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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 878 · 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 28th term of the AP 18, 27, 36, 45, …? (a) 252 (b) 243 (c) 261 (d) 270
  2. 2.Which term of the AP 7, 16, 25, 34, … is 151? (a) 19th (b) 17th (c) 18th (d) 16th
  3. 3.What is the 26th term of the AP 3, 7, 11, 15, …? (a) 103 (b) 104 (c) 107 (d) 100
  4. 4.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 161 (b) 182 (c) 322 (d) 41
  5. 5.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 558 (b) 55 (c) 306 (d) 279
  6. 6.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 240 (c) 138 (d) 120
  7. 7.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 18 (b) 15 (c) 17 (d) 16
  8. 8.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 26 (b) 27 (c) 35 (d) 28
  9. 9.Which term of the AP 5, 7, 9, 11, … is 27? (a) 12th (b) 14th (c) 11th (d) 13th
  10. 10.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 30 (b) 456 (c) 228 (d) 240
  11. 11.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 51 (d) 676
  12. 12.What is the 36th term of the AP 15, 18, 21, 24, …? (a) 105 (b) 123 (c) 120 (d) 108
  13. 13.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 26 (b) 28 (c) 34 (d) 27
  14. 14.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 28 (b) 30 (c) 35 (d) 29
  15. 15.What is the 39th term of the AP 19, 27, 35, 43, …? (a) 323 (b) 304 (c) 331 (d) 312
  16. 16.What is the 32nd term of the AP 3, 12, 21, 30, …? (a) 288 (b) 291 (c) 279 (d) 282
  17. 17.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 25 (b) 24 (c) 30 (d) 26
  18. 18.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4656 (c) 4608 (d) 4560
  19. 19.What is the 19th term of the AP 17, 20, 23, 26, …? (a) 74 (b) 54 (c) 71 (d) 57
  20. 20.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 1332 (c) 648 (d) 630
  21. 21.What is the 20th term of the AP 4, 11, 18, 25, …? (a) 144 (b) 137 (c) 140 (d) 133
  22. 22.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 444 (b) 70 (c) 480 (d) 888
  23. 23.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 129 (b) 126 (c) 27 (d) 252
  24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  25. 25.What is the 13th term of the AP 20, 26, 32, 38, …? (a) 72 (b) 98 (c) 92 (d) 78
  26. 26.Which term of the AP 8, 13, 18, 23, … is 53? (a) 9th (b) 12th (c) 10th (d) 11th
  27. 27.What is the 17th term of the AP 1, 4, 7, 10, …? (a) 49 (b) 48 (c) 51 (d) 52
  28. 28.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 31 (b) 112 (c) 224 (d) 117
  29. 29.What is the 35th term of the AP 7, 10, 13, 16, …? (a) 112 (b) 102 (c) 105 (d) 109
  30. 30.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 13 (b) 11 (c) 10 (d) 12
  31. 31.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 189 (b) 35 (c) 171 (d) 342
  32. 32.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 200 (b) 37 (c) 184 (d) 368
  33. 33.Which term of the AP 8, 11, 14, 17, … is 53? (a) 15th (b) 18th (c) 17th (d) 16th
  34. 34.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  35. 35.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 210 (d) 231
  36. 36.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 702 (c) 338 (d) 325
  37. 37.What is the 24th term of the AP 15, 21, 27, 33, …? (a) 153 (b) 144 (c) 138 (d) 159
  38. 38.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 190 (b) 175 (c) 350 (d) 31
  39. 39.What is the 10th term of the AP 19, 28, 37, 46, …? (a) 90 (b) 100 (c) 81 (d) 109
  40. 40.What is the 36th term of the AP 11, 13, 15, 17, …? (a) 83 (b) 72 (c) 81 (d) 70

Answer key

  1. 261
  2. 17th
  3. 103
  4. 161
  5. 279
  6. 120
  7. 16
  8. 27
  9. 12th
  10. 228
  11. 676
  12. 120
  13. 27
  14. 29
  15. 323
  16. 282
  17. 25
  18. 4656
  19. 71
  20. 666
  21. 137
  22. 444
  23. 126
  24. 81
  25. 92
  26. 10th
  27. 49
  28. 112
  29. 109
  30. 11
  31. 171
  32. 184
  33. 16th
  34. 144
  35. 231
  36. 351
  37. 153
  38. 175
  39. 100
  40. 81

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