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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 871 · 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 6, 13, ?, 27, 34? (a) 21 (b) 27 (c) 19 (d) 20
  2. 2.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 47 (b) 270 (c) 490 (d) 245
  3. 3.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 32 (b) 140 (c) 280 (d) 154
  4. 4.What is the 30th term of the AP 13, 18, 23, 28, …? (a) 150 (b) 158 (c) 145 (d) 163
  5. 5.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 23 (b) 156 (c) 144 (d) 288
  6. 6.What is the 40th term of the AP 1, 9, 17, 25, …? (a) 313 (b) 320 (c) 321 (d) 312
  7. 7.What is the 14th term of the AP 19, 26, 33, 40, …? (a) 98 (b) 117 (c) 110 (d) 91
  8. 8.What is the 26th term of the AP 17, 22, 27, 32, …? (a) 130 (b) 125 (c) 142 (d) 147
  9. 9.Which term of the AP 17, 25, 33, 41, … is 169? (a) 19th (b) 22nd (c) 21st (d) 20th
  10. 10.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484
  11. 11.What is the 33rd term of the AP 7, 14, 21, 28, …? (a) 238 (b) 232 (c) 231 (d) 224
  12. 12.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 28 (b) 112 (c) 126 (d) 224
  13. 13.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 12 (b) 21 (c) 13 (d) 11
  14. 14.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 264 (b) 32 (c) 504 (d) 252
  15. 15.What is the 31st term of the AP 17, 23, 29, 35, …? (a) 203 (b) 180 (c) 197 (d) 186
  16. 16.What is the 25th term of the AP 10, 12, 14, 16, …? (a) 48 (b) 50 (c) 60 (d) 58
  17. 17.What is the 40th term of the AP 16, 21, 26, 31, …? (a) 200 (b) 211 (c) 195 (d) 216
  18. 18.What is the 34th term of the AP 19, 27, 35, 43, …? (a) 291 (b) 283 (c) 264 (d) 272
  19. 19.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 68 (b) 451 (c) 836 (d) 418
  20. 20.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 29 (d) 225
  21. 21.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 48 (b) 312 (c) 336 (d) 624
  22. 22.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 436 (c) 435 (d) 870
  23. 23.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 40 (b) 360 (c) 200 (d) 180
  24. 24.Which term of the AP 4, 8, 12, 16, … is 60? (a) 16th (b) 15th (c) 14th (d) 17th
  25. 25.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 15 (b) 17 (c) 13 (d) 14
  26. 26.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 55 (d) 19
  27. 27.What is the 10th term of the AP 20, 29, 38, 47, …? (a) 101 (b) 81 (c) 110 (d) 90
  28. 28.What is the 26th term of the AP 5, 9, 13, 17, …? (a) 104 (b) 100 (c) 109 (d) 105
  29. 29.What is the 35th term of the AP 8, 17, 26, 35, …? (a) 306 (b) 315 (c) 323 (d) 314
  30. 30.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 4032 (c) 1953 (d) 2017
  31. 31.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4187 (c) 4186 (d) 4095
  32. 32.Which term of the AP 10, 15, 20, 25, … is 50? (a) 10th (b) 9th (c) 8th (d) 11th
  33. 33.What is the 21st term of the AP 5, 8, 11, 14, …? (a) 68 (b) 60 (c) 65 (d) 63
  34. 34.What is the 23rd term of the AP 5, 11, 17, 23, …? (a) 143 (b) 132 (c) 138 (d) 137
  35. 35.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 114 (b) 29 (c) 99 (d) 198
  36. 36.Which term of the AP 7, 16, 25, 34, … is 232? (a) 25th (b) 27th (c) 28th (d) 26th
  37. 37.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  38. 38.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 68 (b) 456 (c) 420 (d) 840
  39. 39.Which term of the AP 4, 9, 14, 19, … is 129? (a) 27th (b) 28th (c) 25th (d) 26th
  40. 40.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 480 (c) 240 (d) 31

Answer key

  1. 20
  2. 245
  3. 140
  4. 158
  5. 144
  6. 313
  7. 110
  8. 142
  9. 20th
  10. 484
  11. 231
  12. 112
  13. 12
  14. 252
  15. 197
  16. 58
  17. 211
  18. 283
  19. 418
  20. 225
  21. 312
  22. 435
  23. 180
  24. 15th
  25. 14
  26. 100
  27. 101
  28. 105
  29. 314
  30. 2016
  31. 4186
  32. 9th
  33. 65
  34. 137
  35. 99
  36. 26th
  37. 441
  38. 420
  39. 26th
  40. 240

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