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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 216 · 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 39th term of the AP 13, 17, 21, 25, …? (a) 169 (b) 152 (c) 156 (d) 165
  2. 2.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 280 (b) 55 (c) 310 (d) 560
  3. 3.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 1406 (c) 704 (d) 703
  4. 4.What is the 18th term of the AP 20, 29, 38, 47, …? (a) 153 (b) 173 (c) 182 (d) 162
  5. 5.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 150 (b) 80 (c) 25 (d) 75
  6. 6.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 15 (b) 16 (c) 14 (d) 19
  7. 7.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 1176 (c) 2450 (d) 1225
  8. 8.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  9. 9.What is the 15th term of the AP 7, 16, 25, 34, …? (a) 135 (b) 142 (c) 126 (d) 133
  10. 10.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 19 (b) 18 (c) 20 (d) 21
  11. 11.What is the 24th term of the AP 13, 22, 31, 40, …? (a) 207 (b) 220 (c) 216 (d) 229
  12. 12.What is the 19th term of the AP 2, 10, 18, 26, …? (a) 152 (b) 144 (c) 154 (d) 146
  13. 13.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 3306 (c) 1654 (d) 1596
  14. 14.What is the 33rd term of the AP 15, 19, 23, 27, …? (a) 147 (b) 128 (c) 132 (d) 143
  15. 15.What is the 34th term of the AP 7, 12, 17, 22, …? (a) 172 (b) 177 (c) 170 (d) 165
  16. 16.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 22 (b) 24 (c) 23 (d) 27
  17. 17.Which term of the AP 19, 24, 29, 34, … is 94? (a) 17th (b) 16th (c) 18th (d) 15th
  18. 18.What is the 39th term of the AP 19, 27, 35, 43, …? (a) 304 (b) 312 (c) 323 (d) 331
  19. 19.Which term of the AP 4, 10, 16, 22, … is 148? (a) 26th (b) 25th (c) 24th (d) 27th
  20. 20.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 330 (b) 180 (c) 165 (d) 30
  21. 21.What is the 23rd term of the AP 16, 20, 24, 28, …? (a) 108 (b) 104 (c) 88 (d) 92
  22. 22.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2850 (c) 5852 (d) 2926
  23. 23.What is the missing term in the AP 18, 26, ?, 42, 50? (a) 35 (b) 42 (c) 33 (d) 34
  24. 24.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 17 (b) 16 (c) 15 (d) 19
  25. 25.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 138 (c) 120 (d) 240
  26. 26.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 39 (b) 38 (c) 37 (d) 47
  27. 27.What is the 14th term of the AP 9, 15, 21, 27, …? (a) 78 (b) 84 (c) 87 (d) 93
  28. 28.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 24 (b) 70 (c) 75 (d) 140
  29. 29.What is the 19th term of the AP 15, 24, 33, 42, …? (a) 162 (b) 186 (c) 177 (d) 171
  30. 30.What is the 19th term of the AP 11, 20, 29, 38, …? (a) 171 (b) 173 (c) 162 (d) 182
  31. 31.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
  32. 32.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 114 (b) 27 (c) 204 (d) 102
  33. 33.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4656 (c) 4753 (d) 9506
  34. 34.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 31 (b) 24 (c) 25 (d) 26
  35. 35.Which term of the AP 1, 5, 9, 13, … is 69? (a) 20th (b) 17th (c) 18th (d) 19th
  36. 36.What is the 20th term of the AP 3, 10, 17, 24, …? (a) 143 (b) 133 (c) 140 (d) 136
  37. 37.Which term of the AP 5, 7, 9, 11, … is 35? (a) 15th (b) 18th (c) 17th (d) 16th
  38. 38.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 15 (b) 20 (c) 14 (d) 13
  39. 39.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2628 (c) 2556 (d) 2592
  40. 40.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 660 (b) 335 (c) 55 (d) 330

Answer key

  1. 165
  2. 280
  3. 703
  4. 173
  5. 75
  6. 15
  7. 1225
  8. 400
  9. 133
  10. 19
  11. 220
  12. 146
  13. 1653
  14. 143
  15. 172
  16. 23
  17. 16th
  18. 323
  19. 25th
  20. 165
  21. 104
  22. 2926
  23. 34
  24. 16
  25. 120
  26. 38
  27. 87
  28. 70
  29. 177
  30. 173
  31. 729
  32. 102
  33. 4753
  34. 25
  35. 18th
  36. 136
  37. 16th
  38. 14
  39. 2628
  40. 330

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