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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 857 · 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 10, 12, 14, 16, … is 36? (a) 15th (b) 18th (c) 13th (d) 14th
  2. 2.What is the sum of all the whole numbers from 1 to 87? (a) 7656 (b) 3829 (c) 3741 (d) 3828
  3. 3.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4951 (c) 4950 (d) 4851
  4. 4.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 33 (b) 23 (c) 25 (d) 24
  5. 5.Which term of the AP 17, 26, 35, 44, … is 116? (a) 14th (b) 11th (c) 13th (d) 12th
  6. 6.What is the 14th term of the AP 1, 7, 13, 19, …? (a) 84 (b) 79 (c) 78 (d) 85
  7. 7.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 126 (b) 36 (c) 144 (d) 252
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 930 (c) 465 (d) 59
  9. 9.What is the missing term in the AP 16, 22, 28, ?, 40? (a) 33 (b) 40 (c) 35 (d) 34
  10. 10.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 13 (b) 12 (c) 16 (d) 14
  11. 11.What is the 22nd term of the AP 11, 14, 17, 20, …? (a) 74 (b) 66 (c) 63 (d) 77
  12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  13. 13.What is the 18th term of the AP 17, 24, 31, 38, …? (a) 143 (b) 119 (c) 126 (d) 136
  14. 14.What is the 28th term of the AP 1, 6, 11, 16, …? (a) 136 (b) 141 (c) 135 (d) 140
  15. 15.What is the 20th term of the AP 2, 4, 6, 8, …? (a) 42 (b) 41 (c) 38 (d) 40
  16. 16.What is the 23rd term of the AP 4, 9, 14, 19, …? (a) 115 (b) 110 (c) 114 (d) 119
  17. 17.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 275 (b) 50 (c) 270 (d) 540
  18. 18.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 118 (c) 17 (d) 117
  19. 19.Which term of the AP 9, 11, 13, 15, … is 39? (a) 15th (b) 18th (c) 16th (d) 17th
  20. 20.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 841 (d) 435
  21. 21.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 96 (b) 13 (c) 48 (d) 54
  22. 22.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 882 (c) 861 (d) 903
  23. 23.What is the 17th term of the AP 20, 26, 32, 38, …? (a) 116 (b) 102 (c) 122 (d) 96
  24. 24.What is the missing term in the AP 15, 20, ?, 30, 35? (a) 26 (b) 30 (c) 25 (d) 24
  25. 25.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 33 (b) 306 (c) 171 (d) 153
  26. 26.What is the 11th term of the AP 2, 4, 6, 8, …? (a) 20 (b) 24 (c) 22 (d) 23
  27. 27.What is the 13th term of the AP 4, 10, 16, 22, …? (a) 78 (b) 76 (c) 72 (d) 82
  28. 28.What is the 19th term of the AP 13, 18, 23, 28, …? (a) 95 (b) 103 (c) 90 (d) 108
  29. 29.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1128 (c) 2256 (d) 1081
  30. 30.What is the missing term in the AP 1, 10, ?, 28, 37? (a) 28 (b) 20 (c) 18 (d) 19
  31. 31.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 34 (b) 36 (c) 41 (d) 35
  32. 32.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1541 (c) 3080 (d) 1540
  33. 33.What is the 16th term of the AP 18, 25, 32, 39, …? (a) 123 (b) 130 (c) 112 (d) 105
  34. 34.Which term of the AP 20, 25, 30, 35, … is 100? (a) 16th (b) 20th (c) 18th (d) 17th
  35. 35.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 480 (b) 900 (c) 65 (d) 450
  36. 36.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 616 (b) 330 (c) 308 (d) 48
  37. 37.What is the 15th term of the AP 10, 18, 26, 34, …? (a) 130 (b) 120 (c) 122 (d) 112
  38. 38.What is the 17th term of the AP 10, 12, 14, 16, …? (a) 34 (b) 32 (c) 44 (d) 42
  39. 39.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 9 (b) 14 (c) 11 (d) 10
  40. 40.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 238 (b) 26 (c) 122 (d) 119

Answer key

  1. 14th
  2. 3828
  3. 4950
  4. 24
  5. 12th
  6. 79
  7. 126
  8. 900
  9. 34
  10. 13
  11. 74
  12. 100
  13. 136
  14. 136
  15. 40
  16. 114
  17. 270
  18. 117
  19. 16th
  20. 841
  21. 48
  22. 903
  23. 116
  24. 25
  25. 153
  26. 22
  27. 76
  28. 103
  29. 1128
  30. 19
  31. 35
  32. 1540
  33. 123
  34. 17th
  35. 450
  36. 308
  37. 122
  38. 42
  39. 10
  40. 119

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