 351
  11. 11.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 84 (b) 90 (c) 19 (d) 168
  12. 12.What is the 25th term of the AP 11, 13, 15, 17, …? (a) 50 (b) 48 (c) 61 (d) 59
  13. 13.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 300 (c) 288 (d) 600
  14. 14.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 248 (b) 272 (c) 496 (d) 52
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 110 (d) 100
  16. 16.What is the 38th term of the AP 9, 13, 17, 21, …? (a) 148 (b) 161 (c) 152 (d) 157
  17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 49 (d) 28
  18. 18.Which term of the AP 18, 23, 28, 33, … is 68? (a) 13th (b) 10th (c) 11th (d) 12th
  19. 19.What is the 12th term of the AP 15, 18, 21, 24, …? (a) 33 (b) 36 (c) 48 (d) 51
  20. 20.What is the 21st term of the AP 4, 8, 12, 16, …? (a) 85 (b) 80 (c) 84 (d) 88
  21. 21.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 252 (b) 279 (c) 504 (d) 52
  22. 22.Which term of the AP 3, 8, 13, 18, … is 83? (a) 18th (b) 16th (c) 17th (d) 19th
  23. 23.What is the 14th term of the AP 13, 15, 17, 19, …? (a) 41 (b) 28 (c) 39 (d) 26
  24. 24.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 37 (d) 190
  25. 25.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 29 (b) 27 (c) 25 (d) 26
  26. 26.Which term of the AP 6, 9, 12, 15, … is 30? (a) 8th (b) 11th (c) 10th (d) 9th
  27. 27.What is the 28th term of the AP 10, 12, 14, 16, …? (a) 54 (b) 56 (c) 66 (d) 64
  28. 28.What is the 11th term of the AP 6, 15, 24, 33, …? (a) 99 (b) 105 (c) 96 (d) 90
  29. 29.What is the 24th term of the AP 16, 25, 34, 43, …? (a) 216 (b) 232 (c) 207 (d) 223
  30. 30.What is the 31st term of the AP 8, 13, 18, 23, …? (a) 155 (b) 158 (c) 163 (d) 150
  31. 31.What is the missing term in the AP 16, 20, ?, 28, 32? (a) 28 (b) 23 (c) 25 (d) 24
  32. 32.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 174 (b) 87 (c) 22 (d) 96
  33. 33.What is the 36th term of the AP 7, 10, 13, 16, …? (a) 108 (b) 115 (c) 105 (d) 112
  34. 34.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1711 (c) 1770 (d) 1771
  35. 35.What is the 23rd term of the AP 7, 16, 25, 34, …? (a) 198 (b) 207 (c) 205 (d) 214
  36. 36.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 378 (c) 351 (d) 379
  37. 37.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 130 (b) 19 (c) 68 (d) 65
  38. 38.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 32 (b) 26 (c) 24 (d) 25
  39. 39.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 90 (b) 45 (c) 46 (d) 9
  40. 40.What is the 29th term of the AP 19, 27, 35, 43, …? (a) 224 (b) 232 (c) 243 (d) 251

Answer key

  1. 194
  2. 264
  3. 80
  4. 30
  5. 9
  6. 25
  7. 91
  8. 2415
  9. 1540
  10. 676
  11. 84
  12. 59
  13. 300
  14. 248
  15. 100
  16. 157
  17. 49
  18. 11th
  19. 48
  20. 84
  21. 252
  22. 17th
  23. 39
  24. 361
  25. 26
  26. 9th
  27. 64
  28. 96
  29. 223
  30. 158
  31. 24
  32. 87
  33. 112
  34. 1770
  35. 205
  36. 378
  37. 65
  38. 25
  39. 45
  40. 243

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