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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 459 · 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 the first 12 terms of the AP 4, 5, 6, …? (a) 15 (b) 228 (c) 120 (d) 114
  2. 2.What is the 31st term of the AP 10, 17, 24, 31, …? (a) 210 (b) 217 (c) 220 (d) 227
  3. 3.What is the 18th term of the AP 7, 11, 15, 19, …? (a) 79 (b) 68 (c) 75 (d) 72
  4. 4.What is the 35th term of the AP 17, 26, 35, 44, …? (a) 315 (b) 323 (c) 306 (d) 332
  5. 5.Which term of the AP 4, 9, 14, 19, … is 194? (a) 41st (b) 39th (c) 38th (d) 40th
  6. 6.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2926 (c) 5852 (d) 2888
  7. 7.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 35 (c) 40 (d) 11
  8. 8.What is the 23rd term of the AP 17, 19, 21, 23, …? (a) 46 (b) 61 (c) 63 (d) 44
  9. 9.What is the 38th term of the AP 13, 20, 27, 34, …? (a) 259 (b) 279 (c) 266 (d) 272
  10. 10.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1275 (c) 1326 (d) 1327
  11. 11.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 14 (b) 100 (c) 190 (d) 95
  12. 12.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1711 (c) 1682 (d) 1653
  13. 13.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 340 (b) 310 (c) 620 (d) 58
  14. 14.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 330 (b) 600 (c) 300 (d) 57
  15. 15.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 3487 (c) 6972 (d) 3486
  16. 16.What is the 11th term of the AP 6, 14, 22, 30, …? (a) 86 (b) 88 (c) 94 (d) 80
  17. 17.Which term of the AP 2, 5, 8, 11, … is 68? (a) 23rd (b) 22nd (c) 24th (d) 25th
  18. 18.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 204 (b) 384 (c) 27 (d) 192
  19. 19.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1892 (c) 3782 (d) 1891
  20. 20.What is the 16th term of the AP 5, 13, 21, 29, …? (a) 120 (b) 128 (c) 125 (d) 133
  21. 21.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 300 (b) 156 (c) 18 (d) 150
  22. 22.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 187 (b) 26 (c) 176 (d) 352
  23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 196 (c) 210 (d) 27
  24. 24.What is the 26th term of the AP 7, 13, 19, 25, …? (a) 156 (b) 157 (c) 163 (d) 150
  25. 25.Which term of the AP 15, 22, 29, 36, … is 155? (a) 21st (b) 22nd (c) 23rd (d) 20th
  26. 26.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 85 (b) 26 (c) 160 (d) 80
  27. 27.What is the 13th term of the AP 4, 11, 18, 25, …? (a) 91 (b) 95 (c) 88 (d) 84
  28. 28.What is the 40th term of the AP 1, 7, 13, 19, …? (a) 234 (b) 240 (c) 241 (d) 235
  29. 29.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 49 (b) 98 (c) 13 (d) 56
  30. 30.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 90 (b) 180 (c) 100 (d) 26
  31. 31.What is the 36th term of the AP 16, 18, 20, 22, …? (a) 70 (b) 72 (c) 88 (d) 86
  32. 32.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 145 (b) 150 (c) 290 (d) 19
  33. 33.What is the 17th term of the AP 15, 21, 27, 33, …? (a) 117 (b) 96 (c) 102 (d) 111
  34. 34.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 61 (b) 340 (c) 680 (d) 370
  35. 35.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 23 (b) 21 (c) 22 (d) 30
  36. 36.Which term of the AP 2, 10, 18, 26, … is 242? (a) 33rd (b) 30th (c) 32nd (d) 31st
  37. 37.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 45 (b) 46 (c) 90 (d) 11
  38. 38.What is the 36th term of the AP 15, 19, 23, 27, …? (a) 140 (b) 144 (c) 155 (d) 159
  39. 39.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 256 (d) 272
  40. 40.What is the 13th term of the AP 16, 23, 30, 37, …? (a) 91 (b) 84 (c) 100 (d) 107

Answer key

  1. 114
  2. 220
  3. 75
  4. 323
  5. 39th
  6. 2926
  7. 35
  8. 61
  9. 272
  10. 1326
  11. 95
  12. 1711
  13. 310
  14. 300
  15. 3486
  16. 86
  17. 23rd
  18. 192
  19. 1891
  20. 125
  21. 150
  22. 176
  23. 196
  24. 157
  25. 21st
  26. 80
  27. 88
  28. 235
  29. 49
  30. 90
  31. 86
  32. 145
  33. 111
  34. 340
  35. 22
  36. 31st
  37. 45
  38. 155
  39. 256
  40. 100

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