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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 739 · 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 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 35 (c) 40 (d) 70
  2. 2.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 156 (c) 72 (d) 66
  3. 3.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1540 (c) 3080 (d) 1485
  4. 4.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
  5. 5.What is the 16th term of the AP 9, 18, 27, 36, …? (a) 145 (b) 135 (c) 144 (d) 153
  6. 6.Which term of the AP 8, 14, 20, 26, … is 242? (a) 39th (b) 40th (c) 41st (d) 42nd
  7. 7.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 246 (b) 138 (c) 123 (d) 33
  8. 8.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 253 (d) 484
  9. 9.Which term of the AP 9, 11, 13, 15, … is 37? (a) 14th (b) 15th (c) 17th (d) 16th
  10. 10.What is the 30th term of the AP 1, 9, 17, 25, …? (a) 240 (b) 233 (c) 241 (d) 232
  11. 11.Which term of the AP 3, 10, 17, 24, … is 129? (a) 19th (b) 21st (c) 20th (d) 18th
  12. 12.What is the 16th term of the AP 16, 24, 32, 40, …? (a) 144 (b) 120 (c) 136 (d) 128
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 435 (d) 870
  14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 55 (d) 110
  15. 15.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
  16. 16.What is the 12th term of the AP 16, 23, 30, 37, …? (a) 84 (b) 100 (c) 77 (d) 93
  17. 17.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 84 (b) 168 (c) 96 (d) 24
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
  19. 19.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 812 (d) 406
  20. 20.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 171 (c) 191 (d) 190
  21. 21.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 85 (b) 27 (c) 90 (d) 170
  22. 22.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 1953 (d) 2016
  23. 23.What is the 30th term of the AP 2, 7, 12, 17, …? (a) 150 (b) 152 (c) 145 (d) 147
  24. 24.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 12 (b) 17 (c) 13 (d) 14
  25. 25.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 59 (d) 465
  26. 26.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 264 (b) 242 (c) 42 (d) 484
  27. 27.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
  28. 28.What is the missing term in the AP 10, ?, 20, 25, 30? (a) 14 (b) 20 (c) 16 (d) 15
  29. 29.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 39 (b) 30 (c) 31 (d) 32
  30. 30.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 816 (b) 444 (c) 408 (d) 67
  31. 31.What is the 17th term of the AP 15, 23, 31, 39, …? (a) 151 (b) 136 (c) 128 (d) 143
  32. 32.What is the 30th term of the AP 3, 5, 7, 9, …? (a) 58 (b) 63 (c) 61 (d) 60
  33. 33.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 23 (b) 24 (c) 28 (d) 25
  34. 34.What is the 32nd term of the AP 3, 8, 13, 18, …? (a) 163 (b) 160 (c) 155 (d) 158
  35. 35.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 216 (b) 432 (c) 44 (d) 221
  36. 36.Which term of the AP 7, 12, 17, 22, … is 107? (a) 21st (b) 22nd (c) 23rd (d) 20th
  37. 37.What is the 32nd term of the AP 18, 20, 22, 24, …? (a) 64 (b) 80 (c) 62 (d) 82
  38. 38.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72
  39. 39.What is the 36th term of the AP 16, 19, 22, 25, …? (a) 124 (b) 105 (c) 108 (d) 121
  40. 40.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 30 (b) 39 (c) 32 (d) 31

Answer key

  1. 35
  2. 78
  3. 1540
  4. 729
  5. 144
  6. 40th
  7. 123
  8. 484
  9. 15th
  10. 233
  11. 19th
  12. 136
  13. 841
  14. 100
  15. 361
  16. 93
  17. 84
  18. 81
  19. 406
  20. 190
  21. 85
  22. 2016
  23. 147
  24. 13
  25. 900
  26. 242
  27. 121
  28. 15
  29. 31
  30. 408
  31. 143
  32. 61
  33. 24
  34. 158
  35. 216
  36. 21st
  37. 80
  38. 64
  39. 121
  40. 31

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