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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 271 · 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 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 90 (d) 17
  2. 2.What is the 18th term of the AP 2, 5, 8, 11, …? (a) 51 (b) 56 (c) 54 (d) 53
  3. 3.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 741 (c) 1560 (d) 780
  4. 4.What is the 21st term of the AP 7, 14, 21, 28, …? (a) 147 (b) 140 (c) 154 (d) 148
  5. 5.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 5 (b) 7 (c) 6 (d) 10
  6. 6.What is the 15th term of the AP 3, 9, 15, 21, …? (a) 84 (b) 87 (c) 93 (d) 90
  7. 7.What is the 24th term of the AP 7, 14, 21, 28, …? (a) 175 (b) 169 (c) 168 (d) 161
  8. 8.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 492 (b) 71 (c) 456 (d) 912
  9. 9.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 130 (c) 240 (d) 21
  10. 10.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 561 (c) 1122 (d) 562
  11. 11.Which term of the AP 11, 19, 27, 35, … is 195? (a) 26th (b) 23rd (c) 24th (d) 25th
  12. 12.What is the 10th term of the AP 12, 19, 26, 33, …? (a) 82 (b) 70 (c) 75 (d) 63
  13. 13.What is the 26th term of the AP 16, 23, 30, 37, …? (a) 198 (b) 191 (c) 182 (d) 175
  14. 14.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 26 (b) 238 (c) 119 (d) 122
  15. 15.What is the 25th term of the AP 3, 7, 11, 15, …? (a) 103 (b) 96 (c) 100 (d) 99
  16. 16.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 360 (b) 336 (c) 672 (d) 50
  17. 17.What is the 22nd term of the AP 1, 10, 19, 28, …? (a) 190 (b) 189 (c) 199 (d) 198
  18. 18.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 228 (b) 114 (c) 132 (d) 34
  19. 19.What is the 29th term of the AP 1, 9, 17, 25, …? (a) 233 (b) 225 (c) 232 (d) 224
  20. 20.What is the 22nd term of the AP 13, 15, 17, 19, …? (a) 57 (b) 55 (c) 42 (d) 44
  21. 21.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 120 (c) 272 (d) 128
  22. 22.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 406 (c) 378 (d) 392
  23. 23.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 100 (b) 50 (c) 55 (d) 14
  24. 24.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 114 (b) 210 (c) 105 (d) 25
  25. 25.Which term of the AP 15, 17, 19, 21, … is 73? (a) 31st (b) 32nd (c) 29th (d) 30th
  26. 26.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 6 (b) 4 (c) 3 (d) 5
  27. 27.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 24 (b) 90 (c) 160 (d) 80
  28. 28.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 100 (b) 85 (c) 29 (d) 170
  29. 29.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 21 (b) 28 (c) 22 (d) 23
  30. 30.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2080 (c) 4160 (d) 2016
  31. 31.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 600 (b) 330 (c) 57 (d) 300
  32. 32.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 528 (c) 496 (d) 512
  33. 33.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 17 (c) 144 (d) 138
  34. 34.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 5550 (c) 2701 (d) 2738
  35. 35.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 561 (c) 578 (d) 1190
  36. 36.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 14 (b) 60 (c) 108 (d) 54
  37. 37.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 22 (b) 80 (c) 160 (d) 83
  38. 38.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 73 (c) 72 (d) 12
  39. 39.What is the 30th term of the AP 6, 9, 12, 15, …? (a) 96 (b) 87 (c) 90 (d) 93
  40. 40.What is the 27th term of the AP 13, 19, 25, 31, …? (a) 156 (b) 175 (c) 169 (d) 162

Answer key

  1. 81
  2. 53
  3. 780
  4. 147
  5. 6
  6. 87
  7. 168
  8. 456
  9. 120
  10. 561
  11. 24th
  12. 75
  13. 191
  14. 119
  15. 99
  16. 336
  17. 190
  18. 114
  19. 225
  20. 55
  21. 136
  22. 406
  23. 50
  24. 105
  25. 30th
  26. 4
  27. 80
  28. 85
  29. 22
  30. 2080
  31. 300
  32. 528
  33. 138
  34. 2775
  35. 595
  36. 54
  37. 80
  38. 72
  39. 93
  40. 169

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