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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 847 · 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 sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 35 (c) 342 (d) 171
  2. 2.What is the 21st term of the AP 7, 13, 19, 25, …? (a) 127 (b) 120 (c) 133 (d) 126
  3. 3.What is the 13th term of the AP 7, 11, 15, 19, …? (a) 55 (b) 59 (c) 52 (d) 48
  4. 4.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 456 (b) 840 (c) 68 (d) 420
  5. 5.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 342 (b) 372 (c) 56 (d) 684
  6. 6.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 27 (b) 26 (c) 25 (d) 31
  7. 7.What is the 11th term of the AP 5, 8, 11, 14, …? (a) 35 (b) 30 (c) 33 (d) 38
  8. 8.What is the missing term in the AP 7, 15, ?, 31, 39? (a) 23 (b) 24 (c) 31 (d) 22
  9. 9.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 242 (c) 506 (d) 253
  10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  11. 11.What is the 18th term of the AP 17, 19, 21, 23, …? (a) 51 (b) 34 (c) 53 (d) 36
  12. 12.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 153 (d) 306
  13. 13.What is the 29th term of the AP 2, 10, 18, 26, …? (a) 234 (b) 224 (c) 232 (d) 226
  14. 14.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 43 (b) 41 (c) 50 (d) 42
  15. 15.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 7 (b) 6 (c) 8 (d) 13
  16. 16.What is the 20th term of the AP 11, 14, 17, 20, …? (a) 57 (b) 60 (c) 71 (d) 68
  17. 17.Which term of the AP 20, 29, 38, 47, … is 317? (a) 34th (b) 35th (c) 36th (d) 33rd
  18. 18.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 143 (b) 264 (c) 132 (d) 22
  19. 19.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 2016 (c) 2048 (d) 4160
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  21. 21.What is the 34th term of the AP 5, 9, 13, 17, …? (a) 136 (b) 137 (c) 132 (d) 141
  22. 22.What is the 35th term of the AP 6, 13, 20, 27, …? (a) 251 (b) 245 (c) 238 (d) 244
  23. 23.What is the 20th term of the AP 18, 21, 24, 27, …? (a) 60 (b) 78 (c) 75 (d) 57
  24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 36 (d) 42
  25. 25.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 70 (b) 35 (c) 13 (d) 38
  26. 26.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 8930 (c) 4418 (d) 4371
  27. 27.What is the 36th term of the AP 5, 11, 17, 23, …? (a) 210 (b) 216 (c) 221 (d) 215
  28. 28.What is the 19th term of the AP 17, 22, 27, 32, …? (a) 95 (b) 112 (c) 107 (d) 90
  29. 29.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4095 (c) 4186 (d) 8372
  30. 30.What is the 30th term of the AP 12, 20, 28, 36, …? (a) 252 (b) 240 (c) 244 (d) 232
  31. 31.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 20 (b) 110 (c) 120 (d) 220
  32. 32.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 870 (d) 57
  33. 33.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 59 (d) 900
  34. 34.What is the 31st term of the AP 2, 4, 6, 8, …? (a) 63 (b) 62 (c) 64 (d) 60
  35. 35.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 1260 (c) 631 (d) 630
  36. 36.What is the 28th term of the AP 6, 9, 12, 15, …? (a) 90 (b) 84 (c) 81 (d) 87
  37. 37.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 266 (b) 28 (c) 136 (d) 133
  38. 38.What is the 12th term of the AP 16, 18, 20, 22, …? (a) 24 (b) 38 (c) 22 (d) 40
  39. 39.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 165 (b) 176 (c) 330 (d) 25
  40. 40.What is the 40th term of the AP 1, 10, 19, 28, …? (a) 360 (b) 352 (c) 361 (d) 351

Answer key

  1. 324
  2. 127
  3. 55
  4. 420
  5. 342
  6. 26
  7. 35
  8. 23
  9. 253
  10. 25
  11. 51
  12. 289
  13. 226
  14. 42
  15. 7
  16. 68
  17. 34th
  18. 132
  19. 2080
  20. 784
  21. 137
  22. 244
  23. 75
  24. 36
  25. 35
  26. 4465
  27. 215
  28. 107
  29. 4186
  30. 244
  31. 110
  32. 841
  33. 900
  34. 62
  35. 630
  36. 87
  37. 133
  38. 38
  39. 165
  40. 352

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