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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 618 · 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 all the whole numbers from 1 to 69? (a) 2416 (b) 2415 (c) 4830 (d) 2346
  2. 2.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 468 (b) 239 (c) 234 (d) 46
  3. 3.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 31 (b) 32 (c) 41 (d) 33
  4. 4.Which term of the AP 3, 7, 11, 15, … is 107? (a) 26th (b) 29th (c) 28th (d) 27th
  5. 5.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2017 (c) 4032 (d) 2016
  6. 6.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 59 (d) 900
  7. 7.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 4290 (c) 2145 (d) 2080
  8. 8.What is the 29th term of the AP 1, 9, 17, 25, …? (a) 233 (b) 224 (c) 225 (d) 232
  9. 9.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 348 (b) 648 (c) 49 (d) 324
  10. 10.What is the 36th term of the AP 13, 22, 31, 40, …? (a) 328 (b) 315 (c) 324 (d) 337
  11. 11.What is the 12th term of the AP 1, 9, 17, 25, …? (a) 89 (b) 97 (c) 88 (d) 96
  12. 12.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 26 (b) 160 (c) 85 (d) 80
  13. 13.What is the 12th term of the AP 13, 19, 25, 31, …? (a) 85 (b) 72 (c) 79 (d) 66
  14. 14.What is the 27th term of the AP 13, 22, 31, 40, …? (a) 256 (b) 234 (c) 243 (d) 247
  15. 15.Which term of the AP 6, 14, 22, 30, … is 166? (a) 22nd (b) 23rd (c) 21st (d) 20th
  16. 16.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 28 (b) 37 (c) 30 (d) 29
  17. 17.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 600 (c) 300 (d) 330
  18. 18.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 90 (b) 156 (c) 23 (d) 78
  19. 19.Which term of the AP 16, 25, 34, 43, … is 97? (a) 11th (b) 12th (c) 9th (d) 10th
  20. 20.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 72 (d) 36
  21. 21.What is the 11th term of the AP 11, 16, 21, 26, …? (a) 55 (b) 50 (c) 61 (d) 66
  22. 22.What is the 10th term of the AP 17, 21, 25, 29, …? (a) 40 (b) 53 (c) 36 (d) 57
  23. 23.What is the 37th term of the AP 2, 9, 16, 23, …? (a) 261 (b) 254 (c) 252 (d) 259
  24. 24.Which term of the AP 14, 16, 18, 20, … is 80? (a) 40th (b) 35th (c) 34th (d) 33rd
  25. 25.What is the 10th term of the AP 20, 26, 32, 38, …? (a) 60 (b) 80 (c) 74 (d) 54
  26. 26.Which term of the AP 3, 11, 19, 27, … is 83? (a) 13th (b) 12th (c) 11th (d) 10th
  27. 27.Which term of the AP 2, 7, 12, 17, … is 52? (a) 10th (b) 12th (c) 13th (d) 11th
  28. 28.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
  29. 29.What is the 15th term of the AP 16, 19, 22, 25, …? (a) 58 (b) 42 (c) 61 (d) 45
  30. 30.What is the 23rd term of the AP 14, 22, 30, 38, …? (a) 184 (b) 190 (c) 176 (d) 198
  31. 31.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 253 (c) 506 (d) 242
  32. 32.What is the 34th term of the AP 9, 18, 27, 36, …? (a) 306 (b) 297 (c) 307 (d) 315
  33. 33.Which term of the AP 4, 12, 20, 28, … is 220? (a) 30th (b) 28th (c) 29th (d) 27th
  34. 34.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 169 (d) 91
  35. 35.What is the 32nd term of the AP 19, 24, 29, 34, …? (a) 160 (b) 155 (c) 179 (d) 174
  36. 36.What is the 13th term of the AP 11, 18, 25, 32, …? (a) 84 (b) 91 (c) 102 (d) 95
  37. 37.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 378 (b) 189 (c) 45 (d) 210
  38. 38.What is the 14th term of the AP 6, 9, 12, 15, …? (a) 42 (b) 39 (c) 48 (d) 45
  39. 39.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 78 (c) 72 (d) 156
  40. 40.What is the missing term in the AP 19, 22, 25, ?, 31? (a) 27 (b) 31 (c) 28 (d) 29

Answer key

  1. 2415
  2. 234
  3. 32
  4. 27th
  5. 2016
  6. 900
  7. 2145
  8. 225
  9. 324
  10. 328
  11. 89
  12. 80
  13. 79
  14. 247
  15. 21st
  16. 29
  17. 300
  18. 78
  19. 10th
  20. 64
  21. 61
  22. 53
  23. 254
  24. 34th
  25. 74
  26. 11th
  27. 11th
  28. 81
  29. 58
  30. 190
  31. 253
  32. 306
  33. 28th
  34. 169
  35. 174
  36. 95
  37. 189
  38. 45
  39. 78
  40. 28

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