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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 211 · 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 missing term in the AP 19, 26, ?, 40, 47? (a) 33 (b) 40 (c) 32 (d) 34
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  3. 3.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 378 (b) 756 (c) 408 (d) 59
  4. 4.What is the 39th term of the AP 16, 21, 26, 31, …? (a) 206 (b) 211 (c) 195 (d) 190
  5. 5.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 115 (b) 230 (c) 120 (d) 16
  6. 6.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 39 (b) 172 (c) 344 (d) 192
  7. 7.What is the 23rd term of the AP 8, 13, 18, 23, …? (a) 110 (b) 115 (c) 118 (d) 123
  8. 8.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 361 (c) 380 (d) 37
  9. 9.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 5 (b) 6 (c) 8 (d) 4
  10. 10.What is the 17th term of the AP 18, 21, 24, 27, …? (a) 66 (b) 69 (c) 48 (d) 51
  11. 11.What is the 30th term of the AP 5, 11, 17, 23, …? (a) 174 (b) 185 (c) 180 (d) 179
  12. 12.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 17 (b) 57 (c) 114 (d) 66
  13. 13.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 15 (b) 13 (c) 17 (d) 14
  14. 14.What is the 11th term of the AP 18, 25, 32, 39, …? (a) 70 (b) 95 (c) 77 (d) 88
  15. 15.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 98 (b) 196 (c) 26 (d) 112
  16. 16.What is the 21st term of the AP 3, 7, 11, 15, …? (a) 80 (b) 84 (c) 83 (d) 87
  17. 17.What is the 25th term of the AP 8, 17, 26, 35, …? (a) 225 (b) 216 (c) 224 (d) 233
  18. 18.Which term of the AP 4, 9, 14, 19, … is 154? (a) 33rd (b) 31st (c) 30th (d) 32nd
  19. 19.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 175 (b) 308 (c) 40 (d) 154
  20. 20.What is the 34th term of the AP 15, 23, 31, 39, …? (a) 264 (b) 287 (c) 279 (d) 272
  21. 21.What is the 24th term of the AP 14, 16, 18, 20, …? (a) 62 (b) 46 (c) 48 (d) 60
  22. 22.What is the 21st term of the AP 18, 25, 32, 39, …? (a) 147 (b) 158 (c) 140 (d) 165
  23. 23.What is the 27th term of the AP 15, 21, 27, 33, …? (a) 162 (b) 171 (c) 156 (d) 177
  24. 24.What is the 33rd term of the AP 20, 28, 36, 44, …? (a) 256 (b) 284 (c) 276 (d) 264
  25. 25.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 15 (b) 23 (c) 14 (d) 13
  26. 26.What is the 29th term of the AP 15, 20, 25, 30, …? (a) 145 (b) 140 (c) 160 (d) 155
  27. 27.What is the 40th term of the AP 4, 13, 22, 31, …? (a) 364 (b) 360 (c) 355 (d) 351
  28. 28.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 120 (d) 29
  29. 29.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 42 (d) 11
  30. 30.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 3828 (c) 3741 (d) 7656
  31. 31.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 22 (b) 96 (c) 87 (d) 174
  32. 32.What is the 18th term of the AP 8, 10, 12, 14, …? (a) 44 (b) 42 (c) 34 (d) 36
  33. 33.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 23 (b) 130 (c) 65 (d) 70
  34. 34.Which term of the AP 2, 9, 16, 23, … is 51? (a) 9th (b) 10th (c) 8th (d) 7th
  35. 35.What is the sum of all the whole numbers from 1 to 28? (a) 406 (b) 378 (c) 392 (d) 812
  36. 36.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 156 (b) 288 (c) 23 (d) 144
  37. 37.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 70 (b) 36 (c) 8 (d) 35
  38. 38.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 23 (c) 75 (d) 150
  39. 39.Which term of the AP 11, 18, 25, 32, … is 95? (a) 12th (b) 13th (c) 14th (d) 15th
  40. 40.What is the 10th term of the AP 5, 14, 23, 32, …? (a) 95 (b) 90 (c) 86 (d) 81

Answer key

  1. 33
  2. 64
  3. 378
  4. 206
  5. 115
  6. 172
  7. 118
  8. 361
  9. 5
  10. 66
  11. 179
  12. 57
  13. 14
  14. 88
  15. 98
  16. 83
  17. 224
  18. 31st
  19. 154
  20. 279
  21. 60
  22. 158
  23. 171
  24. 276
  25. 14
  26. 155
  27. 355
  28. 225
  29. 36
  30. 3828
  31. 87
  32. 42
  33. 65
  34. 8th
  35. 406
  36. 144
  37. 35
  38. 75
  39. 13th
  40. 86

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