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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 677 · 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 18, 26, 34, 42, … is 330? (a) 39th (b) 41st (c) 42nd (d) 40th
  2. 2.What is the 19th term of the AP 2, 6, 10, 14, …? (a) 74 (b) 72 (c) 78 (d) 76
  3. 3.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 700 (b) 350 (c) 62 (d) 380
  4. 4.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 436 (c) 406 (d) 435
  5. 5.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 576 (d) 600
  6. 6.What is the 15th term of the AP 13, 21, 29, 37, …? (a) 120 (b) 133 (c) 125 (d) 112
  7. 7.What is the 19th term of the AP 20, 28, 36, 44, …? (a) 144 (b) 164 (c) 152 (d) 172
  8. 8.What is the 38th term of the AP 9, 13, 17, 21, …? (a) 152 (b) 148 (c) 161 (d) 157
  9. 9.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 28 (b) 200 (c) 380 (d) 190
  10. 10.What is the 19th term of the AP 6, 8, 10, 12, …? (a) 44 (b) 42 (c) 38 (d) 36
  11. 11.What is the 29th term of the AP 5, 13, 21, 29, …? (a) 237 (b) 229 (c) 232 (d) 224
  12. 12.What is the 18th term of the AP 8, 11, 14, 17, …? (a) 54 (b) 51 (c) 59 (d) 62
  13. 13.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 812 (c) 378 (d) 406
  14. 14.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 66 (b) 36 (c) 8 (d) 33
  15. 15.What is the 25th term of the AP 17, 24, 31, 38, …? (a) 185 (b) 175 (c) 168 (d) 192
  16. 16.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 22 (b) 31 (c) 23 (d) 24
  17. 17.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 42 (d) 11
  18. 18.Which term of the AP 18, 21, 24, 27, … is 75? (a) 21st (b) 19th (c) 25th (d) 20th
  19. 19.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 841 (d) 435
  20. 20.What is the 10th term of the AP 12, 19, 26, 33, …? (a) 75 (b) 63 (c) 70 (d) 82
  21. 21.What is the 17th term of the AP 8, 13, 18, 23, …? (a) 88 (b) 85 (c) 80 (d) 93
  22. 22.Which term of the AP 6, 8, 10, 12, … is 46? (a) 22nd (b) 21st (c) 23rd (d) 20th
  23. 23.What is the missing term in the AP 17, 24, 31, ?, 45? (a) 37 (b) 39 (c) 45 (d) 38
  24. 24.What is the 21st term of the AP 5, 7, 9, 11, …? (a) 45 (b) 40 (c) 47 (d) 42
  25. 25.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 200 (b) 180 (c) 360 (d) 40
  26. 26.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 8 (b) 12 (c) 9 (d) 10
  27. 27.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 11 (b) 10 (c) 14 (d) 9
  28. 28.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 88 (b) 176 (c) 18 (d) 96
  29. 29.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 169 (c) 25 (d) 91
  30. 30.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 3306 (c) 1596 (d) 1653
  31. 31.What is the 34th term of the AP 19, 24, 29, 34, …? (a) 170 (b) 189 (c) 165 (d) 184
  32. 32.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 23 (b) 140 (c) 150 (d) 280
  33. 33.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 210 (b) 105 (c) 119 (d) 27
  34. 34.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 140 (b) 152 (c) 280 (d) 28
  35. 35.What is the 17th term of the AP 7, 15, 23, 31, …? (a) 143 (b) 128 (c) 136 (d) 135
  36. 36.What is the 10th term of the AP 6, 13, 20, 27, …? (a) 70 (b) 76 (c) 69 (d) 63
  37. 37.What is the 27th term of the AP 19, 26, 33, 40, …? (a) 201 (b) 208 (c) 189 (d) 182
  38. 38.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 56 (b) 13 (c) 49 (d) 98
  39. 39.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 20 (b) 117 (c) 108 (d) 216
  40. 40.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 288 (b) 144 (c) 23 (d) 156

Answer key

  1. 40th
  2. 74
  3. 350
  4. 435
  5. 576
  6. 125
  7. 164
  8. 157
  9. 190
  10. 42
  11. 229
  12. 59
  13. 406
  14. 33
  15. 185
  16. 23
  17. 36
  18. 20th
  19. 841
  20. 75
  21. 88
  22. 21st
  23. 38
  24. 45
  25. 180
  26. 9
  27. 10
  28. 88
  29. 169
  30. 1653
  31. 184
  32. 140
  33. 105
  34. 140
  35. 135
  36. 69
  37. 201
  38. 49
  39. 108
  40. 144

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