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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 859 · 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 missing term in the AP 8, 14, ?, 26, 32? (a) 21 (b) 26 (c) 20 (d) 19
  2. 2.What is the 32nd term of the AP 1, 6, 11, 16, …? (a) 156 (b) 160 (c) 155 (d) 161
  3. 3.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 15 (b) 9 (c) 8 (d) 7
  4. 4.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 138 (c) 144 (d) 17
  5. 5.Which term of the AP 12, 16, 20, 24, … is 84? (a) 18th (b) 19th (c) 20th (d) 21st
  6. 6.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  7. 7.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1770 (c) 1771 (d) 3540
  8. 8.What is the 39th term of the AP 5, 13, 21, 29, …? (a) 304 (b) 309 (c) 317 (d) 312
  9. 9.Which term of the AP 12, 16, 20, 24, … is 52? (a) 13th (b) 10th (c) 11th (d) 12th
  10. 10.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 43 (b) 506 (c) 253 (d) 275
  11. 11.What is the missing term in the AP 16, 25, ?, 43, 52? (a) 35 (b) 43 (c) 34 (d) 33
  12. 12.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 80 (b) 20 (c) 77 (d) 154
  13. 13.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3200 (c) 3240 (d) 6480
  14. 14.What is the 11th term of the AP 6, 12, 18, 24, …? (a) 60 (b) 66 (c) 67 (d) 72
  15. 15.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 10 (c) 52 (d) 104
  16. 16.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 70 (b) 63 (c) 15 (d) 126
  17. 17.What is the 39th term of the AP 12, 21, 30, 39, …? (a) 342 (b) 351 (c) 363 (d) 354
  18. 18.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 3 (b) 6 (c) 4 (d) 5
  19. 19.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 26 (c) 25 (d) 50
  20. 20.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 235 (b) 260 (c) 470 (d) 46
  21. 21.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 62 (b) 704 (c) 385 (d) 352
  22. 22.Which term of the AP 4, 9, 14, 19, … is 54? (a) 10th (b) 12th (c) 13th (d) 11th
  23. 23.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 45 (b) 90 (c) 10 (d) 48
  24. 24.What is the 18th term of the AP 11, 15, 19, 23, …? (a) 68 (b) 79 (c) 83 (d) 72
  25. 25.Which term of the AP 20, 22, 24, 26, … is 60? (a) 22nd (b) 20th (c) 21st (d) 30th
  26. 26.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 17 (b) 27 (c) 19 (d) 18
  27. 27.What is the 23rd term of the AP 4, 13, 22, 31, …? (a) 202 (b) 207 (c) 198 (d) 211
  28. 28.What is the 22nd term of the AP 16, 19, 22, 25, …? (a) 82 (b) 63 (c) 79 (d) 66
  29. 29.What is the 17th term of the AP 18, 26, 34, 42, …? (a) 136 (b) 154 (c) 146 (d) 128
  30. 30.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 49 (b) 341 (c) 638 (d) 319
  31. 31.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 1922 (c) 1953 (d) 3906
  32. 32.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  33. 33.Which term of the AP 4, 8, 12, 16, … is 152? (a) 38th (b) 40th (c) 37th (d) 39th
  34. 34.What is the 40th term of the AP 19, 27, 35, 43, …? (a) 339 (b) 331 (c) 320 (d) 312
  35. 35.What is the 37th term of the AP 13, 22, 31, 40, …? (a) 333 (b) 346 (c) 324 (d) 337
  36. 36.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 55 (b) 14 (c) 100 (d) 50
  37. 37.What is the 36th term of the AP 13, 17, 21, 25, …? (a) 144 (b) 140 (c) 153 (d) 157
  38. 38.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 27 (b) 21 (c) 20 (d) 19
  39. 39.Which term of the AP 16, 23, 30, 37, … is 135? (a) 17th (b) 18th (c) 19th (d) 20th
  40. 40.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 51 (b) 243 (c) 486 (d) 270

Answer key

  1. 20
  2. 156
  3. 8
  4. 138
  5. 19th
  6. 144
  7. 1770
  8. 309
  9. 11th
  10. 253
  11. 34
  12. 77
  13. 3240
  14. 66
  15. 52
  16. 63
  17. 354
  18. 4
  19. 25
  20. 235
  21. 352
  22. 11th
  23. 45
  24. 79
  25. 21st
  26. 18
  27. 202
  28. 79
  29. 146
  30. 319
  31. 1953
  32. 529
  33. 38th
  34. 331
  35. 337
  36. 50
  37. 153
  38. 20
  39. 18th
  40. 243

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