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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 740 · 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.Which term of the AP 20, 24, 28, 32, … is 156? (a) 36th (b) 39th (c) 35th (d) 34th
  2. 2.What is the 10th term of the AP 16, 25, 34, 43, …? (a) 81 (b) 106 (c) 90 (d) 97
  3. 3.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 10 (b) 12 (c) 9 (d) 11
  4. 4.Which term of the AP 10, 16, 22, 28, … is 52? (a) 8th (b) 10th (c) 7th (d) 9th
  5. 5.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 19 (b) 16 (c) 17 (d) 15
  6. 6.What is the 14th term of the AP 5, 13, 21, 29, …? (a) 104 (b) 117 (c) 109 (d) 112
  7. 7.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 15 (b) 11 (c) 13 (d) 12
  8. 8.Which term of the AP 15, 17, 19, 21, … is 73? (a) 30th (b) 32nd (c) 29th (d) 31st
  9. 9.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 17 (b) 13 (c) 14 (d) 15
  10. 10.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 24 (b) 96 (c) 168 (d) 84
  11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 45 (d) 529
  12. 12.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 322 (b) 182 (c) 41 (d) 161
  13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
  14. 14.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 108 (b) 126 (c) 216 (d) 33
  15. 15.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 92 (d) 91
  16. 16.What is the 12th term of the AP 10, 16, 22, 28, …? (a) 72 (b) 76 (c) 82 (d) 66
  17. 17.What is the 32nd term of the AP 5, 9, 13, 17, …? (a) 129 (b) 128 (c) 133 (d) 124
  18. 18.What is the 22nd term of the AP 10, 16, 22, 28, …? (a) 136 (b) 142 (c) 132 (d) 126
  19. 19.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 42 (b) 41 (c) 50 (d) 40
  20. 20.What is the sum of all the whole numbers from 1 to 51? (a) 1326 (b) 1275 (c) 1327 (d) 2652
  21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 300 (d) 600
  22. 22.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 12 (b) 13 (c) 15 (d) 11
  23. 23.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 319 (b) 49 (c) 341 (d) 638
  24. 24.What is the 18th term of the AP 19, 21, 23, 25, …? (a) 34 (b) 53 (c) 36 (d) 55
  25. 25.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2016 (c) 4160 (d) 2080
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
  27. 27.What is the 14th term of the AP 18, 23, 28, 33, …? (a) 88 (b) 83 (c) 65 (d) 70
  28. 28.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 22 (b) 19 (c) 18 (d) 17
  29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 55 (d) 110
  30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
  31. 31.What is the 15th term of the AP 8, 13, 18, 23, …? (a) 83 (b) 78 (c) 75 (d) 70
  32. 32.Which term of the AP 2, 10, 18, 26, … is 58? (a) 8th (b) 10th (c) 9th (d) 7th
  33. 33.What is the 10th term of the AP 6, 11, 16, 21, …? (a) 56 (b) 50 (c) 45 (d) 51
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 136 (c) 272 (d) 31
  35. 35.What is the 25th term of the AP 17, 25, 33, 41, …? (a) 200 (b) 217 (c) 192 (d) 209
  36. 36.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 231 (c) 41 (d) 462
  37. 37.What is the 33rd term of the AP 11, 14, 17, 20, …? (a) 110 (b) 99 (c) 107 (d) 96
  38. 38.What is the missing term in the AP 11, 14, ?, 20, 23? (a) 17 (b) 18 (c) 16 (d) 20
  39. 39.What is the 21st term of the AP 6, 9, 12, 15, …? (a) 60 (b) 69 (c) 63 (d) 66
  40. 40.What is the 28th term of the AP 12, 15, 18, 21, …? (a) 96 (b) 84 (c) 93 (d) 81

Answer key

  1. 35th
  2. 97
  3. 10
  4. 8th
  5. 16
  6. 109
  7. 12
  8. 30th
  9. 14
  10. 84
  11. 529
  12. 161
  13. 81
  14. 108
  15. 91
  16. 76
  17. 129
  18. 136
  19. 41
  20. 1326
  21. 576
  22. 12
  23. 319
  24. 53
  25. 2080
  26. 64
  27. 83
  28. 18
  29. 100
  30. 121
  31. 78
  32. 8th
  33. 51
  34. 256
  35. 209
  36. 441
  37. 107
  38. 17
  39. 66
  40. 93

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