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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 937 · 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.Which term of the AP 16, 19, 22, 25, … is 133? (a) 39th (b) 40th (c) 42nd (d) 41st
  2. 2.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 625 (d) 650
  3. 3.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1596 (c) 3192 (d) 1540
  4. 4.What is the 25th term of the AP 16, 24, 32, 40, …? (a) 200 (b) 192 (c) 216 (d) 208
  5. 5.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 108 (b) 14 (c) 60 (d) 54
  6. 6.What is the 33rd term of the AP 8, 10, 12, 14, …? (a) 64 (b) 74 (c) 72 (d) 66
  7. 7.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 35 (b) 184 (c) 168 (d) 336
  8. 8.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 33 (b) 252 (c) 131 (d) 126
  9. 9.What is the 34th term of the AP 3, 12, 21, 30, …? (a) 297 (b) 309 (c) 306 (d) 300
  10. 10.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 7 (b) 29 (c) 28 (d) 56
  11. 11.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 126 (b) 252 (c) 36 (d) 144
  12. 12.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 41 (b) 312 (c) 294 (d) 588
  13. 13.Which term of the AP 4, 6, 8, 10, … is 62? (a) 32nd (b) 29th (c) 31st (d) 30th
  14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  15. 15.What is the missing term in the AP 13, ?, 31, 40, 49? (a) 31 (b) 21 (c) 22 (d) 23
  16. 16.What is the 12th term of the AP 6, 10, 14, 18, …? (a) 44 (b) 48 (c) 50 (d) 54
  17. 17.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 64 (b) 748 (c) 407 (d) 374
  18. 18.What is the 13th term of the AP 20, 23, 26, 29, …? (a) 59 (b) 56 (c) 36 (d) 39
  19. 19.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 276 (b) 300 (c) 45 (d) 552
  20. 20.Which term of the AP 19, 26, 33, 40, … is 138? (a) 20th (b) 19th (c) 18th (d) 17th
  21. 21.Which term of the AP 8, 10, 12, 14, … is 32? (a) 12th (b) 16th (c) 13th (d) 14th
  22. 22.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 26 (c) 25 (d) 50
  23. 23.What is the 16th term of the AP 13, 16, 19, 22, …? (a) 61 (b) 48 (c) 58 (d) 45
  24. 24.Which term of the AP 16, 23, 30, 37, … is 107? (a) 15th (b) 16th (c) 13th (d) 14th
  25. 25.Which term of the AP 20, 22, 24, 26, … is 52? (a) 16th (b) 17th (c) 26th (d) 18th
  26. 26.What is the 19th term of the AP 12, 14, 16, 18, …? (a) 48 (b) 36 (c) 38 (d) 50
  27. 27.What is the missing term in the AP 16, 20, 24, ?, 32? (a) 32 (b) 29 (c) 27 (d) 28
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 49 (d) 13
  29. 29.What is the 33rd term of the AP 16, 21, 26, 31, …? (a) 160 (b) 165 (c) 176 (d) 181
  30. 30.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 228 (b) 240 (c) 456 (d) 30
  31. 31.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 756 (d) 53
  32. 32.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 66 (c) 72 (d) 156
  33. 33.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 8 (b) 40 (c) 72 (d) 36
  34. 34.What is the 37th term of the AP 4, 11, 18, 25, …? (a) 259 (b) 256 (c) 263 (d) 252
  35. 35.What is the 37th term of the AP 2, 10, 18, 26, …? (a) 298 (b) 296 (c) 288 (d) 290
  36. 36.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 90 (d) 17
  37. 37.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 104 (c) 10 (d) 52
  38. 38.What is the 11th term of the AP 2, 7, 12, 17, …? (a) 57 (b) 50 (c) 55 (d) 52
  39. 39.What is the 17th term of the AP 9, 14, 19, 24, …? (a) 85 (b) 94 (c) 80 (d) 89
  40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 33 (c) 153 (d) 306

Answer key

  1. 40th
  2. 625
  3. 1596
  4. 208
  5. 54
  6. 72
  7. 168
  8. 126
  9. 300
  10. 28
  11. 126
  12. 294
  13. 30th
  14. 576
  15. 22
  16. 50
  17. 374
  18. 56
  19. 276
  20. 18th
  21. 13th
  22. 25
  23. 58
  24. 14th
  25. 17th
  26. 48
  27. 28
  28. 49
  29. 176
  30. 228
  31. 729
  32. 78
  33. 36
  34. 256
  35. 290
  36. 81
  37. 52
  38. 52
  39. 89
  40. 289

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