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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 705 · 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.Which term of the AP 3, 9, 15, 21, … is 57? (a) 12th (b) 9th (c) 11th (d) 10th
  2. 2.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 30 (b) 132 (c) 240 (d) 120
  3. 3.What is the missing term in the AP 7, 15, ?, 31, 39? (a) 24 (b) 31 (c) 22 (d) 23
  4. 4.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 46 (b) 576 (c) 312 (d) 288
  5. 5.What is the 23rd term of the AP 8, 15, 22, 29, …? (a) 169 (b) 161 (c) 162 (d) 154
  6. 6.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 322 (b) 38 (c) 161 (d) 166
  7. 7.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 32 (b) 234 (c) 132 (d) 117
  8. 8.What is the 29th term of the AP 3, 11, 19, 27, …? (a) 224 (b) 235 (c) 227 (d) 232
  9. 9.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 63 (c) 13 (d) 126
  10. 10.What is the 38th term of the AP 9, 15, 21, 27, …? (a) 237 (b) 228 (c) 231 (d) 222
  11. 11.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 13 (b) 15 (c) 14 (d) 16
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 53 (d) 756
  13. 13.What is the 16th term of the AP 3, 6, 9, 12, …? (a) 45 (b) 51 (c) 48 (d) 49
  14. 14.What is the 37th term of the AP 13, 18, 23, 28, …? (a) 185 (b) 198 (c) 193 (d) 180
  15. 15.What is the 31st term of the AP 16, 18, 20, 22, …? (a) 76 (b) 78 (c) 62 (d) 60
  16. 16.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 34 (b) 37 (c) 30 (d) 27
  17. 17.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4278 (c) 4186 (d) 4232
  18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
  20. 20.Which term of the AP 15, 17, 19, 21, … is 61? (a) 23rd (b) 24th (c) 25th (d) 26th
  21. 21.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 2162 (c) 1058 (d) 1081
  22. 22.What is the 35th term of the AP 13, 17, 21, 25, …? (a) 153 (b) 149 (c) 140 (d) 136
  23. 23.What is the 17th term of the AP 10, 13, 16, 19, …? (a) 61 (b) 48 (c) 51 (d) 58
  24. 24.What is the 22nd term of the AP 3, 9, 15, 21, …? (a) 135 (b) 132 (c) 129 (d) 126
  25. 25.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 32 (b) 39 (c) 30 (d) 31
  26. 26.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1540 (c) 1541 (d) 3080
  27. 27.What is the 35th term of the AP 7, 14, 21, 28, …? (a) 238 (b) 245 (c) 246 (d) 252
  28. 28.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 300 (b) 150 (c) 168 (d) 40
  29. 29.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 820 (c) 1640 (d) 800
  30. 30.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 66 (b) 396 (c) 429 (d) 792
  31. 31.What is the 11th term of the AP 6, 15, 24, 33, …? (a) 99 (b) 90 (c) 96 (d) 105
  32. 32.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 15 (b) 14 (c) 16 (d) 22
  33. 33.Which term of the AP 1, 6, 11, 16, … is 66? (a) 15th (b) 16th (c) 14th (d) 13th
  34. 34.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 24 (b) 34 (c) 25 (d) 26
  35. 35.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 32 (b) 38 (c) 31 (d) 30
  36. 36.Which term of the AP 3, 12, 21, 30, … is 183? (a) 22nd (b) 20th (c) 23rd (d) 21st
  37. 37.What is the 18th term of the AP 18, 27, 36, 45, …? (a) 153 (b) 180 (c) 171 (d) 162
  38. 38.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 210 (c) 98 (d) 91
  39. 39.What is the 37th term of the AP 8, 11, 14, 17, …? (a) 116 (b) 108 (c) 119 (d) 111
  40. 40.What is the 40th term of the AP 19, 27, 35, 43, …? (a) 339 (b) 312 (c) 331 (d) 320

Answer key

  1. 10th
  2. 120
  3. 23
  4. 288
  5. 162
  6. 161
  7. 117
  8. 227
  9. 63
  10. 231
  11. 14
  12. 729
  13. 48
  14. 193
  15. 76
  16. 34
  17. 4278
  18. 841
  19. 196
  20. 24th
  21. 1081
  22. 149
  23. 58
  24. 129
  25. 31
  26. 1540
  27. 245
  28. 150
  29. 820
  30. 396
  31. 96
  32. 15
  33. 14th
  34. 25
  35. 31
  36. 21st
  37. 171
  38. 105
  39. 116
  40. 331

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