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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 990 · 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 15th term of the AP 14, 21, 28, 35, …? (a) 119 (b) 105 (c) 98 (d) 112
  2. 2.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 11 (b) 12 (c) 10 (d) 9
  3. 3.Which term of the AP 11, 13, 15, 17, … is 27? (a) 11th (b) 9th (c) 10th (d) 8th
  4. 4.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 252 (b) 129 (c) 126 (d) 26
  5. 5.What is the 12th term of the AP 16, 25, 34, 43, …? (a) 108 (b) 99 (c) 124 (d) 115
  6. 6.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 300 (b) 40 (c) 564 (d) 282
  7. 7.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 32 (b) 25 (c) 26 (d) 24
  8. 8.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 25 (b) 26 (c) 50 (d) 7
  9. 9.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 12 (b) 8 (c) 10 (d) 9
  10. 10.What is the 18th term of the AP 11, 18, 25, 32, …? (a) 137 (b) 126 (c) 119 (d) 130
  11. 11.What is the 24th term of the AP 8, 14, 20, 26, …? (a) 138 (b) 152 (c) 144 (d) 146
  12. 12.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 180 (c) 90 (d) 91
  13. 13.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 180 (b) 90 (c) 105 (d) 30
  14. 14.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 253 (c) 277 (d) 552
  15. 15.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 528 (c) 1122 (d) 562
  16. 16.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 858 (b) 462 (c) 429 (d) 69
  17. 17.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 666 (c) 648 (d) 1332
  18. 18.Which term of the AP 17, 19, 21, 23, … is 49? (a) 17th (b) 18th (c) 19th (d) 16th
  19. 19.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 174 (b) 171 (c) 342 (d) 31
  20. 20.What is the 31st term of the AP 19, 26, 33, 40, …? (a) 217 (b) 210 (c) 229 (d) 236
  21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 43 (d) 484
  22. 22.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 364 (b) 182 (c) 203 (d) 44
  23. 23.What is the 27th term of the AP 8, 11, 14, 17, …? (a) 81 (b) 78 (c) 86 (d) 89
  24. 24.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 15 (b) 11 (c) 9 (d) 10
  25. 25.What is the 36th term of the AP 18, 20, 22, 24, …? (a) 90 (b) 72 (c) 70 (d) 88
  26. 26.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 33 (b) 26 (c) 25 (d) 27
  27. 27.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 31 (b) 147 (c) 266 (d) 133
  28. 28.What is the 16th term of the AP 8, 13, 18, 23, …? (a) 80 (b) 75 (c) 83 (d) 88
  29. 29.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 60 (c) 114 (d) 12
  30. 30.What is the 38th term of the AP 10, 18, 26, 34, …? (a) 304 (b) 296 (c) 306 (d) 314
  31. 31.Which term of the AP 3, 12, 21, 30, … is 345? (a) 40th (b) 39th (c) 38th (d) 41st
  32. 32.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 35 (c) 11 (d) 70
  33. 33.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 420 (c) 190 (d) 210
  34. 34.What is the 32nd term of the AP 5, 12, 19, 26, …? (a) 217 (b) 224 (c) 229 (d) 222
  35. 35.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 190 (d) 380
  36. 36.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1711 (c) 1653 (d) 1682
  37. 37.What is the 35th term of the AP 20, 23, 26, 29, …? (a) 105 (b) 102 (c) 122 (d) 125
  38. 38.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 240 (b) 30 (c) 120 (d) 132
  39. 39.What is the 29th term of the AP 9, 11, 13, 15, …? (a) 56 (b) 58 (c) 67 (d) 65
  40. 40.What is the 14th term of the AP 15, 21, 27, 33, …? (a) 93 (b) 99 (c) 78 (d) 84

Answer key

  1. 112
  2. 10
  3. 9th
  4. 126
  5. 115
  6. 282
  7. 25
  8. 25
  9. 9
  10. 130
  11. 146
  12. 90
  13. 90
  14. 276
  15. 561
  16. 429
  17. 666
  18. 17th
  19. 171
  20. 229
  21. 484
  22. 182
  23. 86
  24. 10
  25. 88
  26. 26
  27. 133
  28. 83
  29. 57
  30. 306
  31. 39th
  32. 35
  33. 210
  34. 222
  35. 361
  36. 1711
  37. 122
  38. 120
  39. 65
  40. 93

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