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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 880 · 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 38th term of the AP 11, 19, 27, 35, …? (a) 296 (b) 315 (c) 304 (d) 307
  2. 2.What is the 33rd term of the AP 3, 9, 15, 21, …? (a) 192 (b) 201 (c) 198 (d) 195
  3. 3.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 120 (c) 272 (d) 128
  4. 4.What is the 32nd term of the AP 13, 22, 31, 40, …? (a) 301 (b) 288 (c) 292 (d) 279
  5. 5.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 232 (b) 50 (c) 464 (d) 256
  6. 6.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 9 (b) 7 (c) 12 (d) 8
  7. 7.What is the missing term in the AP 10, 18, 26, ?, 42? (a) 35 (b) 33 (c) 34 (d) 42
  8. 8.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3872 (c) 3916 (d) 7832
  9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  10. 10.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 1008 (c) 504 (d) 540
  11. 11.What is the 18th term of the AP 7, 10, 13, 16, …? (a) 58 (b) 51 (c) 61 (d) 54
  12. 12.Which term of the AP 15, 24, 33, 42, … is 357? (a) 39th (b) 40th (c) 38th (d) 41st
  13. 13.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 484 (d) 253
  14. 14.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 132 (b) 21 (c) 121 (d) 242
  15. 15.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 550 (b) 45 (c) 275 (d) 297
  16. 16.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 484 (b) 245 (c) 37 (d) 242
  17. 17.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 162 (c) 153 (d) 171
  18. 18.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 300 (c) 325 (d) 650
  19. 19.What is the 23rd term of the AP 5, 10, 15, 20, …? (a) 110 (b) 115 (c) 120 (d) 116
  20. 20.Which term of the AP 2, 10, 18, 26, … is 314? (a) 40th (b) 42nd (c) 39th (d) 41st
  21. 21.Which term of the AP 15, 18, 21, 24, … is 66? (a) 22nd (b) 17th (c) 18th (d) 19th
  22. 22.Which term of the AP 13, 16, 19, 22, … is 109? (a) 35th (b) 32nd (c) 34th (d) 33rd
  23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
  24. 24.Which term of the AP 1, 4, 7, 10, … is 64? (a) 21st (b) 23rd (c) 22nd (d) 24th
  25. 25.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 228 (b) 216 (c) 29 (d) 432
  26. 26.Which term of the AP 7, 13, 19, 25, … is 229? (a) 40th (b) 39th (c) 37th (d) 38th
  27. 27.What is the 15th term of the AP 19, 25, 31, 37, …? (a) 103 (b) 84 (c) 90 (d) 109
  28. 28.What is the 12th term of the AP 7, 9, 11, 13, …? (a) 22 (b) 24 (c) 29 (d) 31
  29. 29.What is the 32nd term of the AP 12, 16, 20, 24, …? (a) 136 (b) 128 (c) 124 (d) 140
  30. 30.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 47 (d) 600
  31. 31.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 280 (b) 140 (c) 28 (d) 152
  32. 32.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 1953 (c) 4032 (d) 2016
  33. 33.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 390 (b) 720 (c) 360 (d) 63
  34. 34.Which term of the AP 11, 20, 29, 38, … is 227? (a) 25th (b) 26th (c) 27th (d) 24th
  35. 35.What is the sum of all the whole numbers from 1 to 73? (a) 5402 (b) 2628 (c) 2701 (d) 2702
  36. 36.What is the 30th term of the AP 12, 14, 16, 18, …? (a) 58 (b) 60 (c) 72 (d) 70
  37. 37.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 80 (b) 65 (c) 130 (d) 25
  38. 38.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 812 (c) 392 (d) 406
  39. 39.What is the 15th term of the AP 5, 8, 11, 14, …? (a) 42 (b) 50 (c) 45 (d) 47
  40. 40.Which term of the AP 20, 24, 28, 32, … is 92? (a) 20th (b) 19th (c) 23rd (d) 18th

Answer key

  1. 307
  2. 195
  3. 136
  4. 292
  5. 232
  6. 8
  7. 34
  8. 3916
  9. 64
  10. 504
  11. 58
  12. 39th
  13. 484
  14. 121
  15. 275
  16. 242
  17. 171
  18. 325
  19. 115
  20. 40th
  21. 18th
  22. 33rd
  23. 196
  24. 22nd
  25. 216
  26. 38th
  27. 103
  28. 29
  29. 136
  30. 576
  31. 140
  32. 2016
  33. 360
  34. 25th
  35. 2701
  36. 70
  37. 65
  38. 406
  39. 47
  40. 19th

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