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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 814 · 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 23rd term of the AP 4, 7, 10, 13, …? (a) 73 (b) 66 (c) 69 (d) 70
  2. 2.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 225 (b) 207 (c) 414 (d) 39
  3. 3.What is the 39th term of the AP 20, 29, 38, 47, …? (a) 351 (b) 371 (c) 342 (d) 362
  4. 4.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 297 (b) 45 (c) 550 (d) 275
  5. 5.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 54 (c) 108 (d) 10
  6. 6.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 30 (b) 50 (c) 25 (d) 9
  7. 7.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3004 (c) 2926 (d) 3003
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 676 (d) 702
  9. 9.What is the 29th term of the AP 4, 6, 8, 10, …? (a) 58 (b) 60 (c) 56 (d) 62
  10. 10.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 67 (b) 440 (c) 814 (d) 407
  11. 11.What is the 18th term of the AP 18, 23, 28, 33, …? (a) 103 (b) 108 (c) 90 (d) 85
  12. 12.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 39 (d) 210
  13. 13.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 125 (b) 250 (c) 130 (d) 17
  14. 14.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 168 (b) 91 (c) 84 (d) 18
  15. 15.Which term of the AP 11, 16, 21, 26, … is 56? (a) 11th (b) 9th (c) 12th (d) 10th
  16. 16.What is the 21st term of the AP 11, 18, 25, 32, …? (a) 158 (b) 147 (c) 151 (d) 140
  17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  18. 18.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 72 (c) 66 (d) 156
  19. 19.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 132 (b) 264 (c) 17 (d) 133
  20. 20.What is the missing term in the AP 16, 25, ?, 43, 52? (a) 34 (b) 35 (c) 33 (d) 43
  21. 21.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 50 (b) 16 (c) 100 (d) 53
  22. 22.What is the sum of all the whole numbers from 1 to 41? (a) 862 (b) 861 (c) 1722 (d) 820
  23. 23.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 120 (c) 138 (d) 240
  24. 24.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 1953 (c) 2017 (d) 2016
  25. 25.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 45 (b) 15 (c) 90 (d) 48
  26. 26.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 21 (b) 162 (c) 90 (d) 81
  27. 27.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 600 (d) 47
  28. 28.What is the 21st term of the AP 16, 18, 20, 22, …? (a) 58 (b) 42 (c) 40 (d) 56
  29. 29.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 19 (b) 18 (c) 21 (d) 17
  30. 30.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 50 (c) 45 (d) 13
  31. 31.What is the missing term in the AP 2, 9, ?, 23, 30? (a) 23 (b) 17 (c) 15 (d) 16
  32. 32.What is the 29th term of the AP 16, 19, 22, 25, …? (a) 84 (b) 103 (c) 100 (d) 87
  33. 33.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 152 (b) 80 (c) 76 (d) 13
  34. 34.Which term of the AP 6, 14, 22, 30, … is 118? (a) 14th (b) 17th (c) 15th (d) 16th
  35. 35.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3828 (c) 3916 (d) 7832
  36. 36.Which term of the AP 20, 23, 26, 29, … is 98? (a) 29th (b) 26th (c) 27th (d) 28th
  37. 37.What is the 11th term of the AP 11, 15, 19, 23, …? (a) 55 (b) 40 (c) 44 (d) 51
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  39. 39.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 216 (b) 196 (c) 392 (d) 42
  40. 40.What is the 29th term of the AP 9, 12, 15, 18, …? (a) 84 (b) 93 (c) 87 (d) 96

Answer key

  1. 70
  2. 207
  3. 362
  4. 275
  5. 54
  6. 25
  7. 3003
  8. 676
  9. 60
  10. 407
  11. 103
  12. 400
  13. 125
  14. 84
  15. 10th
  16. 151
  17. 100
  18. 78
  19. 132
  20. 34
  21. 50
  22. 861
  23. 120
  24. 2016
  25. 45
  26. 81
  27. 576
  28. 56
  29. 18
  30. 45
  31. 16
  32. 100
  33. 76
  34. 15th
  35. 3916
  36. 27th
  37. 51
  38. 25
  39. 196
  40. 93

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