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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 32 · 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 12 terms of the AP 8, 13, 18, …? (a) 63 (b) 456 (c) 426 (d) 852
  2. 2.What is the 16th term of the AP 5, 10, 15, 20, …? (a) 75 (b) 80 (c) 85 (d) 81
  3. 3.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 47 (d) 300
  4. 4.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 15 (c) 84 (d) 168
  5. 5.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3655 (c) 3698 (d) 3741
  6. 6.What is the 10th term of the AP 19, 26, 33, 40, …? (a) 70 (b) 63 (c) 82 (d) 89
  7. 7.What is the 14th term of the AP 18, 27, 36, 45, …? (a) 144 (b) 117 (c) 126 (d) 135
  8. 8.Which term of the AP 4, 9, 14, 19, … is 159? (a) 31st (b) 34th (c) 32nd (d) 33rd
  9. 9.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 378 (d) 729
  10. 10.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 49 (b) 13 (c) 98 (d) 56
  11. 11.Which term of the AP 4, 13, 22, 31, … is 175? (a) 20th (b) 22nd (c) 19th (d) 21st
  12. 12.What is the 11th term of the AP 2, 8, 14, 20, …? (a) 66 (b) 68 (c) 60 (d) 62
  13. 13.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 220 (b) 125 (c) 110 (d) 34
  14. 14.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 22 (b) 65 (c) 120 (d) 60
  15. 15.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 175 (b) 40 (c) 350 (d) 180
  16. 16.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 69 (b) 462 (c) 429 (d) 858
  17. 17.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4754 (c) 4753 (d) 4656
  18. 18.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 450 (c) 930 (d) 435
  19. 19.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 120 (d) 29
  20. 20.What is the 16th term of the AP 7, 10, 13, 16, …? (a) 45 (b) 48 (c) 52 (d) 55
  21. 21.What is the 26th term of the AP 15, 18, 21, 24, …? (a) 75 (b) 93 (c) 90 (d) 78
  22. 22.What is the 16th term of the AP 14, 19, 24, 29, …? (a) 80 (b) 89 (c) 94 (d) 75
  23. 23.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 82 (b) 13 (c) 81 (d) 162
  24. 24.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 29 (b) 26 (c) 27 (d) 25
  25. 25.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  26. 26.What is the 30th term of the AP 12, 16, 20, 24, …? (a) 120 (b) 116 (c) 128 (d) 132
  27. 27.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 44 (b) 260 (c) 520 (d) 280
  28. 28.What is the 10th term of the AP 9, 16, 23, 30, …? (a) 63 (b) 79 (c) 70 (d) 72
  29. 29.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 631 (c) 595 (d) 1260
  30. 30.What is the missing term in the AP 14, ?, 32, 41, 50? (a) 22 (b) 24 (c) 32 (d) 23
  31. 31.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 180 (c) 90 (d) 13
  32. 32.What is the 25th term of the AP 8, 10, 12, 14, …? (a) 56 (b) 58 (c) 48 (d) 50
  33. 33.What is the 20th term of the AP 5, 7, 9, 11, …? (a) 45 (b) 38 (c) 43 (d) 40
  34. 34.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 36 (b) 28 (c) 26 (d) 27
  35. 35.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 35 (b) 25 (c) 27 (d) 26
  36. 36.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 318 (b) 43 (c) 636 (d) 336
  37. 37.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 306 (b) 33 (c) 153 (d) 171
  38. 38.Which term of the AP 16, 21, 26, 31, … is 171? (a) 33rd (b) 34th (c) 31st (d) 32nd
  39. 39.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 70 (b) 140 (c) 20 (d) 73
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21

Answer key

  1. 426
  2. 80
  3. 576
  4. 84
  5. 3741
  6. 82
  7. 135
  8. 32nd
  9. 729
  10. 49
  11. 20th
  12. 62
  13. 110
  14. 60
  15. 175
  16. 429
  17. 4753
  18. 465
  19. 225
  20. 52
  21. 90
  22. 89
  23. 81
  24. 26
  25. 289
  26. 128
  27. 260
  28. 72
  29. 630
  30. 23
  31. 90
  32. 56
  33. 43
  34. 27
  35. 26
  36. 318
  37. 153
  38. 32nd
  39. 70
  40. 36

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