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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 225 · 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 17th term of the AP 10, 12, 14, 16, …? (a) 44 (b) 34 (c) 32 (d) 42
  2. 2.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 31 (b) 222 (c) 126 (d) 111
  3. 3.What is the 14th term of the AP 17, 19, 21, 23, …? (a) 45 (b) 28 (c) 43 (d) 26
  4. 4.Which term of the AP 9, 13, 17, 21, … is 57? (a) 12th (b) 13th (c) 14th (d) 15th
  5. 5.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 25 (b) 26 (c) 23 (d) 24
  6. 6.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 308 (b) 46 (c) 572 (d) 286
  7. 7.What is the missing term in the AP 19, 28, ?, 46, 55? (a) 46 (b) 38 (c) 36 (d) 37
  8. 8.What is the 20th term of the AP 15, 17, 19, 21, …? (a) 40 (b) 38 (c) 53 (d) 55
  9. 9.Which term of the AP 3, 9, 15, 21, … is 45? (a) 10th (b) 9th (c) 8th (d) 7th
  10. 10.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 631 (c) 595 (d) 1260
  11. 11.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 3828 (d) 7832
  12. 12.What is the 36th term of the AP 4, 11, 18, 25, …? (a) 245 (b) 256 (c) 249 (d) 252
  13. 13.What is the sum of all the whole numbers from 1 to 76? (a) 2926 (b) 2850 (c) 5852 (d) 2888
  14. 14.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 240 (d) 225
  15. 15.What is the 25th term of the AP 13, 20, 27, 34, …? (a) 168 (b) 188 (c) 175 (d) 181
  16. 16.What is the 32nd term of the AP 8, 11, 14, 17, …? (a) 96 (b) 93 (c) 104 (d) 101
  17. 17.What is the 18th term of the AP 20, 24, 28, 32, …? (a) 92 (b) 72 (c) 68 (d) 88
  18. 18.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 60 (b) 108 (c) 14 (d) 54
  19. 19.What is the 21st term of the AP 8, 10, 12, 14, …? (a) 42 (b) 48 (c) 50 (d) 40
  20. 20.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 150 (b) 15 (c) 75 (d) 78
  21. 21.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 13 (b) 96 (c) 48 (d) 54
  22. 22.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 816 (b) 444 (c) 67 (d) 408
  23. 23.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 465 (c) 497 (d) 496
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  25. 25.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 3906 (c) 1953 (d) 1891
  26. 26.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 31 (c) 192 (d) 114
  27. 27.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 3540 (c) 1770 (d) 1711
  28. 28.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 33 (b) 189 (c) 378 (d) 192
  29. 29.What is the 23rd term of the AP 4, 9, 14, 19, …? (a) 110 (b) 114 (c) 119 (d) 115
  30. 30.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 19 (b) 26 (c) 21 (d) 20
  31. 31.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 4556 (c) 2279 (d) 2211
  32. 32.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 11 (b) 120 (c) 64 (d) 60
  33. 33.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 231 (d) 210
  34. 34.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 24 (b) 21 (c) 42 (d) 6
  35. 35.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 396 (b) 53 (c) 744 (d) 372
  36. 36.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 228 (b) 210 (c) 420 (d) 34
  37. 37.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 207 (b) 39 (c) 225 (d) 414
  38. 38.What is the 31st term of the AP 10, 19, 28, 37, …? (a) 279 (b) 270 (c) 280 (d) 289
  39. 39.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  40. 40.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 8742 (c) 4278 (d) 4372

Answer key

  1. 42
  2. 111
  3. 43
  4. 13th
  5. 24
  6. 286
  7. 37
  8. 53
  9. 8th
  10. 630
  11. 3916
  12. 249
  13. 2926
  14. 225
  15. 181
  16. 101
  17. 88
  18. 54
  19. 48
  20. 75
  21. 48
  22. 408
  23. 496
  24. 100
  25. 1953
  26. 96
  27. 1770
  28. 189
  29. 114
  30. 20
  31. 2278
  32. 60
  33. 231
  34. 21
  35. 372
  36. 210
  37. 207
  38. 280
  39. 121
  40. 4371

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