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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 158 · 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 5, ?, 23, 32, 41? (a) 13 (b) 15 (c) 23 (d) 14
  2. 2.What is the 13th term of the AP 16, 24, 32, 40, …? (a) 104 (b) 112 (c) 96 (d) 120
  3. 3.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 390 (b) 33 (c) 210 (d) 195
  4. 4.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 56 (b) 682 (c) 341 (d) 346
  5. 5.Which term of the AP 11, 17, 23, 29, … is 143? (a) 22nd (b) 25th (c) 23rd (d) 24th
  6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  7. 7.Which term of the AP 10, 16, 22, 28, … is 88? (a) 16th (b) 13th (c) 15th (d) 14th
  8. 8.What is the 36th term of the AP 6, 13, 20, 27, …? (a) 251 (b) 245 (c) 258 (d) 252
  9. 9.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 684 (b) 372 (c) 342 (d) 56
  10. 10.What is the missing term in the AP 14, ?, 24, 29, 34? (a) 24 (b) 20 (c) 19 (d) 18
  11. 11.What is the 32nd term of the AP 16, 18, 20, 22, …? (a) 80 (b) 64 (c) 62 (d) 78
  12. 12.Which term of the AP 20, 26, 32, 38, … is 212? (a) 33rd (b) 35th (c) 34th (d) 32nd
  13. 13.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 100 (b) 30 (c) 105 (d) 200
  14. 14.What is the 24th term of the AP 17, 19, 21, 23, …? (a) 48 (b) 65 (c) 63 (d) 46
  15. 15.What is the 31st term of the AP 17, 19, 21, 23, …? (a) 79 (b) 60 (c) 77 (d) 62
  16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 11 (d) 21
  17. 17.What is the 33rd term of the AP 6, 12, 18, 24, …? (a) 204 (b) 192 (c) 199 (d) 198
  18. 18.What is the 33rd term of the AP 7, 14, 21, 28, …? (a) 232 (b) 231 (c) 224 (d) 238
  19. 19.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 780 (c) 800 (d) 1640
  20. 20.What is the 17th term of the AP 14, 22, 30, 38, …? (a) 142 (b) 128 (c) 150 (d) 136
  21. 21.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 18 (b) 17 (c) 16 (d) 24
  22. 22.What is the 36th term of the AP 13, 16, 19, 22, …? (a) 118 (b) 121 (c) 108 (d) 105
  23. 23.Which term of the AP 5, 7, 9, 11, … is 83? (a) 39th (b) 42nd (c) 40th (d) 41st
  24. 24.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 462 (c) 232 (d) 231
  25. 25.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 100 (b) 50 (c) 60 (d) 18
  26. 26.Which term of the AP 11, 13, 15, 17, … is 31? (a) 10th (b) 12th (c) 11th (d) 13th
  27. 27.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 12 (b) 13 (c) 14 (d) 15
  28. 28.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 119 (b) 238 (c) 124 (d) 32
  29. 29.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1128 (c) 1081 (d) 2256
  30. 30.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 1653 (c) 3422 (d) 1711
  31. 31.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 32 (b) 25 (c) 26 (d) 24
  32. 32.What is the 13th term of the AP 1, 5, 9, 13, …? (a) 48 (b) 53 (c) 49 (d) 52
  33. 33.What is the missing term in the AP 10, ?, 20, 25, 30? (a) 16 (b) 14 (c) 20 (d) 15
  34. 34.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
  35. 35.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 192 (b) 208 (c) 384 (d) 38
  36. 36.Which term of the AP 14, 23, 32, 41, … is 158? (a) 17th (b) 18th (c) 19th (d) 16th
  37. 37.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 2048 (c) 2016 (d) 4160
  38. 38.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 780 (c) 1560 (d) 781
  39. 39.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 862 (c) 1722 (d) 861
  40. 40.What is the missing term in the AP 3, 10, 17, ?, 31? (a) 23 (b) 31 (c) 25 (d) 24

Answer key

  1. 14
  2. 112
  3. 195
  4. 341
  5. 23rd
  6. 441
  7. 14th
  8. 251
  9. 342
  10. 19
  11. 78
  12. 33rd
  13. 100
  14. 63
  15. 77
  16. 36
  17. 198
  18. 231
  19. 820
  20. 142
  21. 17
  22. 118
  23. 40th
  24. 231
  25. 50
  26. 11th
  27. 13
  28. 119
  29. 1128
  30. 1711
  31. 25
  32. 49
  33. 15
  34. 784
  35. 192
  36. 17th
  37. 2080
  38. 780
  39. 861
  40. 24

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