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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 86 · 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.Which term of the AP 4, 11, 18, 25, … is 81? (a) 13th (b) 12th (c) 14th (d) 11th
  2. 2.What is the 15th term of the AP 3, 8, 13, 18, …? (a) 70 (b) 75 (c) 73 (d) 78
  3. 3.Which term of the AP 12, 15, 18, 21, … is 75? (a) 22nd (b) 23rd (c) 25th (d) 21st
  4. 4.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 360 (b) 390 (c) 720 (d) 63
  5. 5.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 190 (c) 380 (d) 171
  6. 6.What is the missing term in the AP 14, 23, ?, 41, 50? (a) 41 (b) 32 (c) 33 (d) 31
  7. 7.Which term of the AP 1, 6, 11, 16, … is 196? (a) 39th (b) 41st (c) 42nd (d) 40th
  8. 8.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 154 (b) 308 (c) 24 (d) 165
  9. 9.What is the 11th term of the AP 13, 20, 27, 34, …? (a) 90 (b) 70 (c) 83 (d) 77
  10. 10.Which term of the AP 1, 5, 9, 13, … is 117? (a) 29th (b) 31st (c) 30th (d) 32nd
  11. 11.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1891 (c) 1830 (d) 1892
  12. 12.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 184 (b) 104 (c) 92 (d) 22
  13. 13.What is the 36th term of the AP 15, 24, 33, 42, …? (a) 330 (b) 339 (c) 315 (d) 324
  14. 14.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2017 (c) 1953 (d) 2016
  15. 15.What is the missing term in the AP 16, 23, 30, ?, 44? (a) 36 (b) 44 (c) 38 (d) 37
  16. 16.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 28 (d) 56
  17. 17.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 300 (c) 150 (d) 160
  18. 18.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 25 (b) 20 (c) 19 (d) 18
  19. 19.What is the 37th term of the AP 20, 23, 26, 29, …? (a) 108 (b) 128 (c) 131 (d) 111
  20. 20.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 45 (b) 10 (c) 48 (d) 90
  21. 21.What is the 38th term of the AP 6, 8, 10, 12, …? (a) 74 (b) 76 (c) 82 (d) 80
  22. 22.What is the 12th term of the AP 6, 10, 14, 18, …? (a) 44 (b) 54 (c) 50 (d) 48
  23. 23.What is the 18th term of the AP 18, 24, 30, 36, …? (a) 126 (b) 102 (c) 120 (d) 108
  24. 24.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 328 (b) 38 (c) 184 (d) 164
  25. 25.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 64 (b) 63 (c) 126 (d) 11
  26. 26.What is the 15th term of the AP 15, 17, 19, 21, …? (a) 28 (b) 30 (c) 45 (d) 43
  27. 27.What is the 19th term of the AP 6, 8, 10, 12, …? (a) 44 (b) 36 (c) 38 (d) 42
  28. 28.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 5050 (c) 10100 (d) 4950
  29. 29.Which term of the AP 8, 14, 20, 26, … is 98? (a) 16th (b) 15th (c) 18th (d) 17th
  30. 30.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 18 (b) 15 (c) 16 (d) 14
  31. 31.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 24 (b) 26 (c) 32 (d) 25
  32. 32.What is the 16th term of the AP 12, 20, 28, 36, …? (a) 128 (b) 140 (c) 120 (d) 132
  33. 33.Which term of the AP 17, 25, 33, 41, … is 281? (a) 35th (b) 36th (c) 33rd (d) 34th
  34. 34.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1800 (c) 1830 (d) 1770
  35. 35.What is the missing term in the AP 14, 22, ?, 38, 46? (a) 29 (b) 31 (c) 30 (d) 38
  36. 36.What is the 12th term of the AP 3, 11, 19, 27, …? (a) 91 (b) 96 (c) 99 (d) 88
  37. 37.What is the missing term in the AP 4, 9, 14, ?, 24? (a) 20 (b) 18 (c) 24 (d) 19
  38. 38.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 490 (b) 47 (c) 270 (d) 245
  39. 39.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 51 (b) 310 (c) 285 (d) 570
  40. 40.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 90 (b) 14 (c) 180 (d) 91

Answer key

  1. 12th
  2. 73
  3. 22nd
  4. 360
  5. 190
  6. 32
  7. 40th
  8. 154
  9. 83
  10. 30th
  11. 1891
  12. 92
  13. 330
  14. 2016
  15. 37
  16. 49
  17. 150
  18. 19
  19. 128
  20. 45
  21. 80
  22. 50
  23. 120
  24. 164
  25. 63
  26. 43
  27. 42
  28. 5050
  29. 16th
  30. 15
  31. 25
  32. 132
  33. 34th
  34. 1830
  35. 30
  36. 91
  37. 19
  38. 245
  39. 285
  40. 90

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