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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 536 · 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 missing term in the AP 10, 15, 20, ?, 30? (a) 25 (b) 30 (c) 24 (d) 26
  2. 2.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 39 (c) 400 (d) 210
  3. 3.What is the 39th term of the AP 4, 6, 8, 10, …? (a) 82 (b) 78 (c) 76 (d) 80
  4. 4.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 90 (b) 25 (c) 180 (d) 102
  5. 5.What is the 14th term of the AP 17, 22, 27, 32, …? (a) 82 (b) 70 (c) 65 (d) 87
  6. 6.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 17 (b) 11 (c) 13 (d) 12
  7. 7.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 841 (d) 870
  8. 8.What is the 19th term of the AP 6, 11, 16, 21, …? (a) 96 (b) 101 (c) 95 (d) 90
  9. 9.What is the missing term in the AP 8, 16, 24, ?, 40? (a) 32 (b) 31 (c) 33 (d) 40
  10. 10.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 225 (d) 29
  11. 11.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 1332 (c) 630 (d) 648
  12. 12.What is the 20th term of the AP 2, 5, 8, 11, …? (a) 62 (b) 57 (c) 60 (d) 59
  13. 13.What is the 33rd term of the AP 4, 9, 14, 19, …? (a) 160 (b) 164 (c) 169 (d) 165
  14. 14.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 210 (b) 105 (c) 30 (d) 120
  15. 15.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 17 (b) 234 (c) 118 (d) 117
  16. 16.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 136 (b) 133 (c) 28 (d) 266
  17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 81 (d) 90
  19. 19.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 65 (b) 450 (c) 900 (d) 480
  20. 20.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 416 (b) 47 (c) 208 (d) 232
  21. 21.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 34 (b) 26 (c) 25 (d) 24
  22. 22.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 15 (b) 11 (c) 12 (d) 13
  23. 23.Which term of the AP 5, 9, 13, 17, … is 33? (a) 8th (b) 10th (c) 9th (d) 7th
  24. 24.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 406 (c) 55 (d) 784
  25. 25.Which term of the AP 5, 13, 21, 29, … is 253? (a) 34th (b) 31st (c) 32nd (d) 33rd
  26. 26.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 408 (b) 756 (c) 378 (d) 59
  27. 27.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 25 (b) 336 (c) 180 (d) 168
  28. 28.What is the 24th term of the AP 20, 25, 30, 35, …? (a) 140 (b) 120 (c) 135 (d) 115
  29. 29.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 168 (b) 19 (c) 84 (d) 90
  30. 30.What is the 20th term of the AP 9, 16, 23, 30, …? (a) 149 (b) 133 (c) 140 (d) 142
  31. 31.What is the 20th term of the AP 6, 14, 22, 30, …? (a) 160 (b) 166 (c) 152 (d) 158
  32. 32.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 16 (b) 15 (c) 17 (d) 14
  33. 33.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 16 (b) 17 (c) 14 (d) 15
  34. 34.Which term of the AP 13, 19, 25, 31, … is 79? (a) 12th (b) 13th (c) 11th (d) 14th
  35. 35.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2346 (c) 2415 (d) 2416
  36. 36.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 3828 (d) 7832
  37. 37.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 8930 (c) 4371 (d) 4418
  38. 38.What is the 17th term of the AP 7, 10, 13, 16, …? (a) 51 (b) 58 (c) 48 (d) 55
  39. 39.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 68 (c) 65 (d) 130
  40. 40.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 72 (d) 36

Answer key

  1. 25
  2. 400
  3. 80
  4. 90
  5. 82
  6. 12
  7. 841
  8. 96
  9. 32
  10. 225
  11. 666
  12. 59
  13. 164
  14. 105
  15. 117
  16. 133
  17. 100
  18. 81
  19. 450
  20. 208
  21. 25
  22. 12
  23. 8th
  24. 784
  25. 32nd
  26. 378
  27. 168
  28. 135
  29. 84
  30. 142
  31. 158
  32. 15
  33. 15
  34. 12th
  35. 2415
  36. 3916
  37. 4465
  38. 55
  39. 65
  40. 64

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