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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 518 · 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 20th term of the AP 15, 19, 23, 27, …? (a) 91 (b) 95 (c) 76 (d) 80
  2. 2.What is the 37th term of the AP 12, 20, 28, 36, …? (a) 288 (b) 300 (c) 296 (d) 308
  3. 3.What is the 37th term of the AP 11, 17, 23, 29, …? (a) 222 (b) 227 (c) 216 (d) 233
  4. 4.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 154 (c) 153 (d) 306
  5. 5.What is the 15th term of the AP 3, 6, 9, 12, …? (a) 46 (b) 48 (c) 45 (d) 42
  6. 6.What is the 20th term of the AP 7, 16, 25, 34, …? (a) 180 (b) 187 (c) 178 (d) 171
  7. 7.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 49 (b) 266 (c) 522 (d) 261
  8. 8.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 100 (b) 200 (c) 23 (d) 112
  9. 9.What is the 25th term of the AP 4, 7, 10, 13, …? (a) 76 (b) 75 (c) 79 (d) 72
  10. 10.What is the 17th term of the AP 4, 11, 18, 25, …? (a) 119 (b) 112 (c) 123 (d) 116
  11. 11.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 57 (b) 11 (c) 56 (d) 112
  12. 12.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 168 (b) 18 (c) 84 (d) 91
  13. 13.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 20 (b) 22 (c) 23 (d) 21
  14. 14.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 140 (b) 70 (c) 71 (d) 13
  15. 15.What is the 29th term of the AP 12, 19, 26, 33, …? (a) 215 (b) 208 (c) 196 (d) 203
  16. 16.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2211 (d) 2145
  17. 17.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 42 (b) 203 (c) 396 (d) 198
  18. 18.What is the 30th term of the AP 9, 11, 13, 15, …? (a) 58 (b) 69 (c) 67 (d) 60
  19. 19.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 44 (b) 35 (c) 34 (d) 36
  20. 20.What is the missing term in the AP 4, 12, 20, ?, 36? (a) 27 (b) 29 (c) 36 (d) 28
  21. 21.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 108 (c) 102 (d) 14
  22. 22.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 168 (b) 300 (c) 40 (d) 150
  23. 23.What is the 21st term of the AP 11, 15, 19, 23, …? (a) 84 (b) 91 (c) 80 (d) 95
  24. 24.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 15 (b) 105 (c) 110 (d) 210
  25. 25.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 120 (b) 224 (c) 21 (d) 112
  26. 26.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 155 (b) 308 (c) 154 (d) 19
  27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15
  28. 28.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 120 (c) 136 (d) 272
  29. 29.What is the 33rd term of the AP 18, 25, 32, 39, …? (a) 224 (b) 231 (c) 249 (d) 242
  30. 30.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 105 (b) 196 (c) 98 (d) 20
  31. 31.What is the 36th term of the AP 3, 7, 11, 15, …? (a) 143 (b) 144 (c) 147 (d) 140
  32. 32.What is the 25th term of the AP 2, 5, 8, 11, …? (a) 74 (b) 77 (c) 75 (d) 72
  33. 33.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 15 (b) 21 (c) 16 (d) 17
  34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729
  35. 35.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 20 (b) 18 (c) 25 (d) 19
  36. 36.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 224 (b) 200 (c) 400 (d) 46
  37. 37.What is the missing term in the AP 5, 9, 13, ?, 21? (a) 17 (b) 18 (c) 16 (d) 21
  38. 38.Which term of the AP 8, 12, 16, 20, … is 76? (a) 19th (b) 18th (c) 20th (d) 17th
  39. 39.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 25 (b) 35 (c) 26 (d) 27
  40. 40.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 55 (c) 50 (d) 110

Answer key

  1. 91
  2. 300
  3. 227
  4. 153
  5. 45
  6. 178
  7. 261
  8. 100
  9. 76
  10. 116
  11. 56
  12. 84
  13. 21
  14. 70
  15. 208
  16. 2211
  17. 198
  18. 67
  19. 35
  20. 28
  21. 102
  22. 150
  23. 91
  24. 105
  25. 112
  26. 154
  27. 64
  28. 136
  29. 242
  30. 98
  31. 143
  32. 74
  33. 16
  34. 729
  35. 19
  36. 200
  37. 17
  38. 18th
  39. 26
  40. 55

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