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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 802 · 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 6 terms of the AP 3, 5, 7, …? (a) 96 (b) 13 (c) 48 (d) 54
  2. 2.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 136 (d) 256
  3. 3.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 25 (b) 21 (c) 19 (d) 20
  4. 4.Which term of the AP 4, 10, 16, 22, … is 106? (a) 17th (b) 18th (c) 20th (d) 19th
  5. 5.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 288 (b) 261 (c) 53 (d) 522
  6. 6.What is the 32nd term of the AP 11, 13, 15, 17, …? (a) 75 (b) 62 (c) 64 (d) 73
  7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 729 (d) 378
  8. 8.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 13 (b) 17 (c) 15 (d) 14
  9. 9.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 127 (b) 126 (c) 18 (d) 252
  10. 10.What is the 24th term of the AP 8, 14, 20, 26, …? (a) 144 (b) 138 (c) 146 (d) 152
  11. 11.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 154 (b) 20 (c) 77 (d) 80
  12. 12.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 132 (c) 67 (d) 66
  13. 13.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 528 (c) 561 (d) 562
  14. 14.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  15. 15.What is the 15th term of the AP 15, 21, 27, 33, …? (a) 84 (b) 90 (c) 99 (d) 105
  16. 16.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3828 (c) 7656 (d) 3829
  17. 17.What is the 35th term of the AP 10, 17, 24, 31, …? (a) 245 (b) 248 (c) 238 (d) 255
  18. 18.What is the 22nd term of the AP 20, 22, 24, 26, …? (a) 44 (b) 42 (c) 62 (d) 64
  19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 33 (d) 153
  20. 20.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 13 (b) 19 (c) 12 (d) 14
  21. 21.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 174 (b) 96 (c) 22 (d) 87
  22. 22.What is the missing term in the AP 14, ?, 24, 29, 34? (a) 19 (b) 20 (c) 24 (d) 18
  23. 23.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 374 (b) 682 (c) 61 (d) 341
  24. 24.What is the 38th term of the AP 15, 21, 27, 33, …? (a) 222 (b) 228 (c) 243 (d) 237
  25. 25.Which term of the AP 19, 22, 25, 28, … is 118? (a) 33rd (b) 34th (c) 36th (d) 35th
  26. 26.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 14 (b) 88 (c) 168 (d) 84
  27. 27.What is the missing term in the AP 11, 15, 19, ?, 27? (a) 24 (b) 27 (c) 23 (d) 22
  28. 28.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 67 (b) 407 (c) 440 (d) 814
  29. 29.What is the 15th term of the AP 16, 25, 34, 43, …? (a) 126 (b) 135 (c) 142 (d) 151
  30. 30.Which term of the AP 2, 8, 14, 20, … is 68? (a) 11th (b) 13th (c) 14th (d) 12th
  31. 31.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 13 (b) 89 (c) 176 (d) 88
  32. 32.What is the 28th term of the AP 5, 8, 11, 14, …? (a) 89 (b) 84 (c) 81 (d) 86
  33. 33.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2415 (c) 4970 (d) 2485
  34. 34.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 595 (c) 630 (d) 631
  35. 35.What is the 10th term of the AP 11, 16, 21, 26, …? (a) 45 (b) 50 (c) 61 (d) 56
  36. 36.What is the 38th term of the AP 6, 8, 10, 12, …? (a) 82 (b) 76 (c) 80 (d) 74
  37. 37.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 12 (b) 7 (c) 6 (d) 8
  38. 38.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 7482 (c) 3698 (d) 3741
  39. 39.Which term of the AP 6, 8, 10, 12, … is 20? (a) 9th (b) 10th (c) 7th (d) 8th
  40. 40.What is the 32nd term of the AP 2, 5, 8, 11, …? (a) 96 (b) 95 (c) 98 (d) 93

Answer key

  1. 48
  2. 256
  3. 20
  4. 18th
  5. 261
  6. 73
  7. 729
  8. 14
  9. 126
  10. 146
  11. 77
  12. 66
  13. 561
  14. 81
  15. 99
  16. 3828
  17. 248
  18. 62
  19. 289
  20. 13
  21. 87
  22. 19
  23. 341
  24. 237
  25. 34th
  26. 84
  27. 23
  28. 407
  29. 142
  30. 12th
  31. 88
  32. 86
  33. 2485
  34. 630
  35. 56
  36. 80
  37. 7
  38. 3741
  39. 8th
  40. 95

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