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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 954 · 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 1, 6, 11, …? (a) 110 (b) 55 (c) 21 (d) 60
  2. 2.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 150 (c) 264 (d) 132
  3. 3.What is the 28th term of the AP 2, 5, 8, 11, …? (a) 86 (b) 81 (c) 84 (d) 83
  4. 4.What is the 27th term of the AP 13, 22, 31, 40, …? (a) 243 (b) 247 (c) 256 (d) 234
  5. 5.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 9 (b) 10 (c) 8 (d) 13
  6. 6.Which term of the AP 10, 12, 14, 16, … is 88? (a) 40th (b) 41st (c) 39th (d) 44th
  7. 7.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 57 (b) 112 (c) 56 (d) 11
  8. 8.What is the 29th term of the AP 10, 12, 14, 16, …? (a) 56 (b) 68 (c) 58 (d) 66
  9. 9.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 20 (b) 22 (c) 21 (d) 28
  10. 10.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 7140 (c) 3486 (d) 3570
  11. 11.What is the 24th term of the AP 11, 13, 15, 17, …? (a) 59 (b) 46 (c) 57 (d) 48
  12. 12.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 171 (b) 174 (c) 31 (d) 342
  13. 13.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 576 (d) 47
  14. 14.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 8 (b) 9 (c) 6 (d) 7
  15. 15.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 277 (c) 253 (d) 276
  16. 16.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 168 (b) 24 (c) 156 (d) 312
  17. 17.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 120 (b) 204 (c) 102 (d) 32
  18. 18.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 29 (b) 100 (c) 85 (d) 170
  19. 19.What is the 34th term of the AP 9, 17, 25, 33, …? (a) 264 (b) 272 (c) 281 (d) 273
  20. 20.What is the 40th term of the AP 5, 7, 9, 11, …? (a) 85 (b) 78 (c) 80 (d) 83
  21. 21.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 65 (b) 120 (c) 60 (d) 22
  22. 22.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 3570 (c) 3656 (d) 7310
  23. 23.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  24. 24.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 625 (d) 49
  25. 25.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 43 (b) 408 (c) 224 (d) 204
  26. 26.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2017 (c) 1953 (d) 2016
  27. 27.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 880 (b) 473 (c) 440 (d) 70
  28. 28.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 390 (b) 60 (c) 770 (d) 385
  29. 29.What is the 26th term of the AP 20, 23, 26, 29, …? (a) 98 (b) 75 (c) 95 (d) 78
  30. 30.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 992 (d) 496
  31. 31.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 220 (b) 34 (c) 125 (d) 110
  32. 32.What is the 39th term of the AP 11, 14, 17, 20, …? (a) 128 (b) 114 (c) 125 (d) 117
  33. 33.Which term of the AP 4, 7, 10, 13, … is 88? (a) 31st (b) 29th (c) 28th (d) 30th
  34. 34.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 63 (c) 126 (d) 13
  35. 35.What is the 14th term of the AP 7, 15, 23, 31, …? (a) 119 (b) 111 (c) 104 (d) 112
  36. 36.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 242 (b) 245 (c) 484 (d) 37
  37. 37.What is the 19th term of the AP 12, 17, 22, 27, …? (a) 95 (b) 102 (c) 90 (d) 107
  38. 38.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 11 (b) 12 (c) 10 (d) 9
  39. 39.What is the 34th term of the AP 17, 25, 33, 41, …? (a) 281 (b) 264 (c) 272 (d) 289
  40. 40.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 212 (b) 44 (c) 424 (d) 232

Answer key

  1. 55
  2. 132
  3. 83
  4. 247
  5. 9
  6. 40th
  7. 56
  8. 66
  9. 21
  10. 3570
  11. 57
  12. 171
  13. 576
  14. 7
  15. 276
  16. 156
  17. 102
  18. 85
  19. 273
  20. 83
  21. 60
  22. 3655
  23. 169
  24. 625
  25. 204
  26. 2016
  27. 440
  28. 385
  29. 95
  30. 496
  31. 110
  32. 125
  33. 29th
  34. 63
  35. 111
  36. 242
  37. 102
  38. 10
  39. 281
  40. 212

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