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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 454 · 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 sum of the first 11 terms of the AP 7, 12, 17, …? (a) 357 (b) 57 (c) 352 (d) 704
  2. 2.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 700 (b) 380 (c) 62 (d) 350
  3. 3.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 189 (b) 207 (c) 378 (d) 37
  4. 4.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 1540 (c) 3192 (d) 1568
  5. 5.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 55 (d) 406
  6. 6.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 16 (b) 15 (c) 21 (d) 14
  7. 7.What is the 11th term of the AP 4, 10, 16, 22, …? (a) 60 (b) 64 (c) 70 (d) 66
  8. 8.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 252 (b) 18 (c) 127 (d) 126
  9. 9.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 22 (b) 72 (c) 84 (d) 144
  10. 10.What is the 31st term of the AP 19, 23, 27, 31, …? (a) 143 (b) 120 (c) 124 (d) 139
  11. 11.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 360 (b) 180 (c) 183 (d) 32
  12. 12.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 18 (b) 120 (c) 63 (d) 60
  13. 13.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 13 (b) 11 (c) 12 (d) 15
  14. 14.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 53 (b) 372 (c) 396 (d) 744
  15. 15.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 308 (b) 53 (c) 313 (d) 616
  16. 16.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 212 (b) 43 (c) 414 (d) 207
  17. 17.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 396 (b) 198 (c) 33 (d) 201
  18. 18.What is the 20th term of the AP 13, 22, 31, 40, …? (a) 193 (b) 180 (c) 184 (d) 171
  19. 19.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 120 (c) 136 (d) 128
  20. 20.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 35 (b) 280 (c) 140 (d) 145
  21. 21.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5050 (c) 5000 (d) 4950
  22. 22.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 27 (b) 360 (c) 190 (d) 180
  23. 23.What is the 29th term of the AP 2, 9, 16, 23, …? (a) 203 (b) 205 (c) 196 (d) 198
  24. 24.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 26 (b) 176 (c) 352 (d) 187
  25. 25.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 324 (b) 171 (c) 162 (d) 26
  26. 26.What is the 14th term of the AP 7, 13, 19, 25, …? (a) 85 (b) 91 (c) 84 (d) 78
  27. 27.What is the 40th term of the AP 13, 20, 27, 34, …? (a) 273 (b) 280 (c) 293 (d) 286
  28. 28.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78
  29. 29.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 6 (b) 5 (c) 9 (d) 4
  30. 30.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 19 (b) 17 (c) 18 (d) 22
  31. 31.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 27 (b) 28 (c) 35 (d) 26
  32. 32.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 240 (d) 120
  33. 33.Which term of the AP 6, 10, 14, 18, … is 62? (a) 16th (b) 17th (c) 14th (d) 15th
  34. 34.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 30 (b) 180 (c) 165 (d) 330
  35. 35.What is the 33rd term of the AP 2, 7, 12, 17, …? (a) 160 (b) 165 (c) 162 (d) 167
  36. 36.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 16 (b) 15 (c) 17 (d) 21
  37. 37.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 70 (b) 35 (c) 38 (d) 13
  38. 38.What is the 18th term of the AP 14, 23, 32, 41, …? (a) 167 (b) 153 (c) 162 (d) 176
  39. 39.Which term of the AP 4, 13, 22, 31, … is 76? (a) 10th (b) 11th (c) 9th (d) 8th
  40. 40.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 204 (b) 192 (c) 27 (d) 384

Answer key

  1. 352
  2. 350
  3. 189
  4. 1596
  5. 784
  6. 15
  7. 64
  8. 126
  9. 72
  10. 139
  11. 180
  12. 60
  13. 12
  14. 372
  15. 308
  16. 207
  17. 198
  18. 184
  19. 136
  20. 140
  21. 5050
  22. 180
  23. 198
  24. 176
  25. 162
  26. 85
  27. 286
  28. 144
  29. 5
  30. 18
  31. 27
  32. 225
  33. 15th
  34. 165
  35. 162
  36. 16
  37. 35
  38. 167
  39. 9th
  40. 192

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