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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 238 · 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 27th term of the AP 1, 3, 5, 7, …? (a) 55 (b) 54 (c) 53 (d) 52
  2. 2.What is the 26th term of the AP 6, 13, 20, 27, …? (a) 175 (b) 181 (c) 182 (d) 188
  3. 3.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 861 (c) 1722 (d) 862
  4. 4.What is the 21st term of the AP 1, 5, 9, 13, …? (a) 81 (b) 84 (c) 85 (d) 80
  5. 5.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 210 (d) 231
  6. 6.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 297 (b) 594 (c) 52 (d) 302
  7. 7.Which term of the AP 14, 17, 20, 23, … is 62? (a) 19th (b) 17th (c) 18th (d) 16th
  8. 8.What is the missing term in the AP 6, 12, 18, ?, 30? (a) 24 (b) 25 (c) 23 (d) 30
  9. 9.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 55 (d) 784
  10. 10.What is the 15th term of the AP 17, 24, 31, 38, …? (a) 98 (b) 105 (c) 122 (d) 115
  11. 11.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 63 (b) 60 (c) 18 (d) 120
  12. 12.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 352 (b) 50 (c) 330 (d) 660
  13. 13.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 41 (b) 44 (c) 39 (d) 42
  14. 14.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 50 (b) 90 (c) 45 (d) 13
  15. 15.What is the 31st term of the AP 5, 14, 23, 32, …? (a) 275 (b) 284 (c) 270 (d) 279
  16. 16.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  17. 17.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  18. 18.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 30 (b) 231 (c) 440 (d) 220
  19. 19.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 420 (b) 210 (c) 39 (d) 230
  20. 20.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 184 (b) 336 (c) 168 (d) 35
  21. 21.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 800 (c) 820 (d) 780
  22. 22.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 216 (b) 396 (c) 38 (d) 198
  23. 23.What is the 11th term of the AP 12, 21, 30, 39, …? (a) 99 (b) 111 (c) 102 (d) 90
  24. 24.What is the 32nd term of the AP 17, 23, 29, 35, …? (a) 192 (b) 203 (c) 186 (d) 209
  25. 25.What is the 37th term of the AP 8, 15, 22, 29, …? (a) 267 (b) 252 (c) 260 (d) 259
  26. 26.What is the 10th term of the AP 5, 9, 13, 17, …? (a) 36 (b) 45 (c) 40 (d) 41
  27. 27.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 5852 (c) 2926 (d) 2888
  28. 28.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 250 (c) 43 (d) 270
  29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 576 (d) 300
  30. 30.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 75 (b) 21 (c) 65 (d) 130
  31. 31.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 55 (b) 60 (c) 10 (d) 110
  32. 32.What is the 39th term of the AP 11, 18, 25, 32, …? (a) 284 (b) 277 (c) 273 (d) 266
  33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  34. 34.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 496 (c) 512 (d) 1056
  35. 35.What is the 18th term of the AP 3, 8, 13, 18, …? (a) 93 (b) 90 (c) 85 (d) 88
  36. 36.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 112 (b) 17 (c) 108 (d) 216
  37. 37.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1128 (c) 1129 (d) 1081
  38. 38.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 3160 (c) 6320 (d) 3081
  39. 39.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 20 (b) 25 (c) 19 (d) 18
  40. 40.What is the 35th term of the AP 1, 7, 13, 19, …? (a) 204 (b) 205 (c) 211 (d) 210

Answer key

  1. 53
  2. 181
  3. 861
  4. 81
  5. 231
  6. 297
  7. 17th
  8. 24
  9. 784
  10. 115
  11. 60
  12. 330
  13. 41
  14. 45
  15. 275
  16. 361
  17. 324
  18. 220
  19. 210
  20. 168
  21. 820
  22. 198
  23. 102
  24. 203
  25. 260
  26. 41
  27. 2926
  28. 250
  29. 576
  30. 65
  31. 55
  32. 277
  33. 144
  34. 528
  35. 88
  36. 108
  37. 1128
  38. 3160
  39. 19
  40. 205

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