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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 26 · 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 8, ?, 22, 29, 36? (a) 16 (b) 22 (c) 14 (d) 15
  2. 2.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 190 (c) 200 (d) 210
  3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 90 (d) 45
  4. 4.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 930 (c) 435 (d) 450
  5. 5.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 21 (b) 19 (c) 20 (d) 23
  6. 6.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 528 (c) 1122 (d) 561
  7. 7.What is the 25th term of the AP 11, 14, 17, 20, …? (a) 72 (b) 83 (c) 86 (d) 75
  8. 8.What is the 40th term of the AP 5, 10, 15, 20, …? (a) 195 (b) 201 (c) 205 (d) 200
  9. 9.What is the 20th term of the AP 11, 14, 17, 20, …? (a) 71 (b) 60 (c) 68 (d) 57
  10. 10.What is the 19th term of the AP 11, 20, 29, 38, …? (a) 182 (b) 162 (c) 173 (d) 171
  11. 11.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 110 (b) 13 (c) 55 (d) 56
  12. 12.What is the 19th term of the AP 15, 21, 27, 33, …? (a) 129 (b) 114 (c) 108 (d) 123
  13. 13.Which term of the AP 2, 7, 12, 17, … is 47? (a) 12th (b) 11th (c) 9th (d) 10th
  14. 14.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 342 (d) 324
  15. 15.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1654 (c) 1653 (d) 1596
  16. 16.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 34 (b) 36 (c) 44 (d) 35
  17. 17.What is the 29th term of the AP 1, 10, 19, 28, …? (a) 261 (b) 253 (c) 262 (d) 252
  18. 18.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 161 (b) 166 (c) 322 (d) 38
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  20. 20.What is the 31st term of the AP 8, 11, 14, 17, …? (a) 101 (b) 98 (c) 93 (d) 90
  21. 21.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 15 (b) 14 (c) 17 (d) 13
  22. 22.Which term of the AP 16, 22, 28, 34, … is 106? (a) 15th (b) 16th (c) 17th (d) 18th
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 100 (d) 19
  24. 24.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 176 (b) 26 (c) 187 (d) 352
  25. 25.What is the 39th term of the AP 19, 23, 27, 31, …? (a) 171 (b) 152 (c) 175 (d) 156
  26. 26.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1275 (c) 1250 (d) 1225
  27. 27.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 33 (b) 216 (c) 108 (d) 126
  28. 28.What is the 25th term of the AP 3, 9, 15, 21, …? (a) 150 (b) 153 (c) 147 (d) 144
  29. 29.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 25 (b) 17 (c) 18 (d) 16
  30. 30.What is the sum of all the whole numbers from 1 to 66? (a) 2145 (b) 2178 (c) 4422 (d) 2211
  31. 31.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 325 (d) 625
  32. 32.Which term of the AP 20, 27, 34, 41, … is 195? (a) 28th (b) 27th (c) 25th (d) 26th
  33. 33.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 212 (b) 418 (c) 34 (d) 209
  34. 34.What is the 37th term of the AP 4, 8, 12, 16, …? (a) 148 (b) 144 (c) 149 (d) 152
  35. 35.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 14 (b) 69 (c) 72 (d) 138
  36. 36.Which term of the AP 15, 22, 29, 36, … is 260? (a) 36th (b) 38th (c) 37th (d) 35th
  37. 37.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 702 (d) 351
  38. 38.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 105 (c) 196 (d) 27
  39. 39.What is the 22nd term of the AP 4, 7, 10, 13, …? (a) 70 (b) 63 (c) 66 (d) 67
  40. 40.What is the 22nd term of the AP 8, 12, 16, 20, …? (a) 96 (b) 84 (c) 88 (d) 92

Answer key

  1. 15
  2. 210
  3. 81
  4. 465
  5. 20
  6. 561
  7. 83
  8. 200
  9. 68
  10. 173
  11. 55
  12. 123
  13. 10th
  14. 324
  15. 1653
  16. 35
  17. 253
  18. 161
  19. 25
  20. 98
  21. 14
  22. 16th
  23. 100
  24. 176
  25. 171
  26. 1275
  27. 108
  28. 147
  29. 17
  30. 2211
  31. 625
  32. 26th
  33. 209
  34. 148
  35. 69
  36. 36th
  37. 676
  38. 196
  39. 67
  40. 92

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