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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 332 · 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 3, 6, 9, 12, … is 69? (a) 24th (b) 22nd (c) 23rd (d) 25th
  2. 2.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 506 (c) 242 (d) 253
  3. 3.What is the 28th term of the AP 4, 10, 16, 22, …? (a) 168 (b) 162 (c) 172 (d) 166
  4. 4.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 16 (b) 15 (c) 22 (d) 14
  5. 5.Which term of the AP 2, 4, 6, 8, … is 40? (a) 22nd (b) 20th (c) 21st (d) 19th
  6. 6.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 27 (b) 28 (c) 36 (d) 29
  7. 7.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 32 (b) 41 (c) 34 (d) 33
  8. 8.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 210 (c) 91 (d) 98
  9. 9.What is the 32nd term of the AP 20, 28, 36, 44, …? (a) 276 (b) 248 (c) 256 (d) 268
  10. 10.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 1800 (c) 1830 (d) 3660
  11. 11.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 138 (b) 135 (c) 27 (d) 270
  12. 12.Which term of the AP 3, 9, 15, 21, … is 195? (a) 35th (b) 34th (c) 32nd (d) 33rd
  13. 13.What is the 34th term of the AP 20, 27, 34, 41, …? (a) 238 (b) 251 (c) 258 (d) 231
  14. 14.Which term of the AP 4, 9, 14, 19, … is 99? (a) 22nd (b) 21st (c) 19th (d) 20th
  15. 15.Which term of the AP 16, 18, 20, 22, … is 74? (a) 31st (b) 30th (c) 29th (d) 37th
  16. 16.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 12 (c) 60 (d) 114
  17. 17.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 19 (b) 20 (c) 26 (d) 21
  18. 18.What is the 29th term of the AP 12, 15, 18, 21, …? (a) 84 (b) 87 (c) 99 (d) 96
  19. 19.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 26 (b) 28 (c) 35 (d) 27
  20. 20.Which term of the AP 5, 8, 11, 14, … is 113? (a) 36th (b) 38th (c) 37th (d) 39th
  21. 21.What is the 21st term of the AP 2, 4, 6, 8, …? (a) 40 (b) 44 (c) 43 (d) 42
  22. 22.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1891 (c) 1953 (d) 3906
  23. 23.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 85 (b) 26 (c) 80 (d) 160
  24. 24.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 506 (c) 253 (d) 38
  25. 25.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 191 (c) 190 (d) 380
  26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 21 (d) 132
  27. 27.Which term of the AP 14, 17, 20, 23, … is 80? (a) 24th (b) 23rd (c) 22nd (d) 25th
  28. 28.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 5112 (c) 2485 (d) 2556
  29. 29.Which term of the AP 7, 13, 19, 25, … is 61? (a) 12th (b) 10th (c) 11th (d) 9th
  30. 30.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2016 (c) 2080 (d) 2048
  31. 31.What is the missing term in the AP 14, ?, 18, 20, 22? (a) 15 (b) 16 (c) 18 (d) 17
  32. 32.What is the 34th term of the AP 12, 18, 24, 30, …? (a) 216 (b) 198 (c) 204 (d) 210
  33. 33.What is the 29th term of the AP 14, 22, 30, 38, …? (a) 238 (b) 232 (c) 224 (d) 246
  34. 34.Which term of the AP 5, 10, 15, 20, … is 110? (a) 22nd (b) 21st (c) 23rd (d) 24th
  35. 35.What is the 18th term of the AP 18, 26, 34, 42, …? (a) 162 (b) 144 (c) 154 (d) 136
  36. 36.What is the 21st term of the AP 11, 19, 27, 35, …? (a) 160 (b) 168 (c) 171 (d) 179
  37. 37.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 1653 (c) 3306 (d) 1596
  38. 38.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 594 (b) 52 (c) 297 (d) 302
  39. 39.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 147 (b) 28 (c) 288 (d) 144
  40. 40.What is the 27th term of the AP 3, 10, 17, 24, …? (a) 192 (b) 182 (c) 189 (d) 185

Answer key

  1. 23rd
  2. 253
  3. 166
  4. 15
  5. 20th
  6. 28
  7. 33
  8. 105
  9. 268
  10. 1830
  11. 135
  12. 33rd
  13. 251
  14. 20th
  15. 30th
  16. 57
  17. 20
  18. 96
  19. 27
  20. 37th
  21. 42
  22. 1953
  23. 80
  24. 253
  25. 190
  26. 121
  27. 23rd
  28. 2556
  29. 10th
  30. 2080
  31. 16
  32. 210
  33. 238
  34. 22nd
  35. 154
  36. 171
  37. 1653
  38. 297
  39. 144
  40. 185

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