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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 607 · 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 25th term of the AP 11, 17, 23, 29, …? (a) 150 (b) 144 (c) 161 (d) 155
  2. 2.What is the 17th term of the AP 5, 11, 17, 23, …? (a) 107 (b) 101 (c) 96 (d) 102
  3. 3.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 2162 (c) 1058 (d) 1081
  4. 4.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 27 (b) 37 (c) 29 (d) 28
  5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  6. 6.What is the 14th term of the AP 9, 13, 17, 21, …? (a) 65 (b) 52 (c) 61 (d) 56
  7. 7.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 30 (b) 31 (c) 32 (d) 37
  8. 8.What is the 25th term of the AP 12, 19, 26, 33, …? (a) 175 (b) 168 (c) 187 (d) 180
  9. 9.Which term of the AP 17, 25, 33, 41, … is 217? (a) 25th (b) 27th (c) 28th (d) 26th
  10. 10.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 6 (b) 7 (c) 5 (d) 9
  11. 11.What is the missing term in the AP 17, 21, 25, ?, 33? (a) 29 (b) 33 (c) 28 (d) 30
  12. 12.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 12 (b) 18 (c) 13 (d) 14
  13. 13.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1458 (c) 1485 (d) 2970
  14. 14.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 140 (b) 70 (c) 19 (d) 73
  15. 15.What is the 16th term of the AP 6, 8, 10, 12, …? (a) 30 (b) 38 (c) 36 (d) 32
  16. 16.What is the 18th term of the AP 15, 21, 27, 33, …? (a) 123 (b) 117 (c) 108 (d) 102
  17. 17.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 168 (b) 40 (c) 150 (d) 300
  18. 18.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 729 (c) 378 (d) 53
  19. 19.What is the missing term in the AP 15, ?, 19, 21, 23? (a) 18 (b) 19 (c) 16 (d) 17
  20. 20.What is the 28th term of the AP 3, 9, 15, 21, …? (a) 171 (b) 162 (c) 168 (d) 165
  21. 21.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4753 (c) 9506 (d) 4754
  22. 22.Which term of the AP 4, 11, 18, 25, … is 221? (a) 34th (b) 32nd (c) 31st (d) 33rd
  23. 23.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 45 (c) 50 (d) 110
  24. 24.What is the 16th term of the AP 19, 26, 33, 40, …? (a) 112 (b) 124 (c) 131 (d) 105
  25. 25.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 3306 (c) 1596 (d) 1653
  26. 26.Which term of the AP 5, 10, 15, 20, … is 165? (a) 35th (b) 33rd (c) 34th (d) 32nd
  27. 27.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 18 (b) 20 (c) 25 (d) 19
  28. 28.What is the 12th term of the AP 15, 19, 23, 27, …? (a) 63 (b) 44 (c) 48 (d) 59
  29. 29.What is the 30th term of the AP 20, 22, 24, 26, …? (a) 58 (b) 78 (c) 60 (d) 80
  30. 30.What is the 38th term of the AP 1, 6, 11, 16, …? (a) 186 (b) 191 (c) 190 (d) 185
  31. 31.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 27 (b) 19 (c) 17 (d) 18
  32. 32.What is the 16th term of the AP 20, 29, 38, 47, …? (a) 135 (b) 155 (c) 164 (d) 144
  33. 33.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 169 (d) 182
  34. 34.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 11 (d) 36
  35. 35.What is the 22nd term of the AP 6, 11, 16, 21, …? (a) 105 (b) 116 (c) 110 (d) 111
  36. 36.What is the 35th term of the AP 6, 10, 14, 18, …? (a) 142 (b) 136 (c) 146 (d) 140
  37. 37.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 42 (b) 168 (c) 189 (d) 336
  38. 38.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 22 (b) 21 (c) 27 (d) 23
  39. 39.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 102 (b) 60 (c) 16 (d) 51
  40. 40.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 40 (b) 282 (c) 300 (d) 564

Answer key

  1. 155
  2. 101
  3. 1081
  4. 28
  5. 196
  6. 61
  7. 31
  8. 180
  9. 26th
  10. 6
  11. 29
  12. 13
  13. 1485
  14. 70
  15. 36
  16. 117
  17. 150
  18. 729
  19. 17
  20. 165
  21. 4753
  22. 32nd
  23. 55
  24. 124
  25. 1653
  26. 33rd
  27. 19
  28. 59
  29. 78
  30. 186
  31. 18
  32. 155
  33. 169
  34. 36
  35. 111
  36. 142
  37. 168
  38. 22
  39. 51
  40. 282

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