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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 110 · 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 15, 22, ?, 36, 43? (a) 28 (b) 36 (c) 29 (d) 30
  2. 2.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 64 (b) 120 (c) 11 (d) 60
  3. 3.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 13 (b) 56 (c) 110 (d) 55
  4. 4.Which term of the AP 18, 24, 30, 36, … is 198? (a) 33rd (b) 30th (c) 32nd (d) 31st
  5. 5.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 90 (b) 162 (c) 17 (d) 81
  6. 6.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 414 (b) 828 (c) 62 (d) 444
  7. 7.What is the sum of all the whole numbers from 1 to 50? (a) 1250 (b) 2550 (c) 1275 (d) 1225
  8. 8.What is the 10th term of the AP 4, 13, 22, 31, …? (a) 85 (b) 90 (c) 94 (d) 81
  9. 9.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 112 (b) 117 (c) 224 (d) 31
  10. 10.Which term of the AP 5, 8, 11, 14, … is 47? (a) 14th (b) 15th (c) 16th (d) 17th
  11. 11.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 441 (d) 462
  12. 12.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4371 (c) 4465 (d) 4418
  13. 13.Which term of the AP 3, 7, 11, 15, … is 139? (a) 35th (b) 37th (c) 36th (d) 34th
  14. 14.What is the 20th term of the AP 13, 17, 21, 25, …? (a) 76 (b) 80 (c) 93 (d) 89
  15. 15.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 120 (b) 240 (c) 128 (d) 22
  16. 16.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 80 (b) 43 (c) 40 (d) 14
  17. 17.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 261 (b) 522 (c) 288 (d) 53
  18. 18.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 10 (b) 108 (c) 55 (d) 54
  19. 19.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 13 (b) 11 (c) 12 (d) 15
  20. 20.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 625 (d) 325
  21. 21.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 216 (c) 112 (d) 108
  22. 22.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 50 (c) 45 (d) 110
  23. 23.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 52 (b) 496 (c) 248 (d) 272
  24. 24.Which term of the AP 1, 7, 13, 19, … is 49? (a) 10th (b) 9th (c) 11th (d) 8th
  25. 25.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5000 (c) 10100 (d) 5050
  26. 26.What is the 12th term of the AP 1, 6, 11, 16, …? (a) 61 (b) 55 (c) 60 (d) 56
  27. 27.What is the 13th term of the AP 3, 9, 15, 21, …? (a) 72 (b) 78 (c) 75 (d) 81
  28. 28.What is the 11th term of the AP 15, 21, 27, 33, …? (a) 60 (b) 81 (c) 75 (d) 66
  29. 29.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 240 (c) 31 (d) 480
  30. 30.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 204 (b) 102 (c) 32 (d) 120
  31. 31.What is the missing term in the AP 12, 20, 28, ?, 44? (a) 44 (b) 37 (c) 35 (d) 36
  32. 32.What is the 34th term of the AP 9, 17, 25, 33, …? (a) 264 (b) 272 (c) 273 (d) 281
  33. 33.What is the 16th term of the AP 12, 16, 20, 24, …? (a) 72 (b) 64 (c) 76 (d) 60
  34. 34.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 3422 (c) 1653 (d) 1711
  35. 35.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 13 (b) 17 (c) 14 (d) 15
  36. 36.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 240 (b) 21 (c) 130 (d) 120
  37. 37.What is the 11th term of the AP 2, 5, 8, 11, …? (a) 35 (b) 32 (c) 30 (d) 33
  38. 38.What is the 34th term of the AP 15, 18, 21, 24, …? (a) 114 (b) 117 (c) 102 (d) 99
  39. 39.Which term of the AP 17, 19, 21, 23, … is 43? (a) 14th (b) 13th (c) 16th (d) 15th
  40. 40.What is the 12th term of the AP 17, 20, 23, 26, …? (a) 33 (b) 50 (c) 36 (d) 53

Answer key

  1. 29
  2. 60
  3. 55
  4. 31st
  5. 81
  6. 414
  7. 1275
  8. 85
  9. 112
  10. 15th
  11. 441
  12. 4465
  13. 35th
  14. 89
  15. 120
  16. 40
  17. 261
  18. 54
  19. 12
  20. 625
  21. 108
  22. 55
  23. 248
  24. 9th
  25. 5050
  26. 56
  27. 75
  28. 75
  29. 240
  30. 102
  31. 36
  32. 273
  33. 72
  34. 1711
  35. 14
  36. 120
  37. 32
  38. 114
  39. 14th
  40. 50

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