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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 76 · 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 18th term of the AP 20, 23, 26, 29, …? (a) 74 (b) 71 (c) 54 (d) 51
  2. 2.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 120 (c) 136 (d) 128
  3. 3.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 2652 (c) 1327 (d) 1326
  4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 441 (d) 462
  5. 5.What is the 33rd term of the AP 2, 10, 18, 26, …? (a) 266 (b) 256 (c) 264 (d) 258
  6. 6.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 756 (d) 378
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  8. 8.What is the 25th term of the AP 3, 12, 21, 30, …? (a) 216 (b) 228 (c) 225 (d) 219
  9. 9.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 2017 (c) 1953 (d) 4032
  10. 10.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 33 (c) 36 (d) 66
  11. 11.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 216 (b) 221 (c) 44 (d) 432
  12. 12.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 57 (d) 841
  13. 13.What is the 20th term of the AP 18, 20, 22, 24, …? (a) 56 (b) 58 (c) 38 (d) 40
  14. 14.What is the missing term in the AP 12, ?, 16, 18, 20? (a) 14 (b) 13 (c) 16 (d) 15
  15. 15.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 100 (b) 50 (c) 16 (d) 53
  16. 16.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
  17. 17.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 23 (b) 90 (c) 156 (d) 78
  18. 18.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 170 (b) 155 (c) 29 (d) 310
  19. 19.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 27 (b) 26 (c) 25 (d) 33
  20. 20.What is the 25th term of the AP 3, 9, 15, 21, …? (a) 153 (b) 144 (c) 150 (d) 147
  21. 21.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 24 (b) 22 (c) 26 (d) 23
  22. 22.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 162 (b) 17 (c) 90 (d) 81
  23. 23.What is the 29th term of the AP 5, 11, 17, 23, …? (a) 168 (b) 179 (c) 174 (d) 173
  24. 24.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 138 (b) 78 (c) 69 (d) 19
  25. 25.What is the 32nd term of the AP 14, 20, 26, 32, …? (a) 200 (b) 206 (c) 186 (d) 192
  26. 26.Which term of the AP 15, 18, 21, 24, … is 120? (a) 35th (b) 37th (c) 40th (d) 36th
  27. 27.What is the 28th term of the AP 20, 22, 24, 26, …? (a) 74 (b) 54 (c) 76 (d) 56
  28. 28.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 45 (b) 13 (c) 90 (d) 50
  29. 29.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 400 (d) 39
  30. 30.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 53 (d) 729
  31. 31.What is the 15th term of the AP 10, 17, 24, 31, …? (a) 115 (b) 98 (c) 105 (d) 108
  32. 32.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 900 (d) 930
  33. 33.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 105 (c) 91 (d) 98
  34. 34.What is the sum of all the whole numbers from 1 to 46? (a) 2162 (b) 1058 (c) 1081 (d) 1035
  35. 35.What is the 17th term of the AP 8, 15, 22, 29, …? (a) 112 (b) 120 (c) 119 (d) 127
  36. 36.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 198 (b) 360 (c) 180 (d) 36
  37. 37.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 153 (c) 162 (d) 171
  38. 38.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 4290 (c) 2146 (d) 2080
  39. 39.What is the 22nd term of the AP 13, 18, 23, 28, …? (a) 118 (b) 110 (c) 105 (d) 123
  40. 40.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 16 (b) 17 (c) 19 (d) 18

Answer key

  1. 71
  2. 136
  3. 1326
  4. 441
  5. 258
  6. 378
  7. 81
  8. 219
  9. 2016
  10. 33
  11. 216
  12. 841
  13. 56
  14. 14
  15. 50
  16. 25
  17. 78
  18. 155
  19. 26
  20. 147
  21. 23
  22. 81
  23. 173
  24. 69
  25. 200
  26. 36th
  27. 74
  28. 45
  29. 400
  30. 729
  31. 108
  32. 900
  33. 105
  34. 1081
  35. 120
  36. 180
  37. 171
  38. 2145
  39. 118
  40. 17

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