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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 553 · 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 16th term of the AP 19, 26, 33, 40, …? (a) 124 (b) 131 (c) 105 (d) 112
  2. 2.What is the 29th term of the AP 13, 15, 17, 19, …? (a) 56 (b) 58 (c) 69 (d) 71
  3. 3.What is the 28th term of the AP 8, 15, 22, 29, …? (a) 189 (b) 196 (c) 204 (d) 197
  4. 4.What is the 32nd term of the AP 10, 19, 28, 37, …? (a) 279 (b) 298 (c) 289 (d) 288
  5. 5.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 2070 (c) 1036 (d) 1035
  6. 6.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 39 (c) 210 (d) 420
  7. 7.What is the 19th term of the AP 17, 22, 27, 32, …? (a) 90 (b) 112 (c) 95 (d) 107
  8. 8.What is the 14th term of the AP 2, 10, 18, 26, …? (a) 104 (b) 114 (c) 112 (d) 106
  9. 9.What is the missing term in the AP 20, 24, 28, ?, 36? (a) 33 (b) 36 (c) 32 (d) 31
  10. 10.Which term of the AP 2, 6, 10, 14, … is 102? (a) 26th (b) 25th (c) 28th (d) 27th
  11. 11.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 21 (b) 26 (c) 22 (d) 20
  12. 12.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 120 (b) 28 (c) 216 (d) 108
  13. 13.What is the 32nd term of the AP 4, 9, 14, 19, …? (a) 155 (b) 159 (c) 164 (d) 160
  14. 14.What is the 11th term of the AP 14, 18, 22, 26, …? (a) 40 (b) 44 (c) 58 (d) 54
  15. 15.What is the missing term in the AP 8, 11, ?, 17, 20? (a) 14 (b) 13 (c) 15 (d) 17
  16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 506 (d) 43
  17. 17.Which term of the AP 13, 15, 17, 19, … is 33? (a) 12th (b) 10th (c) 11th (d) 13th
  18. 18.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 26 (b) 25 (c) 23 (d) 24
  19. 19.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 96 (b) 92 (c) 15 (d) 184
  20. 20.What is the 30th term of the AP 6, 12, 18, 24, …? (a) 181 (b) 186 (c) 174 (d) 180
  21. 21.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 140 (b) 70 (c) 77 (d) 16
  22. 22.What is the 27th term of the AP 15, 19, 23, 27, …? (a) 119 (b) 123 (c) 108 (d) 104
  23. 23.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 903 (c) 946 (d) 947
  24. 24.What is the missing term in the AP 12, 17, ?, 27, 32? (a) 23 (b) 22 (c) 27 (d) 21
  25. 25.What is the 22nd term of the AP 6, 11, 16, 21, …? (a) 105 (b) 111 (c) 116 (d) 110
  26. 26.What is the 32nd term of the AP 15, 18, 21, 24, …? (a) 93 (b) 108 (c) 111 (d) 96
  27. 27.Which term of the AP 17, 21, 25, 29, … is 97? (a) 20th (b) 22nd (c) 21st (d) 23rd
  28. 28.Which term of the AP 18, 22, 26, 30, … is 46? (a) 7th (b) 8th (c) 10th (d) 9th
  29. 29.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  30. 30.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 24 (c) 105 (d) 210
  31. 31.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 192 (b) 26 (c) 360 (d) 180
  32. 32.What is the 12th term of the AP 10, 14, 18, 22, …? (a) 48 (b) 54 (c) 44 (d) 58
  33. 33.What is the 29th term of the AP 20, 22, 24, 26, …? (a) 56 (b) 58 (c) 76 (d) 78
  34. 34.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 351 (c) 756 (d) 378
  35. 35.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 240 (b) 120 (c) 30 (d) 132
  36. 36.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 162 (b) 21 (c) 81 (d) 90
  37. 37.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 700 (b) 350 (c) 380 (d) 62
  38. 38.What is the 38th term of the AP 8, 12, 16, 20, …? (a) 160 (b) 156 (c) 148 (d) 152
  39. 39.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 31 (b) 266 (c) 147 (d) 133
  40. 40.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 136 (b) 120 (c) 29 (d) 240

Answer key

  1. 124
  2. 69
  3. 197
  4. 289
  5. 1035
  6. 400
  7. 107
  8. 106
  9. 32
  10. 26th
  11. 21
  12. 108
  13. 159
  14. 54
  15. 14
  16. 484
  17. 11th
  18. 24
  19. 92
  20. 180
  21. 70
  22. 119
  23. 946
  24. 22
  25. 111
  26. 108
  27. 21st
  28. 8th
  29. 256
  30. 105
  31. 180
  32. 54
  33. 76
  34. 378
  35. 120
  36. 81
  37. 350
  38. 156
  39. 133
  40. 120

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