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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 330 · 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 4, 6, 8, 10, … is 28? (a) 13th (b) 15th (c) 14th (d) 12th
  2. 2.Which term of the AP 5, 8, 11, 14, … is 101? (a) 33rd (b) 32nd (c) 34th (d) 35th
  3. 3.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 190 (d) 200
  4. 4.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 7 (b) 5 (c) 10 (d) 6
  5. 5.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 2485 (c) 2450 (d) 4970
  6. 6.What is the 38th term of the AP 10, 19, 28, 37, …? (a) 342 (b) 343 (c) 333 (d) 352
  7. 7.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 216 (b) 45 (c) 192 (d) 384
  8. 8.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 288 (b) 147 (c) 28 (d) 144
  9. 9.What is the 37th term of the AP 12, 19, 26, 33, …? (a) 259 (b) 271 (c) 264 (d) 252
  10. 10.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 36 (b) 33 (c) 8 (d) 66
  11. 11.What is the 16th term of the AP 4, 7, 10, 13, …? (a) 52 (b) 49 (c) 45 (d) 48
  12. 12.What is the 19th term of the AP 19, 21, 23, 25, …? (a) 55 (b) 57 (c) 36 (d) 38
  13. 13.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 11 (b) 7 (c) 8 (d) 9
  14. 14.What is the 11th term of the AP 1, 5, 9, 13, …? (a) 45 (b) 40 (c) 44 (d) 41
  15. 15.Which term of the AP 7, 9, 11, 13, … is 69? (a) 33rd (b) 32nd (c) 31st (d) 34th
  16. 16.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 105 (b) 114 (c) 210 (d) 25
  17. 17.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 156 (c) 72 (d) 66
  18. 18.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 73 (b) 140 (c) 70 (d) 20
  19. 19.What is the 26th term of the AP 9, 11, 13, 15, …? (a) 50 (b) 61 (c) 59 (d) 52
  20. 20.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 77 (c) 78 (d) 154
  21. 21.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 4851 (c) 9702 (d) 4802
  22. 22.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 26 (b) 25 (c) 7 (d) 50
  23. 23.Which term of the AP 18, 26, 34, 42, … is 266? (a) 31st (b) 34th (c) 33rd (d) 32nd
  24. 24.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 10 (b) 9 (c) 8 (d) 15
  25. 25.What is the 32nd term of the AP 20, 27, 34, 41, …? (a) 217 (b) 224 (c) 244 (d) 237
  26. 26.What is the 15th term of the AP 3, 12, 21, 30, …? (a) 135 (b) 126 (c) 138 (d) 129
  27. 27.Which term of the AP 17, 26, 35, 44, … is 134? (a) 13th (b) 15th (c) 16th (d) 14th
  28. 28.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1922 (c) 1891 (d) 1953
  29. 29.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 100 (b) 30 (c) 105 (d) 200
  30. 30.Which term of the AP 16, 19, 22, 25, … is 118? (a) 36th (b) 37th (c) 34th (d) 35th
  31. 31.What is the 13th term of the AP 19, 22, 25, 28, …? (a) 36 (b) 58 (c) 39 (d) 55
  32. 32.What is the 21st term of the AP 5, 11, 17, 23, …? (a) 125 (b) 131 (c) 126 (d) 120
  33. 33.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 66 (b) 429 (c) 792 (d) 396
  34. 34.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 26 (b) 248 (c) 124 (d) 136
  35. 35.What is the 37th term of the AP 5, 13, 21, 29, …? (a) 296 (b) 293 (c) 301 (d) 288
  36. 36.Which term of the AP 11, 16, 21, 26, … is 116? (a) 21st (b) 22nd (c) 24th (d) 23rd
  37. 37.What is the 22nd term of the AP 5, 11, 17, 23, …? (a) 137 (b) 126 (c) 131 (d) 132
  38. 38.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
  39. 39.What is the 36th term of the AP 13, 20, 27, 34, …? (a) 252 (b) 258 (c) 265 (d) 245
  40. 40.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4656 (c) 4560 (d) 4608

Answer key

  1. 13th
  2. 33rd
  3. 210
  4. 6
  5. 2485
  6. 343
  7. 192
  8. 144
  9. 264
  10. 33
  11. 49
  12. 55
  13. 8
  14. 41
  15. 32nd
  16. 105
  17. 78
  18. 70
  19. 59
  20. 77
  21. 4851
  22. 25
  23. 32nd
  24. 9
  25. 237
  26. 129
  27. 14th
  28. 1953
  29. 100
  30. 35th
  31. 55
  32. 125
  33. 396
  34. 124
  35. 293
  36. 22nd
  37. 131
  38. 225
  39. 258
  40. 4656

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