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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 995 · 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 14th term of the AP 18, 20, 22, 24, …? (a) 28 (b) 44 (c) 26 (d) 46
  2. 2.What is the 12th term of the AP 8, 10, 12, 14, …? (a) 24 (b) 32 (c) 30 (d) 22
  3. 3.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 26 (b) 28 (c) 32 (d) 27
  4. 4.Which term of the AP 6, 11, 16, 21, … is 51? (a) 9th (b) 10th (c) 12th (d) 11th
  5. 5.What is the 10th term of the AP 13, 15, 17, 19, …? (a) 18 (b) 20 (c) 31 (d) 33
  6. 6.What is the 12th term of the AP 7, 13, 19, 25, …? (a) 79 (b) 66 (c) 73 (d) 72
  7. 7.What is the 21st term of the AP 17, 19, 21, 23, …? (a) 57 (b) 59 (c) 40 (d) 42
  8. 8.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 37 (b) 484 (c) 245 (d) 242
  9. 9.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 1431 (c) 1458 (d) 2970
  10. 10.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 392 (c) 378 (d) 406
  11. 11.Which term of the AP 8, 11, 14, 17, … is 119? (a) 37th (b) 40th (c) 39th (d) 38th
  12. 12.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 72 (d) 64
  13. 13.Which term of the AP 17, 24, 31, 38, … is 199? (a) 28th (b) 29th (c) 27th (d) 26th
  14. 14.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 344 (b) 172 (c) 192 (d) 39
  15. 15.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 210 (d) 105
  16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 53 (d) 729
  17. 17.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 23 (b) 21 (c) 20 (d) 19
  18. 18.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 320 (b) 56 (c) 290 (d) 580
  19. 19.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 15 (b) 9 (c) 8 (d) 10
  20. 20.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 22 (c) 126 (d) 135
  21. 21.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4608 (c) 4560 (d) 9312
  22. 22.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 25 (b) 28 (c) 27 (d) 26
  23. 23.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 36 (b) 198 (c) 360 (d) 180
  24. 24.What is the missing term in the AP 4, 8, ?, 16, 20? (a) 13 (b) 11 (c) 16 (d) 12
  25. 25.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 261 (b) 234 (c) 468 (d) 50
  26. 26.Which term of the AP 6, 10, 14, 18, … is 114? (a) 27th (b) 30th (c) 29th (d) 28th
  27. 27.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 174 (b) 96 (c) 87 (d) 22
  28. 28.Which term of the AP 1, 3, 5, 7, … is 71? (a) 36th (b) 37th (c) 35th (d) 38th
  29. 29.What is the 16th term of the AP 18, 21, 24, 27, …? (a) 66 (b) 63 (c) 48 (d) 45
  30. 30.What is the 39th term of the AP 18, 21, 24, 27, …? (a) 114 (b) 132 (c) 117 (d) 135
  31. 31.What is the 12th term of the AP 5, 7, 9, 11, …? (a) 29 (b) 22 (c) 24 (d) 27
  32. 32.What is the 25th term of the AP 10, 12, 14, 16, …? (a) 58 (b) 48 (c) 60 (d) 50
  33. 33.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 210 (c) 91 (d) 105
  34. 34.What is the 34th term of the AP 14, 21, 28, 35, …? (a) 238 (b) 231 (c) 252 (d) 245
  35. 35.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 625 (d) 49
  36. 36.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
  37. 37.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 26 (b) 96 (c) 192 (d) 108
  38. 38.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 302 (b) 52 (c) 297 (d) 594
  39. 39.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 408 (b) 54 (c) 384 (d) 768
  40. 40.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 631 (c) 595 (d) 630

Answer key

  1. 44
  2. 30
  3. 27
  4. 10th
  5. 31
  6. 73
  7. 57
  8. 242
  9. 1485
  10. 406
  11. 38th
  12. 64
  13. 27th
  14. 172
  15. 196
  16. 729
  17. 20
  18. 290
  19. 9
  20. 126
  21. 4656
  22. 26
  23. 180
  24. 12
  25. 234
  26. 28th
  27. 87
  28. 36th
  29. 63
  30. 132
  31. 27
  32. 58
  33. 105
  34. 245
  35. 625
  36. 121
  37. 96
  38. 297
  39. 384
  40. 630

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