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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 697 · 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 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  2. 2.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 90 (b) 85 (c) 170 (d) 13
  3. 3.What is the 32nd term of the AP 12, 20, 28, 36, …? (a) 256 (b) 248 (c) 260 (d) 268
  4. 4.What is the 38th term of the AP 10, 19, 28, 37, …? (a) 343 (b) 342 (c) 333 (d) 352
  5. 5.What is the 39th term of the AP 7, 9, 11, 13, …? (a) 76 (b) 78 (c) 85 (d) 83
  6. 6.What is the 10th term of the AP 2, 7, 12, 17, …? (a) 50 (b) 47 (c) 45 (d) 52
  7. 7.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 480 (b) 444 (c) 888 (d) 70
  8. 8.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 272 (d) 31
  9. 9.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 648 (c) 630 (d) 1332
  10. 10.What is the 40th term of the AP 5, 12, 19, 26, …? (a) 280 (b) 278 (c) 285 (d) 273
  11. 11.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 816 (b) 408 (c) 67 (d) 444
  12. 12.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 156 (c) 72 (d) 78
  13. 13.What is the 25th term of the AP 4, 12, 20, 28, …? (a) 192 (b) 196 (c) 204 (d) 200
  14. 14.What is the 10th term of the AP 6, 9, 12, 15, …? (a) 33 (b) 30 (c) 36 (d) 27
  15. 15.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 21 (b) 75 (c) 130 (d) 65
  16. 16.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 25 (b) 26 (c) 32 (d) 27
  17. 17.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 42 (d) 11
  18. 18.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 18 (b) 168 (c) 84 (d) 91
  19. 19.What is the 24th term of the AP 14, 21, 28, 35, …? (a) 168 (b) 182 (c) 161 (d) 175
  20. 20.What is the 16th term of the AP 7, 13, 19, 25, …? (a) 103 (b) 97 (c) 96 (d) 90
  21. 21.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 55 (b) 280 (c) 560 (d) 310
  22. 22.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 150 (b) 145 (c) 19 (d) 290
  23. 23.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 2162 (c) 1081 (d) 1058
  24. 24.What is the 32nd term of the AP 14, 18, 22, 26, …? (a) 138 (b) 142 (c) 124 (d) 128
  25. 25.What is the 35th term of the AP 15, 17, 19, 21, …? (a) 68 (b) 70 (c) 85 (d) 83
  26. 26.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 4032 (c) 1953 (d) 2017
  27. 27.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 600 (d) 47
  28. 28.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 26 (b) 7 (c) 50 (d) 25
  29. 29.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 17 (b) 16 (c) 14 (d) 15
  30. 30.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4851 (c) 4950 (d) 4951
  31. 31.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 462 (c) 231 (d) 232
  32. 32.Which term of the AP 1, 7, 13, 19, … is 229? (a) 40th (b) 39th (c) 41st (d) 38th
  33. 33.Which term of the AP 9, 15, 21, 27, … is 243? (a) 40th (b) 41st (c) 39th (d) 42nd
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 25 (d) 30
  35. 35.What is the 40th term of the AP 2, 11, 20, 29, …? (a) 360 (b) 362 (c) 351 (d) 353
  36. 36.What is the 17th term of the AP 17, 20, 23, 26, …? (a) 68 (b) 48 (c) 51 (d) 65
  37. 37.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 379 (b) 59 (c) 374 (d) 748
  38. 38.What is the 26th term of the AP 17, 19, 21, 23, …? (a) 50 (b) 67 (c) 52 (d) 69
  39. 39.What is the 26th term of the AP 1, 5, 9, 13, …? (a) 105 (b) 100 (c) 101 (d) 104
  40. 40.What is the 37th term of the AP 18, 21, 24, 27, …? (a) 108 (b) 126 (c) 129 (d) 111

Answer key

  1. 64
  2. 85
  3. 260
  4. 343
  5. 83
  6. 47
  7. 444
  8. 256
  9. 666
  10. 278
  11. 408
  12. 78
  13. 196
  14. 33
  15. 65
  16. 26
  17. 36
  18. 84
  19. 175
  20. 97
  21. 280
  22. 145
  23. 1081
  24. 138
  25. 83
  26. 2016
  27. 576
  28. 25
  29. 15
  30. 4950
  31. 231
  32. 39th
  33. 40th
  34. 25
  35. 353
  36. 65
  37. 374
  38. 67
  39. 101
  40. 126

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