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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 447 · 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 8 terms of the AP 3, 8, 13, …? (a) 328 (b) 164 (c) 184 (d) 38
  2. 2.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 15 (b) 13 (c) 14 (d) 17
  3. 3.What is the 22nd term of the AP 5, 11, 17, 23, …? (a) 126 (b) 137 (c) 131 (d) 132
  4. 4.What is the 32nd term of the AP 9, 18, 27, 36, …? (a) 297 (b) 289 (c) 279 (d) 288
  5. 5.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 420 (b) 780 (c) 60 (d) 390
  6. 6.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 240 (b) 225 (c) 36 (d) 450
  7. 7.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 392 (d) 406
  8. 8.What is the 18th term of the AP 4, 11, 18, 25, …? (a) 130 (b) 123 (c) 126 (d) 119
  9. 9.Which term of the AP 2, 10, 18, 26, … is 170? (a) 23rd (b) 24th (c) 22nd (d) 21st
  10. 10.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 2016 (d) 1953
  11. 11.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 132 (c) 66 (d) 55
  12. 12.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  13. 13.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 3321 (c) 6642 (d) 3240
  14. 14.Which term of the AP 20, 22, 24, 26, … is 40? (a) 20th (b) 12th (c) 11th (d) 10th
  15. 15.Which term of the AP 19, 22, 25, 28, … is 49? (a) 11th (b) 12th (c) 13th (d) 10th
  16. 16.Which term of the AP 3, 7, 11, 15, … is 139? (a) 37th (b) 34th (c) 36th (d) 35th
  17. 17.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 100 (b) 180 (c) 26 (d) 90
  18. 18.What is the 22nd term of the AP 17, 22, 27, 32, …? (a) 110 (b) 122 (c) 105 (d) 127
  19. 19.Which term of the AP 8, 16, 24, 32, … is 152? (a) 19th (b) 20th (c) 21st (d) 18th
  20. 20.What is the 30th term of the AP 20, 23, 26, 29, …? (a) 87 (b) 90 (c) 110 (d) 107
  21. 21.What is the sum of all the whole numbers from 1 to 79? (a) 6320 (b) 3161 (c) 3160 (d) 3081
  22. 22.Which term of the AP 3, 11, 19, 27, … is 291? (a) 38th (b) 39th (c) 37th (d) 36th
  23. 23.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 63 (b) 852 (c) 456 (d) 426
  24. 24.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 231 (c) 232 (d) 462
  25. 25.What is the 36th term of the AP 3, 12, 21, 30, …? (a) 315 (b) 324 (c) 318 (d) 327
  26. 26.What is the 22nd term of the AP 15, 19, 23, 27, …? (a) 103 (b) 84 (c) 99 (d) 88
  27. 27.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 22 (c) 91 (d) 94
  28. 28.Which term of the AP 11, 18, 25, 32, … is 151? (a) 20th (b) 22nd (c) 21st (d) 23rd
  29. 29.Which term of the AP 14, 16, 18, 20, … is 92? (a) 46th (b) 40th (c) 41st (d) 39th
  30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 15 (d) 36
  31. 31.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 702 (d) 351
  32. 32.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 112 (b) 11 (c) 57 (d) 56
  33. 33.What is the 16th term of the AP 13, 20, 27, 34, …? (a) 112 (b) 118 (c) 105 (d) 125
  34. 34.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 7 (b) 5 (c) 6 (d) 4
  35. 35.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 650 (b) 350 (c) 55 (d) 325
  36. 36.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 435 (c) 436 (d) 406
  37. 37.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 264 (b) 32 (c) 504 (d) 252
  38. 38.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 154 (b) 77 (c) 14 (d) 78
  39. 39.What is the 21st term of the AP 20, 23, 26, 29, …? (a) 80 (b) 63 (c) 60 (d) 83
  40. 40.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 300 (c) 326 (d) 325

Answer key

  1. 164
  2. 14
  3. 131
  4. 288
  5. 390
  6. 225
  7. 406
  8. 123
  9. 22nd
  10. 2016
  11. 66
  12. 121
  13. 3321
  14. 11th
  15. 11th
  16. 35th
  17. 90
  18. 122
  19. 19th
  20. 107
  21. 3160
  22. 37th
  23. 426
  24. 231
  25. 318
  26. 99
  27. 91
  28. 21st
  29. 40th
  30. 64
  31. 676
  32. 56
  33. 118
  34. 5
  35. 325
  36. 435
  37. 252
  38. 77
  39. 80
  40. 325

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