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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 893 · 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 6, 14, 22, 30, …? (a) 134 (b) 128 (c) 120 (d) 126
  2. 2.Which term of the AP 13, 20, 27, 34, … is 139? (a) 19th (b) 21st (c) 20th (d) 18th
  3. 3.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 34 (b) 114 (c) 228 (d) 132
  4. 4.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 703 (c) 704 (d) 666
  5. 5.What is the 14th term of the AP 12, 21, 30, 39, …? (a) 138 (b) 129 (c) 117 (d) 126
  6. 6.What is the 15th term of the AP 7, 10, 13, 16, …? (a) 42 (b) 52 (c) 45 (d) 49
  7. 7.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1129 (c) 2256 (d) 1128
  8. 8.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 17 (b) 12 (c) 14 (d) 13
  9. 9.What is the 28th term of the AP 14, 17, 20, 23, …? (a) 98 (b) 81 (c) 84 (d) 95
  10. 10.What is the 20th term of the AP 5, 11, 17, 23, …? (a) 120 (b) 114 (c) 119 (d) 125
  11. 11.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 288 (b) 23 (c) 156 (d) 144
  12. 12.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  13. 13.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 140 (b) 70 (c) 80 (d) 22
  14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 576 (d) 600
  15. 15.What is the 18th term of the AP 1, 5, 9, 13, …? (a) 69 (b) 68 (c) 73 (d) 72
  16. 16.What is the 17th term of the AP 5, 8, 11, 14, …? (a) 51 (b) 56 (c) 53 (d) 48
  17. 17.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 15 (c) 63 (d) 70
  18. 18.What is the 19th term of the AP 20, 24, 28, 32, …? (a) 96 (b) 72 (c) 76 (d) 92
  19. 19.Which term of the AP 7, 13, 19, 25, … is 235? (a) 40th (b) 39th (c) 38th (d) 41st
  20. 20.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 34 (b) 110 (c) 125 (d) 220
  21. 21.What is the 14th term of the AP 10, 15, 20, 25, …? (a) 70 (b) 65 (c) 75 (d) 80
  22. 22.What is the 26th term of the AP 1, 8, 15, 22, …? (a) 182 (b) 176 (c) 175 (d) 183
  23. 23.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 43 (b) 53 (c) 45 (d) 44
  24. 24.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 153 (d) 289
  25. 25.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 812 (d) 406
  26. 26.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 325 (c) 338 (d) 351
  27. 27.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 330 (b) 660 (c) 360 (d) 60
  28. 28.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 50 (b) 45 (c) 13 (d) 90
  29. 29.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 204 (b) 102 (c) 32 (d) 120
  30. 30.What is the 22nd term of the AP 14, 17, 20, 23, …? (a) 63 (b) 66 (c) 80 (d) 77
  31. 31.What is the 35th term of the AP 14, 20, 26, 32, …? (a) 224 (b) 210 (c) 204 (d) 218
  32. 32.Which term of the AP 4, 9, 14, 19, … is 184? (a) 36th (b) 37th (c) 39th (d) 38th
  33. 33.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 37 (b) 207 (c) 378 (d) 189
  34. 34.What is the 18th term of the AP 1, 7, 13, 19, …? (a) 109 (b) 102 (c) 103 (d) 108
  35. 35.Which term of the AP 14, 20, 26, 32, … is 140? (a) 24th (b) 23rd (c) 21st (d) 22nd
  36. 36.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 27 (d) 105
  37. 37.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 76 (b) 13 (c) 80 (d) 152
  38. 38.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 136 (d) 256
  39. 39.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 196 (b) 98 (c) 23 (d) 101
  40. 40.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 160 (b) 26 (c) 85 (d) 80

Answer key

  1. 126
  2. 19th
  3. 114
  4. 703
  5. 129
  6. 49
  7. 1128
  8. 13
  9. 95
  10. 119
  11. 144
  12. 400
  13. 70
  14. 576
  15. 69
  16. 53
  17. 63
  18. 92
  19. 39th
  20. 110
  21. 75
  22. 176
  23. 44
  24. 289
  25. 406
  26. 351
  27. 330
  28. 45
  29. 102
  30. 77
  31. 218
  32. 37th
  33. 189
  34. 103
  35. 22nd
  36. 196
  37. 76
  38. 256
  39. 98
  40. 80

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