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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 712 · 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 7, 9, ?, 13, 15? (a) 12 (b) 10 (c) 13 (d) 11
  2. 2.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1128 (c) 1081 (d) 2256
  3. 3.What is the 16th term of the AP 2, 8, 14, 20, …? (a) 96 (b) 90 (c) 98 (d) 92
  4. 4.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 496 (b) 52 (c) 272 (d) 248
  5. 5.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 45 (b) 90 (c) 50 (d) 13
  6. 6.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 120 (c) 204 (d) 102
  7. 7.What is the 31st term of the AP 13, 18, 23, 28, …? (a) 150 (b) 163 (c) 155 (d) 168
  8. 8.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 232 (c) 462 (d) 210
  9. 9.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 1332 (c) 648 (d) 666
  10. 10.What is the 19th term of the AP 12, 18, 24, 30, …? (a) 120 (b) 114 (c) 126 (d) 108
  11. 11.What is the 10th term of the AP 19, 26, 33, 40, …? (a) 63 (b) 70 (c) 89 (d) 82
  12. 12.Which term of the AP 18, 27, 36, 45, … is 126? (a) 15th (b) 12th (c) 13th (d) 14th
  13. 13.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 21 (c) 6 (d) 40
  14. 14.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 11 (b) 13 (c) 12 (d) 18
  15. 15.What is the 10th term of the AP 9, 12, 15, 18, …? (a) 36 (b) 27 (c) 30 (d) 39
  16. 16.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 288 (b) 28 (c) 147 (d) 144
  17. 17.What is the 29th term of the AP 5, 12, 19, 26, …? (a) 196 (b) 201 (c) 208 (d) 203
  18. 18.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 50 (b) 12 (c) 51 (d) 100
  19. 19.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 175 (b) 154 (c) 308 (d) 40
  20. 20.What is the 35th term of the AP 16, 25, 34, 43, …? (a) 315 (b) 306 (c) 331 (d) 322
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 11 (d) 36
  22. 22.What is the 27th term of the AP 18, 20, 22, 24, …? (a) 54 (b) 72 (c) 70 (d) 52
  23. 23.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 7482 (c) 3741 (d) 3655
  24. 24.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4656 (c) 4608 (d) 4560
  25. 25.What is the 35th term of the AP 16, 23, 30, 37, …? (a) 238 (b) 245 (c) 261 (d) 254
  26. 26.Which term of the AP 14, 17, 20, 23, … is 86? (a) 26th (b) 24th (c) 25th (d) 27th
  27. 27.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 126 (b) 111 (c) 222 (d) 31
  28. 28.What is the 13th term of the AP 15, 17, 19, 21, …? (a) 26 (b) 41 (c) 39 (d) 24
  29. 29.Which term of the AP 11, 19, 27, 35, … is 323? (a) 42nd (b) 41st (c) 39th (d) 40th
  30. 30.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 66 (b) 429 (c) 396 (d) 792
  31. 31.What is the 23rd term of the AP 1, 9, 17, 25, …? (a) 176 (b) 184 (c) 177 (d) 185
  32. 32.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 8 (c) 35 (d) 70
  33. 33.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 2775 (c) 5550 (d) 2701
  34. 34.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 171 (b) 324 (c) 162 (d) 26
  35. 35.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 162 (b) 144 (c) 39 (d) 288
  36. 36.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 361 (d) 190
  37. 37.What is the 19th term of the AP 10, 19, 28, 37, …? (a) 171 (b) 181 (c) 172 (d) 162
  38. 38.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 60 (b) 10 (c) 30 (d) 35
  39. 39.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 156 (d) 23
  40. 40.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 174 (b) 102 (c) 27 (d) 87

Answer key

  1. 11
  2. 1128
  3. 92
  4. 248
  5. 45
  6. 102
  7. 163
  8. 231
  9. 666
  10. 120
  11. 82
  12. 13th
  13. 20
  14. 12
  15. 36
  16. 144
  17. 201
  18. 50
  19. 154
  20. 322
  21. 36
  22. 70
  23. 3741
  24. 4656
  25. 254
  26. 25th
  27. 111
  28. 39
  29. 40th
  30. 396
  31. 177
  32. 35
  33. 2775
  34. 162
  35. 144
  36. 361
  37. 172
  38. 30
  39. 144
  40. 87

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