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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 42 · 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 12th term of the AP 6, 14, 22, 30, …? (a) 88 (b) 102 (c) 94 (d) 96
  2. 2.What is the 12th term of the AP 16, 18, 20, 22, …? (a) 22 (b) 40 (c) 24 (d) 38
  3. 3.Which term of the AP 5, 13, 21, 29, … is 149? (a) 18th (b) 19th (c) 20th (d) 21st
  4. 4.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 126 (b) 108 (c) 216 (d) 33
  5. 5.What is the 22nd term of the AP 3, 10, 17, 24, …? (a) 154 (b) 157 (c) 150 (d) 147
  6. 6.What is the 20th term of the AP 1, 4, 7, 10, …? (a) 57 (b) 61 (c) 58 (d) 60
  7. 7.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 191 (c) 171 (d) 380
  8. 8.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 800 (c) 780 (d) 820
  9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 15 (d) 36
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 702 (d) 676
  11. 11.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 326 (c) 650 (d) 300
  12. 12.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 13 (b) 14 (c) 20 (d) 15
  13. 13.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 36 (d) 42
  14. 14.What is the 19th term of the AP 6, 12, 18, 24, …? (a) 115 (b) 120 (c) 114 (d) 108
  15. 15.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 275 (b) 297 (c) 550 (d) 45
  16. 16.What is the 26th term of the AP 19, 27, 35, 43, …? (a) 208 (b) 227 (c) 200 (d) 219
  17. 17.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 756 (d) 53
  18. 18.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 58 (b) 612 (c) 333 (d) 306
  19. 19.What is the 31st term of the AP 12, 21, 30, 39, …? (a) 282 (b) 279 (c) 291 (d) 270
  20. 20.Which term of the AP 15, 20, 25, 30, … is 155? (a) 31st (b) 29th (c) 30th (d) 28th
  21. 21.What is the 14th term of the AP 11, 18, 25, 32, …? (a) 91 (b) 102 (c) 98 (d) 109
  22. 22.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 50 (c) 26 (d) 25
  23. 23.Which term of the AP 8, 17, 26, 35, … is 125? (a) 13th (b) 15th (c) 14th (d) 16th
  24. 24.Which term of the AP 7, 15, 23, 31, … is 135? (a) 19th (b) 16th (c) 18th (d) 17th
  25. 25.What is the 21st term of the AP 5, 8, 11, 14, …? (a) 68 (b) 65 (c) 60 (d) 63
  26. 26.Which term of the AP 7, 15, 23, 31, … is 303? (a) 40th (b) 39th (c) 37th (d) 38th
  27. 27.What is the 27th term of the AP 20, 26, 32, 38, …? (a) 176 (b) 162 (c) 156 (d) 182
  28. 28.What is the 31st term of the AP 1, 9, 17, 25, …? (a) 248 (b) 240 (c) 249 (d) 241
  29. 29.What is the 10th term of the AP 12, 17, 22, 27, …? (a) 45 (b) 62 (c) 50 (d) 57
  30. 30.What is the 17th term of the AP 12, 14, 16, 18, …? (a) 44 (b) 32 (c) 34 (d) 46
  31. 31.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 232 (b) 128 (c) 25 (d) 116
  32. 32.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 182 (b) 203 (c) 364 (d) 44
  33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  34. 34.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 33 (b) 8 (c) 66 (d) 36
  35. 35.Which term of the AP 6, 8, 10, 12, … is 82? (a) 40th (b) 39th (c) 41st (d) 38th
  36. 36.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 12 (b) 11 (c) 10 (d) 9
  37. 37.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 390 (b) 60 (c) 770 (d) 385
  38. 38.What is the 30th term of the AP 1, 6, 11, 16, …? (a) 145 (b) 146 (c) 151 (d) 150
  39. 39.Which term of the AP 20, 25, 30, 35, … is 180? (a) 34th (b) 33rd (c) 32nd (d) 36th
  40. 40.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 504 (b) 264 (c) 252 (d) 32

Answer key

  1. 94
  2. 38
  3. 19th
  4. 108
  5. 150
  6. 58
  7. 190
  8. 820
  9. 64
  10. 676
  11. 325
  12. 14
  13. 36
  14. 114
  15. 275
  16. 219
  17. 729
  18. 306
  19. 282
  20. 29th
  21. 102
  22. 25
  23. 14th
  24. 17th
  25. 65
  26. 38th
  27. 176
  28. 241
  29. 57
  30. 44
  31. 116
  32. 182
  33. 25
  34. 33
  35. 39th
  36. 10
  37. 385
  38. 146
  39. 33rd
  40. 252

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