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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 415 · 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 sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 17 (d) 45
  2. 2.What is the 11th term of the AP 16, 18, 20, 22, …? (a) 36 (b) 20 (c) 38 (d) 22
  3. 3.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 49 (b) 50 (c) 10 (d) 98
  4. 4.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 182 (c) 78 (d) 91
  5. 5.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 561 (d) 578
  6. 6.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 21 (b) 81 (c) 90 (d) 162
  7. 7.What is the 14th term of the AP 6, 10, 14, 18, …? (a) 52 (b) 62 (c) 56 (d) 58
  8. 8.What is the 10th term of the AP 13, 16, 19, 22, …? (a) 40 (b) 30 (c) 43 (d) 27
  9. 9.What is the 39th term of the AP 19, 23, 27, 31, …? (a) 171 (b) 156 (c) 152 (d) 175
  10. 10.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 552 (c) 276 (d) 253
  11. 11.What is the 17th term of the AP 1, 9, 17, 25, …? (a) 137 (b) 129 (c) 128 (d) 136
  12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 21 (d) 11
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  14. 14.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 3906 (c) 1953 (d) 1922
  15. 15.What is the 24th term of the AP 7, 10, 13, 16, …? (a) 79 (b) 69 (c) 76 (d) 72
  16. 16.What is the 11th term of the AP 3, 10, 17, 24, …? (a) 80 (b) 77 (c) 73 (d) 70
  17. 17.What is the 15th term of the AP 3, 10, 17, 24, …? (a) 98 (b) 101 (c) 105 (d) 108
  18. 18.Which term of the AP 10, 18, 26, 34, … is 130? (a) 16th (b) 15th (c) 18th (d) 17th
  19. 19.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  20. 20.What is the sum of all the whole numbers from 1 to 73? (a) 5402 (b) 2701 (c) 2628 (d) 2702
  21. 21.What is the missing term in the AP 11, 17, ?, 29, 35? (a) 24 (b) 22 (c) 29 (d) 23
  22. 22.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 780 (c) 1640 (d) 800
  23. 23.What is the 14th term of the AP 3, 6, 9, 12, …? (a) 43 (b) 45 (c) 39 (d) 42
  24. 24.What is the 19th term of the AP 20, 23, 26, 29, …? (a) 74 (b) 77 (c) 54 (d) 57
  25. 25.What is the 13th term of the AP 3, 10, 17, 24, …? (a) 94 (b) 87 (c) 91 (d) 84
  26. 26.What is the 18th term of the AP 16, 19, 22, 25, …? (a) 70 (b) 54 (c) 51 (d) 67
  27. 27.What is the 27th term of the AP 1, 9, 17, 25, …? (a) 208 (b) 209 (c) 216 (d) 217
  28. 28.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 75 (b) 130 (c) 21 (d) 65
  29. 29.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 225 (b) 450 (c) 36 (d) 240
  30. 30.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 112 (b) 108 (c) 17 (d) 216
  31. 31.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 342 (c) 171 (d) 153
  32. 32.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 36 (b) 192 (c) 176 (d) 352
  33. 33.What is the 23rd term of the AP 8, 14, 20, 26, …? (a) 138 (b) 146 (c) 132 (d) 140
  34. 34.What is the sum of all the whole numbers from 1 to 15? (a) 120 (b) 240 (c) 105 (d) 121
  35. 35.What is the 21st term of the AP 20, 22, 24, 26, …? (a) 62 (b) 40 (c) 60 (d) 42
  36. 36.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 40 (b) 282 (c) 564 (d) 300
  37. 37.What is the 15th term of the AP 18, 25, 32, 39, …? (a) 123 (b) 116 (c) 105 (d) 98
  38. 38.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 406 (d) 784
  39. 39.What is the 36th term of the AP 6, 12, 18, 24, …? (a) 216 (b) 210 (c) 222 (d) 217
  40. 40.What is the 31st term of the AP 13, 15, 17, 19, …? (a) 62 (b) 73 (c) 75 (d) 60

Answer key

  1. 81
  2. 36
  3. 49
  4. 91
  5. 595
  6. 81
  7. 58
  8. 40
  9. 171
  10. 276
  11. 129
  12. 36
  13. 900
  14. 1953
  15. 76
  16. 73
  17. 101
  18. 16th
  19. 441
  20. 2701
  21. 23
  22. 820
  23. 42
  24. 74
  25. 87
  26. 67
  27. 209
  28. 65
  29. 225
  30. 108
  31. 171
  32. 176
  33. 140
  34. 120
  35. 60
  36. 282
  37. 116
  38. 784
  39. 216
  40. 73

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