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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 247 · 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 11, 20, 29, ?, 47? (a) 39 (b) 38 (c) 47 (d) 37
  2. 2.Which term of the AP 2, 10, 18, 26, … is 274? (a) 35th (b) 36th (c) 34th (d) 37th
  3. 3.What is the 14th term of the AP 7, 10, 13, 16, …? (a) 49 (b) 39 (c) 46 (d) 42
  4. 4.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 147 (b) 294 (c) 168 (d) 39
  5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
  6. 6.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 16 (b) 12 (c) 13 (d) 14
  7. 7.What is the missing term in the AP 20, 29, 38, ?, 56? (a) 47 (b) 56 (c) 46 (d) 48
  8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 55 (d) 812
  9. 9.Which term of the AP 18, 21, 24, 27, … is 78? (a) 26th (b) 21st (c) 22nd (d) 20th
  10. 10.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2850 (c) 2775 (d) 2851
  11. 11.What is the 11th term of the AP 19, 25, 31, 37, …? (a) 79 (b) 66 (c) 60 (d) 85
  12. 12.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 28 (b) 26 (c) 35 (d) 27
  13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  14. 14.What is the 31st term of the AP 7, 12, 17, 22, …? (a) 157 (b) 162 (c) 155 (d) 150
  15. 15.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 720 (b) 384 (c) 52 (d) 360
  16. 16.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 17 (b) 13 (c) 12 (d) 14
  17. 17.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 9 (b) 8 (c) 10 (d) 7
  18. 18.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 153 (c) 342 (d) 162
  19. 19.Which term of the AP 1, 9, 17, 25, … is 97? (a) 15th (b) 14th (c) 12th (d) 13th
  20. 20.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 48 (b) 84 (c) 42 (d) 12
  21. 21.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 16 (b) 77 (c) 140 (d) 70
  22. 22.Which term of the AP 6, 14, 22, 30, … is 262? (a) 34th (b) 35th (c) 33rd (d) 32nd
  23. 23.What is the 15th term of the AP 16, 22, 28, 34, …? (a) 84 (b) 100 (c) 90 (d) 106
  24. 24.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 378 (c) 351 (d) 756
  25. 25.Which term of the AP 14, 17, 20, 23, … is 116? (a) 35th (b) 37th (c) 36th (d) 34th
  26. 26.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 14 (b) 15 (c) 18 (d) 13
  27. 27.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4560 (c) 4465 (d) 4561
  28. 28.What is the 34th term of the AP 12, 17, 22, 27, …? (a) 177 (b) 182 (c) 165 (d) 170
  29. 29.What is the sum of all the whole numbers from 1 to 21? (a) 462 (b) 232 (c) 231 (d) 210
  30. 30.Which term of the AP 19, 21, 23, 25, … is 55? (a) 20th (b) 19th (c) 21st (d) 18th
  31. 31.What is the 10th term of the AP 11, 17, 23, 29, …? (a) 60 (b) 65 (c) 71 (d) 54
  32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 324 (d) 35
  33. 33.What is the 32nd term of the AP 17, 19, 21, 23, …? (a) 64 (b) 79 (c) 62 (d) 81
  34. 34.What is the 19th term of the AP 18, 23, 28, 33, …? (a) 113 (b) 90 (c) 95 (d) 108
  35. 35.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 342 (b) 171 (c) 35 (d) 189
  36. 36.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 153 (c) 33 (d) 306
  37. 37.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 60 (b) 120 (c) 15 (d) 66
  38. 38.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 78 (b) 77 (c) 14 (d) 154
  39. 39.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 702 (d) 51
  40. 40.Which term of the AP 10, 12, 14, 16, … is 48? (a) 24th (b) 21st (c) 19th (d) 20th

Answer key

  1. 38
  2. 35th
  3. 46
  4. 147
  5. 36
  6. 13
  7. 47
  8. 784
  9. 21st
  10. 2850
  11. 79
  12. 27
  13. 121
  14. 157
  15. 360
  16. 13
  17. 8
  18. 171
  19. 13th
  20. 42
  21. 70
  22. 33rd
  23. 100
  24. 378
  25. 35th
  26. 14
  27. 4560
  28. 177
  29. 231
  30. 19th
  31. 65
  32. 324
  33. 79
  34. 108
  35. 171
  36. 289
  37. 60
  38. 77
  39. 676
  40. 20th

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