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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 733 · 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 6 terms of the AP 3, 9, 15, …? (a) 126 (b) 108 (c) 216 (d) 33
  2. 2.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 94 (b) 91 (c) 182 (d) 22
  3. 3.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 24 (b) 272 (c) 144 (d) 136
  4. 4.What is the 17th term of the AP 14, 16, 18, 20, …? (a) 48 (b) 46 (c) 32 (d) 34
  5. 5.What is the 20th term of the AP 3, 6, 9, 12, …? (a) 61 (b) 63 (c) 57 (d) 60
  6. 6.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 29 (b) 170 (c) 100 (d) 85
  7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 56 (d) 49
  8. 8.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 242 (c) 253 (d) 506
  9. 9.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 90 (b) 102 (c) 180 (d) 25
  10. 10.What is the 37th term of the AP 4, 13, 22, 31, …? (a) 324 (b) 337 (c) 333 (d) 328
  11. 11.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 781 (c) 741 (d) 1560
  12. 12.What is the 30th term of the AP 12, 15, 18, 21, …? (a) 90 (b) 102 (c) 99 (d) 87
  13. 13.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 55 (b) 14 (c) 100 (d) 50
  14. 14.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 406 (c) 812 (d) 392
  15. 15.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 171 (c) 153 (d) 162
  16. 16.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 35 (c) 171 (d) 342
  17. 17.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 56 (b) 98 (c) 49 (d) 13
  18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 552 (d) 276
  19. 19.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 18 (b) 16 (c) 17 (d) 25
  20. 20.Which term of the AP 4, 8, 12, 16, … is 116? (a) 30th (b) 28th (c) 31st (d) 29th
  21. 21.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3486 (c) 3403 (d) 6972
  22. 22.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 10 (b) 104 (c) 52 (d) 56
  23. 23.What is the 21st term of the AP 6, 8, 10, 12, …? (a) 40 (b) 46 (c) 42 (d) 48
  24. 24.What is the missing term in the AP 8, 16, 24, ?, 40? (a) 33 (b) 31 (c) 32 (d) 40
  25. 25.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 561 (c) 595 (d) 1190
  26. 26.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 22 (b) 21 (c) 23 (d) 30
  27. 27.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 16 (b) 200 (c) 104 (d) 100
  28. 28.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 71 (b) 13 (c) 70 (d) 140
  29. 29.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 26 (b) 23 (c) 24 (d) 22
  30. 30.What is the 38th term of the AP 6, 14, 22, 30, …? (a) 296 (b) 310 (c) 302 (d) 304
  31. 31.What is the 13th term of the AP 5, 9, 13, 17, …? (a) 52 (b) 57 (c) 48 (d) 53
  32. 32.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 630 (d) 648
  33. 33.What is the missing term in the AP 17, 21, ?, 29, 33? (a) 26 (b) 24 (c) 29 (d) 25
  34. 34.Which term of the AP 17, 26, 35, 44, … is 179? (a) 21st (b) 20th (c) 19th (d) 18th
  35. 35.Which term of the AP 7, 11, 15, 19, … is 163? (a) 40th (b) 39th (c) 41st (d) 42nd
  36. 36.What is the 28th term of the AP 5, 13, 21, 29, …? (a) 229 (b) 221 (c) 224 (d) 216
  37. 37.What is the 21st term of the AP 17, 23, 29, 35, …? (a) 126 (b) 120 (c) 137 (d) 143
  38. 38.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 4753 (c) 4802 (d) 9702
  39. 39.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 27 (b) 36 (c) 28 (d) 26
  40. 40.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 4951 (c) 4950 (d) 9900

Answer key

  1. 108
  2. 91
  3. 136
  4. 46
  5. 60
  6. 85
  7. 49
  8. 253
  9. 90
  10. 328
  11. 780
  12. 99
  13. 50
  14. 406
  15. 171
  16. 324
  17. 49
  18. 529
  19. 17
  20. 29th
  21. 3486
  22. 52
  23. 46
  24. 32
  25. 595
  26. 22
  27. 100
  28. 70
  29. 23
  30. 302
  31. 53
  32. 666
  33. 25
  34. 19th
  35. 40th
  36. 221
  37. 137
  38. 4851
  39. 27
  40. 4950

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