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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 692 · 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 1, 4, 7, 10, … is 31? (a) 10th (b) 11th (c) 12th (d) 13th
  2. 2.Which term of the AP 12, 21, 30, 39, … is 318? (a) 35th (b) 34th (c) 37th (d) 36th
  3. 3.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 40 (b) 50 (c) 42 (d) 41
  4. 4.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 12 (b) 16 (c) 14 (d) 13
  5. 5.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 55 (b) 65 (c) 19 (d) 110
  6. 6.What is the 27th term of the AP 6, 12, 18, 24, …? (a) 168 (b) 162 (c) 156 (d) 163
  7. 7.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 204 (b) 114 (c) 102 (d) 27
  8. 8.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1176 (c) 1226 (d) 1225
  9. 9.What is the 37th term of the AP 10, 13, 16, 19, …? (a) 108 (b) 121 (c) 111 (d) 118
  10. 10.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 148 (b) 168 (c) 296 (d) 36
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
  12. 12.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 576 (d) 47
  13. 13.What is the 22nd term of the AP 9, 14, 19, 24, …? (a) 119 (b) 105 (c) 114 (d) 110
  14. 14.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 277 (c) 253 (d) 552
  15. 15.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 57 (b) 66 (c) 17 (d) 114
  16. 16.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 55 (c) 60 (d) 110
  17. 17.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 138 (b) 156 (c) 38 (d) 276
  18. 18.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  19. 19.What is the 19th term of the AP 6, 13, 20, 27, …? (a) 139 (b) 126 (c) 132 (d) 133
  20. 20.What is the 19th term of the AP 16, 18, 20, 22, …? (a) 38 (b) 54 (c) 36 (d) 52
  21. 21.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5000 (c) 10100 (d) 5050
  22. 22.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 12 (b) 15 (c) 13 (d) 14
  23. 23.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 11 (b) 12 (c) 10 (d) 16
  24. 24.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  25. 25.Which term of the AP 15, 23, 31, 39, … is 199? (a) 26th (b) 23rd (c) 24th (d) 25th
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 57 (d) 870
  27. 27.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 29 (b) 95 (c) 190 (d) 100
  28. 28.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 289 (d) 33
  29. 29.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 21 (b) 23 (c) 22 (d) 20
  30. 30.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 240 (c) 120 (d) 105
  31. 31.What is the 24th term of the AP 14, 19, 24, 29, …? (a) 129 (b) 120 (c) 115 (d) 134
  32. 32.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 465 (c) 450 (d) 435
  33. 33.What is the 17th term of the AP 5, 14, 23, 32, …? (a) 144 (b) 149 (c) 153 (d) 158
  34. 34.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 252 (c) 504 (d) 48
  35. 35.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4851 (c) 4753 (d) 4802
  36. 36.What is the 23rd term of the AP 11, 16, 21, 26, …? (a) 115 (b) 110 (c) 121 (d) 126
  37. 37.What is the 40th term of the AP 18, 20, 22, 24, …? (a) 96 (b) 80 (c) 78 (d) 98
  38. 38.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 14 (b) 16 (c) 24 (d) 15
  39. 39.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 248 (b) 47 (c) 243 (d) 486
  40. 40.What is the 14th term of the AP 12, 21, 30, 39, …? (a) 126 (b) 129 (c) 138 (d) 117

Answer key

  1. 11th
  2. 35th
  3. 41
  4. 13
  5. 55
  6. 162
  7. 102
  8. 1225
  9. 118
  10. 148
  11. 144
  12. 576
  13. 114
  14. 276
  15. 57
  16. 55
  17. 138
  18. 441
  19. 132
  20. 52
  21. 5050
  22. 13
  23. 11
  24. 121
  25. 24th
  26. 841
  27. 95
  28. 289
  29. 21
  30. 120
  31. 129
  32. 465
  33. 149
  34. 252
  35. 4851
  36. 121
  37. 96
  38. 15
  39. 243
  40. 129

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