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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 606 · 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 4, 8, 12, ?, 20? (a) 20 (b) 15 (c) 16 (d) 17
  2. 2.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 55 (b) 17 (c) 110 (d) 58
  3. 3.What is the 24th term of the AP 4, 7, 10, 13, …? (a) 73 (b) 76 (c) 69 (d) 72
  4. 4.What is the 21st term of the AP 3, 12, 21, 30, …? (a) 192 (b) 189 (c) 183 (d) 180
  5. 5.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 24 (b) 156 (c) 168 (d) 312
  6. 6.What is the 17th term of the AP 14, 18, 22, 26, …? (a) 64 (b) 82 (c) 68 (d) 78
  7. 7.Which term of the AP 18, 24, 30, 36, … is 204? (a) 33rd (b) 31st (c) 32nd (d) 34th
  8. 8.What is the 25th term of the AP 1, 7, 13, 19, …? (a) 144 (b) 151 (c) 145 (d) 150
  9. 9.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 32 (b) 31 (c) 30 (d) 40
  10. 10.Which term of the AP 8, 16, 24, 32, … is 280? (a) 36th (b) 35th (c) 37th (d) 34th
  11. 11.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 35 (c) 70 (d) 8
  12. 12.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 242 (b) 42 (c) 484 (d) 264
  13. 13.What is the 17th term of the AP 11, 17, 23, 29, …? (a) 102 (b) 96 (c) 107 (d) 113
  14. 14.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 18 (b) 14 (c) 15 (d) 16
  15. 15.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 29 (b) 120 (c) 136 (d) 240
  16. 16.What is the 32nd term of the AP 12, 17, 22, 27, …? (a) 167 (b) 160 (c) 172 (d) 155
  17. 17.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 11 (b) 13 (c) 12 (d) 21
  18. 18.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 88 (b) 176 (c) 18 (d) 96
  19. 19.Which term of the AP 3, 7, 11, 15, … is 99? (a) 27th (b) 26th (c) 25th (d) 24th
  20. 20.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 256 (b) 232 (c) 464 (d) 50
  21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 105 (c) 196 (d) 27
  22. 22.What is the 34th term of the AP 14, 18, 22, 26, …? (a) 146 (b) 132 (c) 150 (d) 136
  23. 23.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 81 (d) 45
  24. 24.What is the 21st term of the AP 6, 8, 10, 12, …? (a) 46 (b) 48 (c) 42 (d) 40
  25. 25.What is the 24th term of the AP 12, 15, 18, 21, …? (a) 84 (b) 72 (c) 81 (d) 69
  26. 26.Which term of the AP 5, 9, 13, 17, … is 69? (a) 19th (b) 17th (c) 18th (d) 16th
  27. 27.What is the missing term in the AP 19, 26, ?, 40, 47? (a) 40 (b) 32 (c) 34 (d) 33
  28. 28.What is the 16th term of the AP 9, 13, 17, 21, …? (a) 60 (b) 73 (c) 64 (d) 69
  29. 29.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 380 (c) 37 (d) 190
  30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 506 (d) 43
  31. 31.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 222 (b) 31 (c) 126 (d) 111
  32. 32.What is the 17th term of the AP 18, 20, 22, 24, …? (a) 50 (b) 52 (c) 32 (d) 34
  33. 33.What is the 30th term of the AP 1, 3, 5, 7, …? (a) 61 (b) 58 (c) 60 (d) 59
  34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  35. 35.What is the missing term in the AP 20, 24, ?, 32, 36? (a) 29 (b) 28 (c) 32 (d) 27
  36. 36.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 212 (b) 232 (c) 44 (d) 424
  37. 37.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 240 (b) 138 (c) 35 (d) 120
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 30 (c) 15 (d) 9
  39. 39.Which term of the AP 3, 7, 11, 15, … is 35? (a) 10th (b) 8th (c) 9th (d) 11th
  40. 40.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 34 (b) 132 (c) 114 (d) 228

Answer key

  1. 16
  2. 55
  3. 73
  4. 183
  5. 156
  6. 78
  7. 32nd
  8. 145
  9. 31
  10. 35th
  11. 35
  12. 242
  13. 107
  14. 15
  15. 120
  16. 167
  17. 12
  18. 88
  19. 25th
  20. 232
  21. 196
  22. 146
  23. 81
  24. 46
  25. 81
  26. 17th
  27. 33
  28. 69
  29. 361
  30. 484
  31. 111
  32. 50
  33. 59
  34. 729
  35. 28
  36. 212
  37. 120
  38. 25
  39. 9th
  40. 114

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