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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 573 · 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 16th term of the AP 1, 3, 5, 7, …? (a) 30 (b) 32 (c) 33 (d) 31
  2. 2.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 152 (b) 140 (c) 280 (d) 28
  3. 3.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 4556 (c) 2211 (d) 2279
  4. 4.What is the 34th term of the AP 8, 10, 12, 14, …? (a) 76 (b) 68 (c) 66 (d) 74
  5. 5.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 216 (b) 120 (c) 24 (d) 108
  6. 6.What is the 17th term of the AP 19, 23, 27, 31, …? (a) 64 (b) 83 (c) 87 (d) 68
  7. 7.What is the 35th term of the AP 5, 9, 13, 17, …? (a) 140 (b) 145 (c) 141 (d) 136
  8. 8.What is the 10th term of the AP 9, 18, 27, 36, …? (a) 81 (b) 90 (c) 99 (d) 91
  9. 9.What is the 23rd term of the AP 4, 11, 18, 25, …? (a) 154 (b) 165 (c) 161 (d) 158
  10. 10.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 120 (b) 65 (c) 16 (d) 60
  11. 11.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  12. 12.What is the 31st term of the AP 15, 23, 31, 39, …? (a) 240 (b) 255 (c) 263 (d) 248
  13. 13.What is the 12th term of the AP 6, 15, 24, 33, …? (a) 105 (b) 99 (c) 108 (d) 114
  14. 14.What is the 27th term of the AP 15, 23, 31, 39, …? (a) 231 (b) 223 (c) 208 (d) 216
  15. 15.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  16. 16.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 136 (d) 154
  17. 17.What is the 40th term of the AP 19, 22, 25, 28, …? (a) 120 (b) 136 (c) 117 (d) 139
  18. 18.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 161 (b) 147 (c) 33 (d) 294
  19. 19.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 190 (b) 374 (c) 187 (d) 32
  20. 20.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 364 (b) 182 (c) 44 (d) 203
  21. 21.What is the 14th term of the AP 18, 23, 28, 33, …? (a) 70 (b) 88 (c) 83 (d) 65
  22. 22.What is the 28th term of the AP 10, 14, 18, 22, …? (a) 122 (b) 118 (c) 108 (d) 112
  23. 23.What is the 13th term of the AP 3, 5, 7, 9, …? (a) 24 (b) 29 (c) 27 (d) 26
  24. 24.What is the 36th term of the AP 7, 12, 17, 22, …? (a) 175 (b) 187 (c) 182 (d) 180
  25. 25.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 1953 (c) 2017 (d) 2016
  26. 26.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 180 (b) 34 (c) 324 (d) 162
  27. 27.Which term of the AP 17, 25, 33, 41, … is 105? (a) 14th (b) 12th (c) 13th (d) 11th
  28. 28.What is the 16th term of the AP 6, 11, 16, 21, …? (a) 80 (b) 75 (c) 81 (d) 86
  29. 29.What is the 33rd term of the AP 2, 4, 6, 8, …? (a) 68 (b) 64 (c) 67 (d) 66
  30. 30.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 17 (b) 13 (c) 12 (d) 11
  31. 31.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 3570 (c) 3656 (d) 7310
  32. 32.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 19 (b) 18 (c) 26 (d) 17
  33. 33.What is the 10th term of the AP 14, 22, 30, 38, …? (a) 86 (b) 94 (c) 80 (d) 72
  34. 34.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 360 (b) 660 (c) 60 (d) 330
  35. 35.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 13 (b) 14 (c) 15 (d) 18
  36. 36.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 4692 (c) 2346 (d) 2278
  37. 37.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 58 (b) 363 (c) 726 (d) 368
  38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 33 (d) 306
  39. 39.What is the 37th term of the AP 7, 11, 15, 19, …? (a) 151 (b) 155 (c) 144 (d) 148
  40. 40.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4232 (c) 4186 (d) 4278

Answer key

  1. 31
  2. 140
  3. 2278
  4. 74
  5. 108
  6. 83
  7. 141
  8. 90
  9. 158
  10. 60
  11. 625
  12. 255
  13. 105
  14. 223
  15. 529
  16. 153
  17. 136
  18. 147
  19. 187
  20. 182
  21. 83
  22. 118
  23. 27
  24. 182
  25. 2016
  26. 162
  27. 12th
  28. 81
  29. 66
  30. 12
  31. 3655
  32. 18
  33. 86
  34. 330
  35. 14
  36. 2346
  37. 363
  38. 289
  39. 151
  40. 4278

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