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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 649 · 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 sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  2. 2.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 1058 (c) 2162 (d) 1081
  3. 3.Which term of the AP 19, 23, 27, 31, … is 63? (a) 14th (b) 13th (c) 11th (d) 12th
  4. 4.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 240 (c) 120 (d) 121
  5. 5.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 129 (b) 27 (c) 252 (d) 126
  6. 6.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 116 (b) 128 (c) 25 (d) 232
  7. 7.What is the 37th term of the AP 1, 8, 15, 22, …? (a) 253 (b) 259 (c) 260 (d) 252
  8. 8.What is the 29th term of the AP 6, 12, 18, 24, …? (a) 174 (b) 175 (c) 168 (d) 180
  9. 9.Which term of the AP 11, 17, 23, 29, … is 95? (a) 14th (b) 17th (c) 15th (d) 16th
  10. 10.What is the 11th term of the AP 15, 18, 21, 24, …? (a) 30 (b) 33 (c) 48 (d) 45
  11. 11.Which term of the AP 10, 18, 26, 34, … is 154? (a) 19th (b) 21st (c) 20th (d) 18th
  12. 12.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 480 (b) 240 (c) 51 (d) 264
  13. 13.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 351 (d) 702
  14. 14.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 110 (c) 45 (d) 55
  15. 15.Which term of the AP 9, 15, 21, 27, … is 87? (a) 13th (b) 16th (c) 14th (d) 15th
  16. 16.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 338 (c) 702 (d) 325
  17. 17.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 5 (b) 16 (c) 30 (d) 15
  18. 18.What is the 32nd term of the AP 5, 12, 19, 26, …? (a) 224 (b) 217 (c) 229 (d) 222
  19. 19.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300
  20. 20.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 138 (b) 38 (c) 156 (d) 276
  21. 21.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 29 (b) 21 (c) 20 (d) 22
  22. 22.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 85 (b) 90 (c) 170 (d) 27
  23. 23.What is the missing term in the AP 8, 10, 12, ?, 16? (a) 14 (b) 16 (c) 13 (d) 15
  24. 24.Which term of the AP 6, 15, 24, 33, … is 303? (a) 33rd (b) 36th (c) 35th (d) 34th
  25. 25.What is the 23rd term of the AP 16, 21, 26, 31, …? (a) 115 (b) 126 (c) 131 (d) 110
  26. 26.Which term of the AP 1, 7, 13, 19, … is 67? (a) 13th (b) 14th (c) 11th (d) 12th
  27. 27.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4278 (c) 4232 (d) 4186
  28. 28.What is the 40th term of the AP 5, 9, 13, 17, …? (a) 156 (b) 160 (c) 161 (d) 165
  29. 29.What is the 36th term of the AP 9, 11, 13, 15, …? (a) 81 (b) 72 (c) 79 (d) 70
  30. 30.What is the sum of all the whole numbers from 1 to 60? (a) 1830 (b) 1800 (c) 3660 (d) 1770
  31. 31.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 10 (c) 54 (d) 108
  32. 32.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 3741 (c) 3698 (d) 7482
  33. 33.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 176 (b) 43 (c) 352 (d) 200
  34. 34.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 3422 (c) 1711 (d) 1682
  35. 35.What is the 17th term of the AP 14, 16, 18, 20, …? (a) 34 (b) 32 (c) 46 (d) 48
  36. 36.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 121 (c) 21 (d) 132
  37. 37.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 3782 (c) 1830 (d) 1892
  38. 38.What is the 18th term of the AP 9, 17, 25, 33, …? (a) 144 (b) 153 (c) 145 (d) 136
  39. 39.What is the 15th term of the AP 11, 19, 27, 35, …? (a) 131 (b) 120 (c) 123 (d) 112
  40. 40.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 25 (c) 320 (d) 170

Answer key

  1. 91
  2. 1081
  3. 12th
  4. 120
  5. 126
  6. 116
  7. 253
  8. 174
  9. 15th
  10. 45
  11. 19th
  12. 240
  13. 676
  14. 55
  15. 14th
  16. 351
  17. 15
  18. 222
  19. 576
  20. 138
  21. 21
  22. 85
  23. 14
  24. 34th
  25. 126
  26. 12th
  27. 4278
  28. 161
  29. 79
  30. 1830
  31. 54
  32. 3741
  33. 176
  34. 1711
  35. 46
  36. 121
  37. 1891
  38. 145
  39. 123
  40. 160

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