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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 615 · 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 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 132 (c) 67 (d) 66
  2. 2.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 31 (b) 33 (c) 32 (d) 38
  3. 3.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 3782 (c) 1892 (d) 1830
  4. 4.What is the 26th term of the AP 8, 10, 12, 14, …? (a) 58 (b) 60 (c) 52 (d) 50
  5. 5.Which term of the AP 2, 9, 16, 23, … is 268? (a) 38th (b) 40th (c) 41st (d) 39th
  6. 6.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 10 (b) 11 (c) 8 (d) 9
  7. 7.Which term of the AP 7, 16, 25, 34, … is 106? (a) 12th (b) 14th (c) 11th (d) 13th
  8. 8.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 201 (b) 33 (c) 396 (d) 198
  9. 9.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 210 (c) 24 (d) 105
  10. 10.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 75 (b) 25 (c) 150 (d) 80
  11. 11.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 430 (b) 230 (c) 215 (d) 35
  12. 12.What is the 38th term of the AP 1, 4, 7, 10, …? (a) 114 (b) 111 (c) 115 (d) 112
  13. 13.Which term of the AP 13, 22, 31, 40, … is 184? (a) 22nd (b) 20th (c) 21st (d) 19th
  14. 14.What is the 23rd term of the AP 18, 26, 34, 42, …? (a) 194 (b) 184 (c) 202 (d) 176
  15. 15.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 80 (b) 154 (c) 20 (d) 77
  16. 16.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 110 (b) 65 (c) 19 (d) 55
  17. 17.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 100 (b) 85 (c) 29 (d) 170
  18. 18.What is the sum of all the whole numbers from 1 to 41? (a) 862 (b) 861 (c) 820 (d) 1722
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 36 (d) 64
  20. 20.Which term of the AP 20, 27, 34, 41, … is 153? (a) 21st (b) 19th (c) 20th (d) 22nd
  21. 21.What is the 18th term of the AP 17, 20, 23, 26, …? (a) 54 (b) 71 (c) 68 (d) 51
  22. 22.What is the 15th term of the AP 19, 22, 25, 28, …? (a) 42 (b) 64 (c) 45 (d) 61
  23. 23.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 110 (c) 45 (d) 55
  24. 24.What is the 40th term of the AP 16, 25, 34, 43, …? (a) 367 (b) 360 (c) 376 (d) 351
  25. 25.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 21 (b) 28 (c) 22 (d) 23
  26. 26.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 6 (b) 7 (c) 11 (d) 8
  27. 27.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 26 (b) 34 (c) 25 (d) 24
  28. 28.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 276 (d) 552
  29. 29.What is the 23rd term of the AP 8, 11, 14, 17, …? (a) 74 (b) 77 (c) 69 (d) 66
  30. 30.Which term of the AP 19, 22, 25, 28, … is 43? (a) 8th (b) 10th (c) 9th (d) 11th
  31. 31.What is the 17th term of the AP 1, 6, 11, 16, …? (a) 80 (b) 86 (c) 85 (d) 81
  32. 32.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 66 (b) 792 (c) 429 (d) 396
  33. 33.What is the 31st term of the AP 9, 12, 15, 18, …? (a) 102 (b) 90 (c) 99 (d) 93
  34. 34.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 231 (d) 441
  35. 35.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 62 (b) 828 (c) 444 (d) 414
  36. 36.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 65 (b) 60 (c) 16 (d) 120
  37. 37.Which term of the AP 13, 20, 27, 34, … is 265? (a) 38th (b) 37th (c) 36th (d) 39th
  38. 38.What is the 10th term of the AP 5, 14, 23, 32, …? (a) 81 (b) 90 (c) 95 (d) 86
  39. 39.What is the 15th term of the AP 10, 17, 24, 31, …? (a) 115 (b) 98 (c) 108 (d) 105
  40. 40.What is the 19th term of the AP 6, 8, 10, 12, …? (a) 44 (b) 36 (c) 38 (d) 42

Answer key

  1. 66
  2. 32
  3. 1891
  4. 58
  5. 39th
  6. 9
  7. 12th
  8. 198
  9. 105
  10. 75
  11. 215
  12. 112
  13. 20th
  14. 194
  15. 77
  16. 55
  17. 85
  18. 861
  19. 64
  20. 20th
  21. 68
  22. 61
  23. 55
  24. 367
  25. 22
  26. 7
  27. 25
  28. 529
  29. 74
  30. 9th
  31. 81
  32. 396
  33. 99
  34. 441
  35. 414
  36. 60
  37. 37th
  38. 86
  39. 108
  40. 42

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