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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 14 · 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 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 600 (d) 47
  2. 2.What is the 19th term of the AP 1, 7, 13, 19, …? (a) 115 (b) 108 (c) 114 (d) 109
  3. 3.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 18 (b) 27 (c) 19 (d) 17
  4. 4.What is the 23rd term of the AP 9, 11, 13, 15, …? (a) 55 (b) 44 (c) 46 (d) 53
  5. 5.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  7. 7.What is the 13th term of the AP 12, 21, 30, 39, …? (a) 120 (b) 129 (c) 108 (d) 117
  8. 8.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 120 (b) 15 (c) 60 (d) 66
  9. 9.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 65 (b) 130 (c) 25 (d) 80
  10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
  11. 11.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 13 (c) 90 (d) 180
  12. 12.Which term of the AP 10, 16, 22, 28, … is 136? (a) 21st (b) 22nd (c) 23rd (d) 24th
  13. 13.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 88 (b) 168 (c) 14 (d) 84
  14. 14.Which term of the AP 13, 21, 29, 37, … is 141? (a) 16th (b) 19th (c) 18th (d) 17th
  15. 15.What is the 34th term of the AP 15, 19, 23, 27, …? (a) 151 (b) 147 (c) 132 (d) 136
  16. 16.What is the 38th term of the AP 1, 10, 19, 28, …? (a) 342 (b) 334 (c) 343 (d) 333
  17. 17.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 360 (b) 63 (c) 390 (d) 720
  18. 18.What is the 27th term of the AP 20, 23, 26, 29, …? (a) 78 (b) 101 (c) 98 (d) 81
  19. 19.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 156 (b) 90 (c) 23 (d) 78
  20. 20.Which term of the AP 17, 23, 29, 35, … is 83? (a) 11th (b) 13th (c) 12th (d) 14th
  21. 21.What is the 27th term of the AP 19, 28, 37, 46, …? (a) 243 (b) 234 (c) 262 (d) 253
  22. 22.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 12 (b) 80 (c) 45 (d) 40
  23. 23.What is the 11th term of the AP 14, 22, 30, 38, …? (a) 88 (b) 102 (c) 80 (d) 94
  24. 24.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 184 (b) 168 (c) 336 (d) 35
  25. 25.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 396 (b) 209 (c) 198 (d) 28
  26. 26.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 56 (d) 49
  27. 27.What is the 33rd term of the AP 6, 13, 20, 27, …? (a) 231 (b) 224 (c) 230 (d) 237
  28. 28.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 225 (d) 29
  29. 29.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 15 (d) 36
  30. 30.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 19 (c) 198 (d) 108
  31. 31.What is the 20th term of the AP 5, 11, 17, 23, …? (a) 114 (b) 125 (c) 119 (d) 120
  32. 32.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 66 (b) 17 (c) 57 (d) 114
  33. 33.Which term of the AP 1, 5, 9, 13, … is 53? (a) 13th (b) 16th (c) 14th (d) 15th
  34. 34.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 38 (b) 256 (c) 253 (d) 506
  35. 35.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 12 (c) 50 (d) 51
  36. 36.What is the 35th term of the AP 11, 15, 19, 23, …? (a) 136 (b) 151 (c) 147 (d) 140
  37. 37.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 44 (b) 203 (c) 182 (d) 364
  38. 38.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 947 (c) 903 (d) 946
  39. 39.What is the 35th term of the AP 12, 14, 16, 18, …? (a) 68 (b) 70 (c) 80 (d) 82
  40. 40.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 21 (b) 29 (c) 20 (d) 19

Answer key

  1. 576
  2. 109
  3. 18
  4. 53
  5. 25
  6. 81
  7. 120
  8. 60
  9. 65
  10. 441
  11. 90
  12. 22nd
  13. 84
  14. 17th
  15. 147
  16. 334
  17. 360
  18. 98
  19. 78
  20. 12th
  21. 253
  22. 40
  23. 94
  24. 168
  25. 198
  26. 49
  27. 230
  28. 225
  29. 64
  30. 99
  31. 119
  32. 57
  33. 14th
  34. 253
  35. 50
  36. 147
  37. 182
  38. 946
  39. 80
  40. 20

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