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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 904 · 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 missing term in the AP 9, 11, ?, 15, 17? (a) 14 (b) 12 (c) 13 (d) 15
  2. 2.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 352 (b) 43 (c) 176 (d) 200
  3. 3.What is the 38th term of the AP 16, 19, 22, 25, …? (a) 111 (b) 127 (c) 114 (d) 130
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
  5. 5.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 56 (b) 98 (c) 49 (d) 13
  6. 6.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 24 (b) 198 (c) 108 (d) 99
  7. 7.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 438 (b) 876 (c) 468 (d) 64
  8. 8.What is the 19th term of the AP 14, 17, 20, 23, …? (a) 54 (b) 71 (c) 68 (d) 57
  9. 9.What is the 13th term of the AP 13, 18, 23, 28, …? (a) 65 (b) 78 (c) 73 (d) 60
  10. 10.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576
  11. 11.What is the 26th term of the AP 20, 25, 30, 35, …? (a) 130 (b) 125 (c) 150 (d) 145
  12. 12.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 70 (c) 11 (d) 65
  13. 13.What is the missing term in the AP 10, 12, 14, ?, 18? (a) 18 (b) 16 (c) 17 (d) 15
  14. 14.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 640 (b) 320 (c) 59 (d) 350
  15. 15.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 240 (d) 225
  16. 16.What is the 13th term of the AP 3, 5, 7, 9, …? (a) 24 (b) 29 (c) 27 (d) 26
  17. 17.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 31 (b) 29 (c) 39 (d) 30
  18. 18.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 70 (b) 8 (c) 35 (d) 36
  19. 19.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2851 (c) 2775 (d) 2850
  20. 20.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 75 (c) 23 (d) 150
  21. 21.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 54 (b) 108 (c) 14 (d) 60
  22. 22.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 138 (b) 33 (c) 246 (d) 123
  23. 23.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 51 (d) 351
  24. 24.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
  25. 25.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 7 (b) 6 (c) 10 (d) 8
  26. 26.What is the 20th term of the AP 17, 23, 29, 35, …? (a) 137 (b) 131 (c) 114 (d) 120
  27. 27.What is the 19th term of the AP 4, 12, 20, 28, …? (a) 152 (b) 148 (c) 144 (d) 156
  28. 28.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 780 (c) 800 (d) 820
  29. 29.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 384 (b) 45 (c) 216 (d) 192
  30. 30.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 264 (b) 246 (c) 37 (d) 492
  31. 31.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 11 (d) 21
  32. 32.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 2312 (c) 2346 (d) 4692
  33. 33.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3741 (c) 7482 (d) 3655
  34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 55 (d) 110
  35. 35.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 65 (b) 418 (c) 770 (d) 385
  36. 36.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 812 (c) 378 (d) 406
  37. 37.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 108 (b) 112 (c) 216 (d) 17
  38. 38.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 930 (c) 59 (d) 465
  39. 39.What is the 27th term of the AP 19, 24, 29, 34, …? (a) 149 (b) 135 (c) 130 (d) 154
  40. 40.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 253 (c) 231 (d) 242

Answer key

  1. 13
  2. 176
  3. 127
  4. 196
  5. 49
  6. 99
  7. 438
  8. 68
  9. 73
  10. 576
  11. 145
  12. 65
  13. 16
  14. 320
  15. 225
  16. 27
  17. 30
  18. 35
  19. 2850
  20. 75
  21. 54
  22. 123
  23. 676
  24. 49
  25. 7
  26. 131
  27. 148
  28. 820
  29. 192
  30. 246
  31. 36
  32. 2346
  33. 3741
  34. 100
  35. 385
  36. 406
  37. 108
  38. 900
  39. 149
  40. 253

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