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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 33 · 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.Which term of the AP 7, 14, 21, 28, … is 273? (a) 38th (b) 41st (c) 39th (d) 40th
  2. 2.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 39 (b) 162 (c) 288 (d) 144
  3. 3.Which term of the AP 19, 24, 29, 34, … is 159? (a) 31st (b) 29th (c) 28th (d) 30th
  4. 4.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 20 (b) 26 (c) 22 (d) 21
  5. 5.What is the 19th term of the AP 4, 6, 8, 10, …? (a) 40 (b) 42 (c) 36 (d) 38
  6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  7. 7.Which term of the AP 5, 11, 17, 23, … is 239? (a) 42nd (b) 39th (c) 41st (d) 40th
  8. 8.What is the 36th term of the AP 6, 15, 24, 33, …? (a) 321 (b) 324 (c) 315 (d) 330
  9. 9.Which term of the AP 10, 15, 20, 25, … is 80? (a) 16th (b) 14th (c) 17th (d) 15th
  10. 10.Which term of the AP 5, 12, 19, 26, … is 187? (a) 26th (b) 27th (c) 28th (d) 29th
  11. 11.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 50 (d) 55
  12. 12.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 42 (b) 45 (c) 46 (d) 49
  13. 13.What is the 25th term of the AP 16, 24, 32, 40, …? (a) 192 (b) 216 (c) 200 (d) 208
  14. 14.What is the sum of all the whole numbers from 1 to 90? (a) 4095 (b) 4005 (c) 8190 (d) 4050
  15. 15.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 55 (b) 306 (c) 558 (d) 279
  16. 16.What is the 15th term of the AP 9, 14, 19, 24, …? (a) 70 (b) 84 (c) 75 (d) 79
  17. 17.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 216 (b) 29 (c) 228 (d) 432
  18. 18.Which term of the AP 17, 19, 21, 23, … is 33? (a) 9th (b) 11th (c) 8th (d) 10th
  19. 19.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 154 (b) 165 (c) 308 (d) 24
  20. 20.What is the 17th term of the AP 3, 7, 11, 15, …? (a) 64 (b) 71 (c) 67 (d) 68
  21. 21.Which term of the AP 3, 10, 17, 24, … is 122? (a) 17th (b) 18th (c) 20th (d) 19th
  22. 22.What is the 30th term of the AP 9, 14, 19, 24, …? (a) 159 (b) 154 (c) 145 (d) 150
  23. 23.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 216 (c) 108 (d) 112
  24. 24.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 56 (d) 49
  26. 26.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 1891 (c) 3782 (d) 1830
  27. 27.What is the 35th term of the AP 17, 26, 35, 44, …? (a) 332 (b) 323 (c) 306 (d) 315
  28. 28.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 85 (b) 170 (c) 13 (d) 90
  29. 29.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 114 (c) 60 (d) 12
  30. 30.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 62 (b) 704 (c) 385 (d) 352
  31. 31.What is the 25th term of the AP 11, 19, 27, 35, …? (a) 200 (b) 192 (c) 211 (d) 203
  32. 32.What is the 25th term of the AP 10, 13, 16, 19, …? (a) 75 (b) 82 (c) 72 (d) 85
  33. 33.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3081 (d) 3042
  34. 34.What is the 26th term of the AP 5, 9, 13, 17, …? (a) 104 (b) 109 (c) 105 (d) 100
  35. 35.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 90 (b) 23 (c) 156 (d) 78
  36. 36.What is the 38th term of the AP 15, 20, 25, 30, …? (a) 205 (b) 185 (c) 200 (d) 190
  37. 37.Which term of the AP 4, 13, 22, 31, … is 121? (a) 13th (b) 14th (c) 16th (d) 15th
  38. 38.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 26 (b) 28 (c) 36 (d) 27
  39. 39.What is the 18th term of the AP 9, 11, 13, 15, …? (a) 43 (b) 34 (c) 36 (d) 45
  40. 40.What is the 40th term of the AP 9, 14, 19, 24, …? (a) 195 (b) 209 (c) 204 (d) 200

Answer key

  1. 39th
  2. 144
  3. 29th
  4. 21
  5. 40
  6. 289
  7. 40th
  8. 321
  9. 15th
  10. 27th
  11. 55
  12. 46
  13. 208
  14. 4095
  15. 279
  16. 79
  17. 216
  18. 9th
  19. 154
  20. 67
  21. 18th
  22. 154
  23. 108
  24. 64
  25. 49
  26. 1891
  27. 323
  28. 85
  29. 57
  30. 352
  31. 203
  32. 82
  33. 3081
  34. 105
  35. 78
  36. 200
  37. 14th
  38. 27
  39. 43
  40. 204

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