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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 224 · 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 16th term of the AP 14, 17, 20, 23, …? (a) 48 (b) 59 (c) 45 (d) 62
  2. 2.What is the missing term in the AP 3, 10, 17, ?, 31? (a) 23 (b) 31 (c) 25 (d) 24
  3. 3.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 408 (b) 43 (c) 224 (d) 204
  4. 4.What is the 26th term of the AP 13, 22, 31, 40, …? (a) 238 (b) 234 (c) 225 (d) 247
  5. 5.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1830 (c) 1770 (d) 1800
  6. 6.What is the 14th term of the AP 15, 22, 29, 36, …? (a) 106 (b) 98 (c) 113 (d) 91
  7. 7.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 7482 (c) 3698 (d) 3655
  8. 8.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 9 (b) 44 (c) 88 (d) 48
  9. 9.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  10. 10.What is the 34th term of the AP 13, 16, 19, 22, …? (a) 99 (b) 102 (c) 112 (d) 115
  11. 11.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 21 (b) 20 (c) 24 (d) 19
  12. 12.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 216 (c) 109 (d) 108
  13. 13.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 196 (b) 105 (c) 20 (d) 98
  14. 14.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 92 (b) 96 (c) 184 (d) 15
  15. 15.What is the 25th term of the AP 9, 15, 21, 27, …? (a) 144 (b) 153 (c) 150 (d) 159
  16. 16.Which term of the AP 17, 26, 35, 44, … is 134? (a) 13th (b) 16th (c) 15th (d) 14th
  17. 17.What is the 25th term of the AP 14, 16, 18, 20, …? (a) 64 (b) 62 (c) 50 (d) 48
  18. 18.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 66 (d) 21
  19. 19.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 19 (b) 15 (c) 16 (d) 17
  20. 20.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 130 (b) 65 (c) 21 (d) 75
  21. 21.What is the 33rd term of the AP 16, 19, 22, 25, …? (a) 112 (b) 99 (c) 115 (d) 96
  22. 22.Which term of the AP 15, 24, 33, 42, … is 177? (a) 20th (b) 18th (c) 21st (d) 19th
  23. 23.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4753 (c) 4656 (d) 4754
  24. 24.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2016 (c) 2080 (d) 4160
  25. 25.What is the 17th term of the AP 1, 10, 19, 28, …? (a) 154 (b) 144 (c) 153 (d) 145
  26. 26.What is the 14th term of the AP 5, 11, 17, 23, …? (a) 83 (b) 89 (c) 84 (d) 78
  27. 27.What is the 28th term of the AP 4, 8, 12, 16, …? (a) 108 (b) 112 (c) 113 (d) 116
  28. 28.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 4187 (c) 4095 (d) 8372
  29. 29.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 465 (c) 497 (d) 496
  30. 30.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1770 (c) 3540 (d) 1771
  31. 31.What is the missing term in the AP 2, 10, ?, 26, 34? (a) 17 (b) 18 (c) 26 (d) 19
  32. 32.What is the missing term in the AP 19, 23, ?, 31, 35? (a) 26 (b) 28 (c) 27 (d) 31
  33. 33.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 45 (b) 550 (c) 297 (d) 275
  34. 34.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1226 (c) 1176 (d) 1225
  35. 35.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 16 (b) 91 (c) 92 (d) 182
  36. 36.Which term of the AP 13, 17, 21, 25, … is 49? (a) 11th (b) 9th (c) 12th (d) 10th
  37. 37.Which term of the AP 11, 19, 27, 35, … is 107? (a) 15th (b) 14th (c) 12th (d) 13th
  38. 38.What is the 39th term of the AP 8, 15, 22, 29, …? (a) 281 (b) 273 (c) 266 (d) 274
  39. 39.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 435 (c) 930 (d) 465
  40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289

Answer key

  1. 59
  2. 24
  3. 204
  4. 238
  5. 1830
  6. 106
  7. 3741
  8. 44
  9. 196
  10. 112
  11. 20
  12. 108
  13. 98
  14. 92
  15. 153
  16. 14th
  17. 62
  18. 121
  19. 16
  20. 65
  21. 112
  22. 19th
  23. 4753
  24. 2080
  25. 145
  26. 83
  27. 112
  28. 4186
  29. 496
  30. 1770
  31. 18
  32. 27
  33. 275
  34. 1225
  35. 91
  36. 10th
  37. 13th
  38. 274
  39. 465
  40. 289

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