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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 272 · 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 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 576 (d) 47
  2. 2.Which term of the AP 2, 9, 16, 23, … is 121? (a) 17th (b) 19th (c) 20th (d) 18th
  3. 3.What is the 17th term of the AP 18, 22, 26, 30, …? (a) 64 (b) 82 (c) 86 (d) 68
  4. 4.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 1431 (c) 2970 (d) 1458
  5. 5.What is the 32nd term of the AP 13, 16, 19, 22, …? (a) 106 (b) 109 (c) 96 (d) 93
  6. 6.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 225 (c) 240 (d) 120
  7. 7.What is the 35th term of the AP 4, 6, 8, 10, …? (a) 68 (b) 70 (c) 72 (d) 74
  8. 8.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 13 (b) 96 (c) 90 (d) 180
  9. 9.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 18 (b) 16 (c) 15 (d) 17
  10. 10.What is the 10th term of the AP 4, 8, 12, 16, …? (a) 36 (b) 41 (c) 44 (d) 40
  11. 11.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 35 (b) 34 (c) 44 (d) 36
  12. 12.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 51 (b) 270 (c) 243 (d) 486
  13. 13.What is the 18th term of the AP 5, 9, 13, 17, …? (a) 68 (b) 73 (c) 77 (d) 72
  14. 14.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  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 sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 198 (c) 108 (d) 19
  17. 17.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 144 (b) 136 (c) 272 (d) 24
  18. 18.What is the 40th term of the AP 4, 12, 20, 28, …? (a) 316 (b) 324 (c) 320 (d) 312
  19. 19.What is the missing term in the AP 8, 15, 22, ?, 36? (a) 36 (b) 30 (c) 28 (d) 29
  20. 20.What is the 13th term of the AP 5, 13, 21, 29, …? (a) 96 (b) 104 (c) 101 (d) 109
  21. 21.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 27 (b) 174 (c) 87 (d) 102
  22. 22.What is the missing term in the AP 8, 10, 12, ?, 16? (a) 16 (b) 15 (c) 13 (d) 14
  23. 23.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 31 (b) 350 (c) 190 (d) 175
  24. 24.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 13 (b) 12 (c) 14 (d) 15
  25. 25.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  26. 26.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 105 (d) 27
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 43 (d) 506
  28. 28.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 66 (b) 132 (c) 67 (d) 11
  29. 29.What is the missing term in the AP 9, 11, ?, 15, 17? (a) 13 (b) 15 (c) 14 (d) 12
  30. 30.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 630 (c) 1260 (d) 595
  31. 31.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 10 (b) 9 (c) 11 (d) 8
  32. 32.What is the 10th term of the AP 18, 22, 26, 30, …? (a) 40 (b) 36 (c) 54 (d) 58
  33. 33.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 112 (b) 28 (c) 126 (d) 224
  34. 34.What is the 21st term of the AP 19, 25, 31, 37, …? (a) 145 (b) 126 (c) 120 (d) 139
  35. 35.Which term of the AP 13, 20, 27, 34, … is 153? (a) 23rd (b) 20th (c) 21st (d) 22nd
  36. 36.What is the 18th term of the AP 19, 26, 33, 40, …? (a) 119 (b) 145 (c) 126 (d) 138
  37. 37.Which term of the AP 14, 18, 22, 26, … is 86? (a) 21st (b) 20th (c) 19th (d) 18th
  38. 38.What is the 15th term of the AP 16, 18, 20, 22, …? (a) 30 (b) 44 (c) 46 (d) 28
  39. 39.What is the 35th term of the AP 17, 19, 21, 23, …? (a) 70 (b) 85 (c) 68 (d) 87
  40. 40.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 212 (b) 209 (c) 418 (d) 34

Answer key

  1. 576
  2. 18th
  3. 82
  4. 1485
  5. 106
  6. 225
  7. 72
  8. 90
  9. 16
  10. 40
  11. 35
  12. 243
  13. 73
  14. 81
  15. 253
  16. 99
  17. 136
  18. 316
  19. 29
  20. 101
  21. 87
  22. 14
  23. 175
  24. 13
  25. 289
  26. 196
  27. 484
  28. 66
  29. 13
  30. 630
  31. 9
  32. 54
  33. 112
  34. 139
  35. 21st
  36. 138
  37. 19th
  38. 44
  39. 85
  40. 209

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