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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 747 · 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.Which term of the AP 16, 24, 32, 40, … is 104? (a) 12th (b) 14th (c) 13th (d) 11th
  2. 2.What is the 14th term of the AP 18, 22, 26, 30, …? (a) 56 (b) 74 (c) 70 (d) 52
  3. 3.What is the 22nd term of the AP 12, 16, 20, 24, …? (a) 96 (b) 88 (c) 100 (d) 84
  4. 4.Which term of the AP 15, 17, 19, 21, … is 37? (a) 11th (b) 13th (c) 14th (d) 12th
  5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 196 (d) 210
  6. 6.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 16 (b) 17 (c) 19 (d) 18
  7. 7.What is the 32nd term of the AP 17, 25, 33, 41, …? (a) 256 (b) 248 (c) 273 (d) 265
  8. 8.What is the 28th term of the AP 18, 23, 28, 33, …? (a) 135 (b) 140 (c) 153 (d) 158
  9. 9.What is the 13th term of the AP 10, 15, 20, 25, …? (a) 75 (b) 60 (c) 70 (d) 65
  10. 10.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 33 (b) 38 (c) 31 (d) 32
  11. 11.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 210 (c) 30 (d) 105
  12. 12.What is the 23rd term of the AP 5, 11, 17, 23, …? (a) 143 (b) 132 (c) 137 (d) 138
  13. 13.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 162 (b) 96 (c) 26 (d) 81
  14. 14.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 2756 (c) 1326 (d) 1378
  15. 15.Which term of the AP 18, 23, 28, 33, … is 188? (a) 34th (b) 37th (c) 35th (d) 36th
  16. 16.Which term of the AP 1, 4, 7, 10, … is 34? (a) 14th (b) 12th (c) 13th (d) 11th
  17. 17.What is the 35th term of the AP 6, 12, 18, 24, …? (a) 204 (b) 211 (c) 210 (d) 216
  18. 18.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 96 (b) 92 (c) 184 (d) 15
  19. 19.Which term of the AP 16, 18, 20, 22, … is 90? (a) 37th (b) 39th (c) 38th (d) 45th
  20. 20.What is the 31st term of the AP 15, 17, 19, 21, …? (a) 62 (b) 75 (c) 60 (d) 77
  21. 21.What is the 20th term of the AP 4, 12, 20, 28, …? (a) 156 (b) 164 (c) 152 (d) 160
  22. 22.What is the 15th term of the AP 13, 15, 17, 19, …? (a) 41 (b) 30 (c) 43 (d) 28
  23. 23.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  24. 24.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 278 (b) 275 (c) 550 (d) 40
  25. 25.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 16 (b) 242 (c) 121 (d) 122
  26. 26.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 8 (b) 5 (c) 6 (d) 7
  27. 27.Which term of the AP 1, 4, 7, 10, … is 64? (a) 22nd (b) 24th (c) 21st (d) 23rd
  28. 28.What is the missing term in the AP 16, 23, 30, ?, 44? (a) 36 (b) 38 (c) 44 (d) 37
  29. 29.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 990 (c) 2070 (d) 1036
  30. 30.What is the 38th term of the AP 3, 6, 9, 12, …? (a) 117 (b) 115 (c) 114 (d) 111
  31. 31.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 15 (b) 64 (c) 128 (d) 72
  32. 32.What is the missing term in the AP 1, 8, 15, ?, 29? (a) 21 (b) 29 (c) 23 (d) 22
  33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 136 (d) 256
  35. 35.What is the 19th term of the AP 9, 12, 15, 18, …? (a) 66 (b) 54 (c) 57 (d) 63
  36. 36.What is the missing term in the AP 15, 17, 19, ?, 23? (a) 23 (b) 21 (c) 22 (d) 20
  37. 37.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 144 (b) 36 (c) 252 (d) 126
  38. 38.Which term of the AP 8, 11, 14, 17, … is 77? (a) 26th (b) 24th (c) 25th (d) 23rd
  39. 39.What is the 17th term of the AP 7, 15, 23, 31, …? (a) 135 (b) 128 (c) 143 (d) 136
  40. 40.What is the 21st term of the AP 3, 8, 13, 18, …? (a) 105 (b) 100 (c) 103 (d) 108

Answer key

  1. 12th
  2. 70
  3. 96
  4. 12th
  5. 196
  6. 17
  7. 265
  8. 153
  9. 70
  10. 32
  11. 105
  12. 137
  13. 81
  14. 1378
  15. 35th
  16. 12th
  17. 210
  18. 92
  19. 38th
  20. 75
  21. 156
  22. 41
  23. 900
  24. 275
  25. 121
  26. 6
  27. 22nd
  28. 37
  29. 1035
  30. 114
  31. 64
  32. 22
  33. 49
  34. 256
  35. 63
  36. 21
  37. 126
  38. 24th
  39. 135
  40. 103

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