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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 667 · 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 the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 529 (d) 45
  2. 2.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 176 (b) 352 (c) 26 (d) 187
  3. 3.What is the 32nd term of the AP 9, 16, 23, 30, …? (a) 224 (b) 217 (c) 226 (d) 233
  4. 4.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 29 (b) 56 (c) 28 (d) 7
  5. 5.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  6. 6.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 135 (b) 126 (c) 22 (d) 252
  7. 7.What is the sum of all the whole numbers from 1 to 74? (a) 5550 (b) 2701 (c) 2775 (d) 2738
  8. 8.What is the 32nd term of the AP 7, 12, 17, 22, …? (a) 155 (b) 162 (c) 160 (d) 167
  9. 9.Which term of the AP 13, 15, 17, 19, … is 37? (a) 14th (b) 13th (c) 15th (d) 12th
  10. 10.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 312 (b) 288 (c) 576 (d) 46
  11. 11.What is the 39th term of the AP 19, 25, 31, 37, …? (a) 247 (b) 234 (c) 228 (d) 253
  12. 12.What is the 10th term of the AP 4, 6, 8, 10, …? (a) 24 (b) 20 (c) 18 (d) 22
  13. 13.What is the 17th term of the AP 3, 12, 21, 30, …? (a) 153 (b) 144 (c) 147 (d) 156
  14. 14.What is the 25th term of the AP 18, 27, 36, 45, …? (a) 225 (b) 234 (c) 243 (d) 216
  15. 15.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 231 (c) 242 (d) 506
  16. 16.What is the 20th term of the AP 2, 8, 14, 20, …? (a) 114 (b) 116 (c) 122 (d) 120
  17. 17.What is the 12th term of the AP 13, 21, 29, 37, …? (a) 101 (b) 109 (c) 88 (d) 96
  18. 18.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 38 (b) 200 (c) 400 (d) 220
  19. 19.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 114 (b) 132 (c) 228 (d) 34
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 812 (d) 406
  21. 21.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 266 (b) 28 (c) 133 (d) 136
  22. 22.What is the 16th term of the AP 13, 15, 17, 19, …? (a) 43 (b) 30 (c) 45 (d) 32
  23. 23.What is the 19th term of the AP 19, 21, 23, 25, …? (a) 55 (b) 38 (c) 57 (d) 36
  24. 24.Which term of the AP 14, 19, 24, 29, … is 164? (a) 30th (b) 33rd (c) 32nd (d) 31st
  25. 25.What is the 28th term of the AP 4, 8, 12, 16, …? (a) 116 (b) 108 (c) 112 (d) 113
  26. 26.What is the 14th term of the AP 16, 24, 32, 40, …? (a) 128 (b) 104 (c) 120 (d) 112
  27. 27.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 2 (b) 4 (c) 3 (d) 5
  28. 28.What is the 36th term of the AP 2, 4, 6, 8, …? (a) 74 (b) 73 (c) 72 (d) 70
  29. 29.What is the 25th term of the AP 12, 19, 26, 33, …? (a) 175 (b) 180 (c) 187 (d) 168
  30. 30.What is the 15th term of the AP 3, 12, 21, 30, …? (a) 126 (b) 135 (c) 138 (d) 129
  31. 31.Which term of the AP 18, 22, 26, 30, … is 142? (a) 33rd (b) 32nd (c) 34th (d) 31st
  32. 32.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 162 (b) 26 (c) 96 (d) 81
  33. 33.Which term of the AP 5, 8, 11, 14, … is 29? (a) 8th (b) 11th (c) 10th (d) 9th
  34. 34.What is the 26th term of the AP 7, 9, 11, 13, …? (a) 57 (b) 59 (c) 52 (d) 50
  35. 35.What is the 11th term of the AP 12, 17, 22, 27, …? (a) 67 (b) 62 (c) 55 (d) 50
  36. 36.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 22 (b) 21 (c) 23 (d) 20
  37. 37.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 121 (b) 242 (c) 132 (d) 21
  38. 38.What is the 11th term of the AP 1, 3, 5, 7, …? (a) 23 (b) 22 (c) 21 (d) 20
  39. 39.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 561 (c) 1190 (d) 578
  40. 40.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 726 (c) 58 (d) 363

Answer key

  1. 529
  2. 176
  3. 226
  4. 28
  5. 81
  6. 126
  7. 2775
  8. 162
  9. 13th
  10. 288
  11. 247
  12. 22
  13. 147
  14. 234
  15. 253
  16. 116
  17. 101
  18. 200
  19. 114
  20. 784
  21. 133
  22. 43
  23. 55
  24. 31st
  25. 112
  26. 120
  27. 3
  28. 72
  29. 180
  30. 129
  31. 32nd
  32. 81
  33. 9th
  34. 57
  35. 62
  36. 21
  37. 121
  38. 21
  39. 595
  40. 363

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