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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 688 · 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 21st term of the AP 6, 8, 10, 12, …? (a) 48 (b) 46 (c) 42 (d) 40
  2. 2.What is the 10th term of the AP 18, 21, 24, 27, …? (a) 48 (b) 30 (c) 45 (d) 27
  3. 3.What is the 28th term of the AP 4, 11, 18, 25, …? (a) 196 (b) 193 (c) 200 (d) 189
  4. 4.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 70 (b) 26 (c) 85 (d) 140
  5. 5.What is the 29th term of the AP 8, 14, 20, 26, …? (a) 176 (b) 168 (c) 182 (d) 174
  6. 6.What is the 17th term of the AP 15, 23, 31, 39, …? (a) 136 (b) 151 (c) 128 (d) 143
  7. 7.What is the missing term in the AP 19, 22, 25, ?, 31? (a) 28 (b) 27 (c) 31 (d) 29
  8. 8.What is the 36th term of the AP 19, 25, 31, 37, …? (a) 210 (b) 216 (c) 235 (d) 229
  9. 9.What is the 14th term of the AP 10, 12, 14, 16, …? (a) 36 (b) 26 (c) 28 (d) 38
  10. 10.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 550 (b) 50 (c) 300 (d) 275
  11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 289 (d) 306
  12. 12.What is the 14th term of the AP 6, 8, 10, 12, …? (a) 26 (b) 28 (c) 32 (d) 34
  13. 13.Which term of the AP 3, 6, 9, 12, … is 51? (a) 18th (b) 19th (c) 16th (d) 17th
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
  15. 15.Which term of the AP 9, 17, 25, 33, … is 265? (a) 32nd (b) 34th (c) 33rd (d) 35th
  16. 16.What is the 18th term of the AP 11, 15, 19, 23, …? (a) 68 (b) 72 (c) 79 (d) 83
  17. 17.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 77 (c) 78 (d) 154
  18. 18.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 130 (c) 65 (d) 68
  19. 19.What is the 25th term of the AP 14, 23, 32, 41, …? (a) 225 (b) 216 (c) 239 (d) 230
  20. 20.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 253 (b) 275 (c) 506 (d) 43
  21. 21.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 756 (c) 351 (d) 378
  22. 22.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 72 (d) 64
  23. 23.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 3828 (c) 3741 (d) 7656
  24. 24.What is the 14th term of the AP 2, 8, 14, 20, …? (a) 84 (b) 86 (c) 80 (d) 78
  25. 25.What is the 29th term of the AP 14, 18, 22, 26, …? (a) 126 (b) 130 (c) 112 (d) 116
  26. 26.What is the 34th term of the AP 19, 24, 29, 34, …? (a) 189 (b) 170 (c) 184 (d) 165
  27. 27.What is the 30th term of the AP 3, 11, 19, 27, …? (a) 240 (b) 235 (c) 243 (d) 232
  28. 28.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 33 (b) 306 (c) 171 (d) 153
  29. 29.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 280 (b) 23 (c) 140 (d) 150
  30. 30.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 8 (b) 10 (c) 6 (d) 7
  31. 31.What is the 21st term of the AP 2, 6, 10, 14, …? (a) 84 (b) 82 (c) 86 (d) 80
  32. 32.What is the 29th term of the AP 1, 8, 15, 22, …? (a) 196 (b) 204 (c) 197 (d) 203
  33. 33.What is the 28th term of the AP 12, 19, 26, 33, …? (a) 201 (b) 196 (c) 189 (d) 208
  34. 34.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 42 (b) 9 (c) 39 (d) 78
  35. 35.What is the 26th term of the AP 6, 15, 24, 33, …? (a) 225 (b) 240 (c) 231 (d) 234
  36. 36.What is the 40th term of the AP 17, 26, 35, 44, …? (a) 351 (b) 368 (c) 377 (d) 360
  37. 37.Which term of the AP 12, 17, 22, 27, … is 187? (a) 36th (b) 35th (c) 38th (d) 37th
  38. 38.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 54 (b) 7 (c) 27 (d) 30
  39. 39.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 54 (b) 108 (c) 10 (d) 55
  40. 40.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 17 (b) 25 (c) 18 (d) 16

Answer key

  1. 46
  2. 45
  3. 193
  4. 70
  5. 176
  6. 143
  7. 28
  8. 229
  9. 36
  10. 275
  11. 289
  12. 32
  13. 17th
  14. 784
  15. 33rd
  16. 79
  17. 77
  18. 65
  19. 230
  20. 253
  21. 378
  22. 64
  23. 3828
  24. 80
  25. 126
  26. 184
  27. 235
  28. 153
  29. 140
  30. 7
  31. 82
  32. 197
  33. 201
  34. 39
  35. 231
  36. 368
  37. 36th
  38. 27
  39. 54
  40. 17

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