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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 75 · 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 39th term of the AP 6, 8, 10, 12, …? (a) 84 (b) 82 (c) 76 (d) 78
  2. 2.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 45 (d) 17
  4. 4.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 24 (b) 272 (c) 144 (d) 136
  5. 5.What is the 24th term of the AP 16, 22, 28, 34, …? (a) 160 (b) 144 (c) 138 (d) 154
  6. 6.What is the 17th term of the AP 4, 11, 18, 25, …? (a) 119 (b) 112 (c) 123 (d) 116
  7. 7.What is the 39th term of the AP 15, 19, 23, 27, …? (a) 167 (b) 156 (c) 152 (d) 171
  8. 8.Which term of the AP 14, 21, 28, 35, … is 168? (a) 24th (b) 25th (c) 23rd (d) 22nd
  9. 9.Which term of the AP 20, 26, 32, 38, … is 74? (a) 10th (b) 11th (c) 9th (d) 12th
  10. 10.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 192 (b) 378 (c) 189 (d) 33
  11. 11.Which term of the AP 9, 11, 13, 15, … is 27? (a) 9th (b) 11th (c) 10th (d) 12th
  12. 12.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 630 (c) 631 (d) 1260
  13. 13.What is the sum of all the whole numbers from 1 to 87? (a) 7656 (b) 3829 (c) 3828 (d) 3741
  14. 14.What is the 27th term of the AP 9, 17, 25, 33, …? (a) 217 (b) 225 (c) 208 (d) 216
  15. 15.What is the 13th term of the AP 15, 21, 27, 33, …? (a) 72 (b) 78 (c) 93 (d) 87
  16. 16.What is the 13th term of the AP 16, 20, 24, 28, …? (a) 64 (b) 52 (c) 68 (d) 48
  17. 17.Which term of the AP 18, 24, 30, 36, … is 204? (a) 31st (b) 33rd (c) 32nd (d) 34th
  18. 18.What is the 25th term of the AP 20, 29, 38, 47, …? (a) 245 (b) 216 (c) 225 (d) 236
  19. 19.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 6 (b) 8 (c) 5 (d) 4
  20. 20.What is the 21st term of the AP 11, 14, 17, 20, …? (a) 74 (b) 60 (c) 71 (d) 63
  21. 21.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 23 (b) 140 (c) 150 (d) 280
  22. 22.Which term of the AP 15, 24, 33, 42, … is 195? (a) 22nd (b) 21st (c) 23rd (d) 20th
  23. 23.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 20 (b) 19 (c) 18 (d) 25
  24. 24.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 34 (b) 27 (c) 28 (d) 26
  25. 25.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 25 (b) 26 (c) 34 (d) 27
  26. 26.Which term of the AP 7, 16, 25, 34, … is 286? (a) 34th (b) 32nd (c) 31st (d) 33rd
  27. 27.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 8 (b) 6 (c) 7 (d) 10
  28. 28.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 506 (d) 484
  29. 29.What is the 11th term of the AP 7, 15, 23, 31, …? (a) 95 (b) 87 (c) 88 (d) 80
  30. 30.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1770 (c) 1771 (d) 1711
  31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210
  32. 32.What is the 33rd term of the AP 17, 20, 23, 26, …? (a) 99 (b) 116 (c) 96 (d) 113
  33. 33.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 36 (b) 38 (c) 37 (d) 46
  34. 34.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 648 (c) 666 (d) 630
  35. 35.What is the 11th term of the AP 6, 10, 14, 18, …? (a) 40 (b) 46 (c) 44 (d) 50
  36. 36.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 176 (b) 89 (c) 13 (d) 88
  37. 37.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 8 (b) 10 (c) 11 (d) 9
  38. 38.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 756 (c) 53 (d) 378
  39. 39.What is the 23rd term of the AP 14, 17, 20, 23, …? (a) 69 (b) 66 (c) 83 (d) 80
  40. 40.What is the 26th term of the AP 11, 13, 15, 17, …? (a) 63 (b) 61 (c) 50 (d) 52

Answer key

  1. 82
  2. 324
  3. 81
  4. 136
  5. 154
  6. 116
  7. 167
  8. 23rd
  9. 10th
  10. 189
  11. 10th
  12. 630
  13. 3828
  14. 217
  15. 87
  16. 64
  17. 32nd
  18. 236
  19. 5
  20. 71
  21. 140
  22. 21st
  23. 19
  24. 27
  25. 26
  26. 32nd
  27. 7
  28. 484
  29. 87
  30. 1770
  31. 196
  32. 113
  33. 37
  34. 666
  35. 46
  36. 88
  37. 9
  38. 729
  39. 80
  40. 61

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