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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 327 · 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 11th term of the AP 7, 13, 19, 25, …? (a) 67 (b) 73 (c) 60 (d) 66
  2. 2.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 10 (b) 11 (c) 12 (d) 9
  3. 3.What is the sum of all the whole numbers from 1 to 77? (a) 2926 (b) 3004 (c) 3003 (d) 6006
  4. 4.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 23 (b) 25 (c) 24 (d) 33
  5. 5.What is the 36th term of the AP 9, 18, 27, 36, …? (a) 333 (b) 315 (c) 324 (d) 325
  6. 6.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 156 (c) 66 (d) 78
  7. 7.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 153 (b) 25 (c) 162 (d) 306
  8. 8.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 29 (b) 28 (c) 30 (d) 35
  9. 9.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 16 (b) 9 (c) 10 (d) 8
  10. 10.Which term of the AP 14, 16, 18, 20, … is 28? (a) 14th (b) 9th (c) 7th (d) 8th
  11. 11.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 28 (b) 26 (c) 34 (d) 27
  12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  13. 13.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 40 (b) 39 (c) 41 (d) 49
  14. 14.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 18 (b) 20 (c) 19 (d) 25
  15. 15.What is the 15th term of the AP 3, 10, 17, 24, …? (a) 101 (b) 108 (c) 105 (d) 98
  16. 16.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 296 (b) 148 (c) 29 (d) 160
  17. 17.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1891 (c) 1953 (d) 1922
  18. 18.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 50 (b) 100 (c) 51 (d) 12
  19. 19.What is the 15th term of the AP 18, 24, 30, 36, …? (a) 90 (b) 84 (c) 102 (d) 108
  20. 20.Which term of the AP 12, 21, 30, 39, … is 120? (a) 14th (b) 15th (c) 12th (d) 13th
  21. 21.Which term of the AP 16, 23, 30, 37, … is 240? (a) 32nd (b) 34th (c) 35th (d) 33rd
  22. 22.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 78 (b) 92 (c) 81 (d) 89
  23. 23.Which term of the AP 11, 20, 29, 38, … is 254? (a) 29th (b) 30th (c) 28th (d) 27th
  24. 24.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 600 (b) 300 (c) 324 (d) 47
  25. 25.What is the missing term in the AP 2, 10, 18, ?, 34? (a) 27 (b) 34 (c) 26 (d) 25
  26. 26.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 21 (b) 20 (c) 22 (d) 30
  27. 27.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 90 (b) 81 (c) 162 (d) 21
  28. 28.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  29. 29.What is the 15th term of the AP 19, 26, 33, 40, …? (a) 117 (b) 98 (c) 124 (d) 105
  30. 30.What is the 32nd term of the AP 18, 26, 34, 42, …? (a) 256 (b) 248 (c) 266 (d) 274
  31. 31.What is the 17th term of the AP 11, 20, 29, 38, …? (a) 153 (b) 164 (c) 155 (d) 144
  32. 32.What is the 10th term of the AP 12, 15, 18, 21, …? (a) 39 (b) 42 (c) 27 (d) 30
  33. 33.What is the 38th term of the AP 6, 9, 12, 15, …? (a) 114 (b) 120 (c) 111 (d) 117
  34. 34.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 27 (b) 138 (c) 270 (d) 135
  35. 35.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 8 (b) 7 (c) 10 (d) 6
  36. 36.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 660 (b) 55 (c) 335 (d) 330
  37. 37.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 186 (b) 93 (c) 23 (d) 102
  38. 38.What is the 17th term of the AP 7, 13, 19, 25, …? (a) 109 (b) 103 (c) 102 (d) 96
  39. 39.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 162 (b) 144 (c) 39 (d) 288
  40. 40.Which term of the AP 16, 21, 26, 31, … is 111? (a) 22nd (b) 19th (c) 21st (d) 20th

Answer key

  1. 67
  2. 10
  3. 3003
  4. 24
  5. 324
  6. 78
  7. 153
  8. 29
  9. 9
  10. 8th
  11. 27
  12. 81
  13. 40
  14. 19
  15. 101
  16. 148
  17. 1953
  18. 50
  19. 102
  20. 13th
  21. 33rd
  22. 89
  23. 28th
  24. 300
  25. 26
  26. 21
  27. 81
  28. 144
  29. 117
  30. 266
  31. 155
  32. 39
  33. 117
  34. 135
  35. 7
  36. 330
  37. 93
  38. 103
  39. 144
  40. 20th

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