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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 50 · 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 2, ?, 6, 8, 10? (a) 3 (b) 4 (c) 5 (d) 6
  2. 2.What is the 38th term of the AP 3, 6, 9, 12, …? (a) 115 (b) 111 (c) 114 (d) 117
  3. 3.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 18 (b) 15 (c) 16 (d) 14
  4. 4.What is the 23rd term of the AP 14, 19, 24, 29, …? (a) 115 (b) 129 (c) 110 (d) 124
  5. 5.Which term of the AP 20, 24, 28, 32, … is 156? (a) 39th (b) 34th (c) 36th (d) 35th
  6. 6.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 18 (b) 19 (c) 23 (d) 20
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 36 (d) 15
  8. 8.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 440 (b) 407 (c) 814 (d) 67
  9. 9.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 100 (b) 112 (c) 23 (d) 200
  10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 529 (c) 45 (d) 552
  11. 11.What is the missing term in the AP 11, 13, 15, ?, 19? (a) 17 (b) 19 (c) 16 (d) 18
  12. 12.What is the 25th term of the AP 18, 25, 32, 39, …? (a) 186 (b) 175 (c) 193 (d) 168
  13. 13.Which term of the AP 6, 8, 10, 12, … is 54? (a) 24th (b) 27th (c) 26th (d) 25th
  14. 14.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 2352 (c) 1152 (d) 1128
  15. 15.Which term of the AP 19, 21, 23, 25, … is 45? (a) 14th (b) 15th (c) 13th (d) 16th
  16. 16.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 300 (b) 40 (c) 168 (d) 150
  17. 17.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 54 (b) 638 (c) 319 (d) 324
  18. 18.What is the 10th term of the AP 20, 26, 32, 38, …? (a) 60 (b) 80 (c) 74 (d) 54
  19. 19.What is the 36th term of the AP 4, 8, 12, 16, …? (a) 148 (b) 140 (c) 145 (d) 144
  20. 20.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 5402 (c) 2701 (d) 2628
  21. 21.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 2016 (c) 4160 (d) 2048
  22. 22.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 43 (b) 9 (c) 42 (d) 84
  23. 23.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 154 (d) 306
  24. 24.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 50 (b) 16 (c) 100 (d) 53
  25. 25.What is the 10th term of the AP 15, 21, 27, 33, …? (a) 75 (b) 54 (c) 60 (d) 69
  26. 26.What is the 20th term of the AP 11, 18, 25, 32, …? (a) 140 (b) 144 (c) 151 (d) 133
  27. 27.What is the 16th term of the AP 2, 7, 12, 17, …? (a) 77 (b) 82 (c) 75 (d) 80
  28. 28.What is the 23rd term of the AP 1, 6, 11, 16, …? (a) 115 (b) 116 (c) 110 (d) 111
  29. 29.What is the 25th term of the AP 8, 11, 14, 17, …? (a) 72 (b) 80 (c) 75 (d) 83
  30. 30.What is the 15th term of the AP 14, 22, 30, 38, …? (a) 126 (b) 120 (c) 112 (d) 134
  31. 31.What is the 34th term of the AP 9, 14, 19, 24, …? (a) 174 (b) 165 (c) 179 (d) 170
  32. 32.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 666 (c) 1332 (d) 630
  33. 33.What is the 29th term of the AP 3, 6, 9, 12, …? (a) 87 (b) 84 (c) 88 (d) 90
  34. 34.What is the 13th term of the AP 3, 7, 11, 15, …? (a) 48 (b) 55 (c) 52 (d) 51
  35. 35.What is the 16th term of the AP 16, 25, 34, 43, …? (a) 144 (b) 160 (c) 135 (d) 151
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 13 (d) 56
  37. 37.What is the 37th term of the AP 2, 4, 6, 8, …? (a) 74 (b) 72 (c) 75 (d) 76
  38. 38.What is the 37th term of the AP 7, 9, 11, 13, …? (a) 81 (b) 74 (c) 79 (d) 72
  39. 39.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 342 (c) 153 (d) 162
  40. 40.What is the 25th term of the AP 16, 24, 32, 40, …? (a) 216 (b) 192 (c) 208 (d) 200

Answer key

  1. 4
  2. 114
  3. 15
  4. 124
  5. 35th
  6. 19
  7. 64
  8. 407
  9. 100
  10. 529
  11. 17
  12. 186
  13. 25th
  14. 1176
  15. 14th
  16. 150
  17. 319
  18. 74
  19. 144
  20. 2701
  21. 2080
  22. 42
  23. 153
  24. 50
  25. 69
  26. 144
  27. 77
  28. 111
  29. 80
  30. 126
  31. 174
  32. 666
  33. 87
  34. 51
  35. 151
  36. 49
  37. 74
  38. 79
  39. 171
  40. 208

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