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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 251 · 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 1, 4, ?, 10, 13? (a) 6 (b) 7 (c) 8 (d) 10
  2. 2.Which term of the AP 6, 8, 10, 12, … is 60? (a) 29th (b) 30th (c) 28th (d) 27th
  3. 3.Which term of the AP 5, 10, 15, 20, … is 70? (a) 15th (b) 14th (c) 16th (d) 13th
  4. 4.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 990 (c) 1980 (d) 968
  5. 5.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 6 (b) 12 (c) 7 (d) 8
  6. 6.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 117 (b) 32 (c) 132 (d) 234
  7. 7.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 65 (b) 70 (c) 23 (d) 130
  8. 8.What is the 35th term of the AP 18, 27, 36, 45, …? (a) 306 (b) 315 (c) 333 (d) 324
  9. 9.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 51 (c) 12 (d) 50
  10. 10.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3200 (c) 3240 (d) 6480
  11. 11.What is the 18th term of the AP 11, 20, 29, 38, …? (a) 173 (b) 153 (c) 164 (d) 162
  12. 12.What is the 30th term of the AP 15, 21, 27, 33, …? (a) 195 (b) 174 (c) 180 (d) 189
  13. 13.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 29 (b) 23 (c) 24 (d) 22
  14. 14.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 320 (b) 34 (c) 176 (d) 160
  15. 15.What is the 16th term of the AP 9, 17, 25, 33, …? (a) 137 (b) 129 (c) 128 (d) 120
  16. 16.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 140 (b) 19 (c) 70 (d) 73
  17. 17.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 352 (b) 385 (c) 62 (d) 704
  18. 18.What is the 12th term of the AP 15, 20, 25, 30, …? (a) 75 (b) 55 (c) 70 (d) 60
  19. 19.Which term of the AP 2, 10, 18, 26, … is 90? (a) 13th (b) 11th (c) 14th (d) 12th
  20. 20.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 264 (c) 252 (d) 504
  21. 21.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 13 (b) 11 (c) 17 (d) 12
  22. 22.What is the 35th term of the AP 20, 28, 36, 44, …? (a) 300 (b) 272 (c) 292 (d) 280
  23. 23.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 540 (b) 39 (c) 288 (d) 270
  24. 24.What is the 18th term of the AP 14, 18, 22, 26, …? (a) 72 (b) 82 (c) 68 (d) 86
  25. 25.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 28 (b) 38 (c) 30 (d) 29
  26. 26.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 600 (c) 276 (d) 288
  27. 27.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 5402 (c) 2628 (d) 2701
  28. 28.What is the 31st term of the AP 1, 7, 13, 19, …? (a) 186 (b) 181 (c) 180 (d) 187
  29. 29.What is the 10th term of the AP 8, 11, 14, 17, …? (a) 35 (b) 38 (c) 30 (d) 27
  30. 30.What is the 13th term of the AP 13, 15, 17, 19, …? (a) 24 (b) 26 (c) 37 (d) 39
  31. 31.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 200 (d) 190
  32. 32.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 84 (b) 12 (c) 78 (d) 156
  33. 33.What is the 12th term of the AP 6, 12, 18, 24, …? (a) 66 (b) 73 (c) 78 (d) 72
  34. 34.Which term of the AP 13, 21, 29, 37, … is 213? (a) 27th (b) 25th (c) 26th (d) 28th
  35. 35.What is the missing term in the AP 17, 25, 33, ?, 49? (a) 42 (b) 40 (c) 49 (d) 41
  36. 36.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 120 (c) 136 (d) 128
  37. 37.What is the missing term in the AP 20, 24, ?, 32, 36? (a) 29 (b) 27 (c) 32 (d) 28
  38. 38.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 13 (b) 152 (c) 76 (d) 80
  39. 39.What is the 18th term of the AP 19, 25, 31, 37, …? (a) 102 (b) 127 (c) 108 (d) 121
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100

Answer key

  1. 7
  2. 28th
  3. 14th
  4. 990
  5. 7
  6. 117
  7. 65
  8. 324
  9. 50
  10. 3240
  11. 164
  12. 189
  13. 23
  14. 160
  15. 129
  16. 70
  17. 352
  18. 70
  19. 12th
  20. 252
  21. 12
  22. 292
  23. 270
  24. 82
  25. 29
  26. 300
  27. 2701
  28. 181
  29. 35
  30. 37
  31. 210
  32. 78
  33. 72
  34. 26th
  35. 41
  36. 136
  37. 28
  38. 76
  39. 121
  40. 100

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