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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 975 · 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 7 terms of the AP 8, 11, 14, …? (a) 122 (b) 238 (c) 26 (d) 119
  2. 2.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 2970 (c) 1458 (d) 1431
  3. 3.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 17 (b) 21 (c) 15 (d) 16
  4. 4.What is the 15th term of the AP 4, 8, 12, 16, …? (a) 60 (b) 64 (c) 56 (d) 61
  5. 5.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 15 (b) 17 (c) 20 (d) 16
  6. 6.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 204 (b) 114 (c) 102 (d) 27
  7. 7.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 12 (b) 10 (c) 19 (d) 11
  8. 8.What is the 18th term of the AP 15, 24, 33, 42, …? (a) 177 (b) 153 (c) 168 (d) 162
  9. 9.What is the 16th term of the AP 8, 15, 22, 29, …? (a) 120 (b) 112 (c) 105 (d) 113
  10. 10.What is the 35th term of the AP 4, 8, 12, 16, …? (a) 140 (b) 144 (c) 136 (d) 141
  11. 11.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 350 (b) 40 (c) 175 (d) 180
  12. 12.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 120 (c) 128 (d) 136
  13. 13.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 264 (b) 37 (c) 492 (d) 246
  14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 47 (d) 576
  15. 15.Which term of the AP 18, 24, 30, 36, … is 198? (a) 33rd (b) 31st (c) 30th (d) 32nd
  16. 16.Which term of the AP 14, 20, 26, 32, … is 224? (a) 36th (b) 38th (c) 37th (d) 35th
  17. 17.Which term of the AP 4, 6, 8, 10, … is 58? (a) 28th (b) 29th (c) 30th (d) 27th
  18. 18.Which term of the AP 5, 7, 9, 11, … is 25? (a) 12th (b) 10th (c) 13th (d) 11th
  19. 19.What is the missing term in the AP 10, ?, 20, 25, 30? (a) 20 (b) 15 (c) 16 (d) 14
  20. 20.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 96 (b) 162 (c) 26 (d) 81
  21. 21.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 23 (b) 22 (c) 30 (d) 21
  22. 22.What is the 21st term of the AP 16, 20, 24, 28, …? (a) 84 (b) 100 (c) 80 (d) 96
  23. 23.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 140 (b) 75 (c) 70 (d) 24
  24. 24.What is the missing term in the AP 20, 29, ?, 47, 56? (a) 47 (b) 38 (c) 39 (d) 37
  25. 25.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 34 (b) 110 (c) 125 (d) 220
  26. 26.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 406 (d) 812
  27. 27.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 17 (b) 13 (c) 12 (d) 14
  28. 28.What is the 16th term of the AP 19, 27, 35, 43, …? (a) 128 (b) 120 (c) 139 (d) 147
  29. 29.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  30. 30.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 55 (b) 17 (c) 58 (d) 110
  31. 31.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 468 (b) 72 (c) 504 (d) 936
  32. 32.Which term of the AP 15, 24, 33, 42, … is 366? (a) 42nd (b) 39th (c) 41st (d) 40th
  33. 33.What is the 26th term of the AP 1, 3, 5, 7, …? (a) 52 (b) 51 (c) 50 (d) 53
  34. 34.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 60 (b) 8 (c) 31 (d) 30
  35. 35.What is the 28th term of the AP 14, 18, 22, 26, …? (a) 108 (b) 126 (c) 122 (d) 112
  36. 36.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 121 (c) 242 (d) 16
  37. 37.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2926 (c) 5852 (d) 2850
  38. 38.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 242 (c) 231 (d) 506
  39. 39.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 22 (b) 65 (c) 120 (d) 60
  40. 40.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 315 (b) 630 (c) 340 (d) 54

Answer key

  1. 119
  2. 1485
  3. 16
  4. 60
  5. 16
  6. 102
  7. 11
  8. 168
  9. 113
  10. 140
  11. 175
  12. 136
  13. 246
  14. 576
  15. 31st
  16. 36th
  17. 28th
  18. 11th
  19. 15
  20. 81
  21. 22
  22. 96
  23. 70
  24. 38
  25. 110
  26. 784
  27. 13
  28. 139
  29. 900
  30. 55
  31. 468
  32. 40th
  33. 51
  34. 30
  35. 122
  36. 121
  37. 2926
  38. 253
  39. 60
  40. 315

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