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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 544 · 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.Which term of the AP 2, 11, 20, 29, … is 137? (a) 15th (b) 17th (c) 18th (d) 16th
  2. 2.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 24 (b) 33 (c) 26 (d) 25
  3. 3.What is the 21st term of the AP 11, 19, 27, 35, …? (a) 160 (b) 168 (c) 171 (d) 179
  4. 4.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 25 (d) 169
  5. 5.What is the 36th term of the AP 14, 17, 20, 23, …? (a) 108 (b) 105 (c) 119 (d) 122
  6. 6.Which term of the AP 3, 10, 17, 24, … is 80? (a) 13th (b) 11th (c) 14th (d) 12th
  7. 7.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 15 (b) 17 (c) 16 (d) 25
  8. 8.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 9 (b) 10 (c) 14 (d) 11
  9. 9.What is the sum of all the whole numbers from 1 to 41? (a) 862 (b) 820 (c) 1722 (d) 861
  10. 10.What is the 12th term of the AP 11, 20, 29, 38, …? (a) 108 (b) 119 (c) 99 (d) 110
  11. 11.What is the 14th term of the AP 9, 12, 15, 18, …? (a) 42 (b) 48 (c) 39 (d) 51
  12. 12.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 9702 (c) 4851 (d) 4802
  13. 13.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 230 (b) 215 (c) 430 (d) 35
  14. 14.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 59 (b) 320 (c) 350 (d) 640
  15. 15.What is the 11th term of the AP 10, 12, 14, 16, …? (a) 30 (b) 20 (c) 22 (d) 32
  16. 16.What is the 17th term of the AP 19, 23, 27, 31, …? (a) 83 (b) 64 (c) 87 (d) 68
  17. 17.What is the 10th term of the AP 3, 8, 13, 18, …? (a) 50 (b) 48 (c) 53 (d) 45
  18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  19. 19.What is the 31st term of the AP 9, 18, 27, 36, …? (a) 280 (b) 279 (c) 270 (d) 288
  20. 20.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 14 (b) 19 (c) 16 (d) 15
  21. 21.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 3192 (c) 1540 (d) 1596
  22. 22.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 5 (b) 4 (c) 6 (d) 7
  23. 23.What is the 23rd term of the AP 2, 5, 8, 11, …? (a) 66 (b) 71 (c) 69 (d) 68
  24. 24.What is the 26th term of the AP 17, 24, 31, 38, …? (a) 182 (b) 192 (c) 199 (d) 175
  25. 25.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 666 (c) 704 (d) 703
  26. 26.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 184 (b) 35 (c) 168 (d) 336
  27. 27.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 154 (b) 143 (c) 286 (d) 23
  28. 28.Which term of the AP 6, 13, 20, 27, … is 62? (a) 11th (b) 9th (c) 10th (d) 8th
  29. 29.What is the 28th term of the AP 15, 17, 19, 21, …? (a) 71 (b) 54 (c) 56 (d) 69
  30. 30.What is the 34th term of the AP 2, 10, 18, 26, …? (a) 274 (b) 264 (c) 272 (d) 266
  31. 31.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 196 (b) 20 (c) 105 (d) 98
  32. 32.What is the 13th term of the AP 9, 11, 13, 15, …? (a) 33 (b) 26 (c) 24 (d) 35
  33. 33.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 24 (b) 108 (c) 120 (d) 216
  34. 34.What is the 13th term of the AP 4, 13, 22, 31, …? (a) 117 (b) 108 (c) 112 (d) 121
  35. 35.What is the 21st term of the AP 2, 9, 16, 23, …? (a) 149 (b) 147 (c) 142 (d) 140
  36. 36.What is the 18th term of the AP 20, 27, 34, 41, …? (a) 146 (b) 126 (c) 119 (d) 139
  37. 37.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 85 (b) 27 (c) 170 (d) 90
  38. 38.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 320 (b) 170 (c) 160 (d) 25
  39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 55 (d) 784
  40. 40.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 11 (b) 56 (c) 57 (d) 112

Answer key

  1. 16th
  2. 25
  3. 171
  4. 169
  5. 119
  6. 12th
  7. 16
  8. 10
  9. 861
  10. 110
  11. 48
  12. 4851
  13. 215
  14. 320
  15. 30
  16. 83
  17. 48
  18. 289
  19. 279
  20. 15
  21. 1596
  22. 5
  23. 68
  24. 192
  25. 703
  26. 168
  27. 143
  28. 9th
  29. 69
  30. 266
  31. 98
  32. 33
  33. 108
  34. 112
  35. 142
  36. 139
  37. 85
  38. 160
  39. 784
  40. 56

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