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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 900 · 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 37th term of the AP 16, 22, 28, 34, …? (a) 216 (b) 222 (c) 238 (d) 232
  2. 2.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 12 (b) 68 (c) 72 (d) 136
  3. 3.Which term of the AP 20, 24, 28, 32, … is 48? (a) 12th (b) 7th (c) 8th (d) 9th
  4. 4.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 6 (b) 21 (c) 40 (d) 20
  5. 5.Which term of the AP 1, 6, 11, 16, … is 56? (a) 11th (b) 12th (c) 14th (d) 13th
  6. 6.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 30 (c) 210 (d) 105
  7. 7.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 272 (c) 128 (d) 120
  8. 8.What is the 14th term of the AP 18, 21, 24, 27, …? (a) 39 (b) 42 (c) 60 (d) 57
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
  10. 10.What is the 14th term of the AP 18, 25, 32, 39, …? (a) 116 (b) 98 (c) 91 (d) 109
  11. 11.What is the sum of all the whole numbers from 1 to 44? (a) 968 (b) 946 (c) 1980 (d) 990
  12. 12.What is the 33rd term of the AP 19, 25, 31, 37, …? (a) 198 (b) 211 (c) 217 (d) 192
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 435 (d) 57
  14. 14.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 2016 (d) 1953
  15. 15.Which term of the AP 11, 16, 21, 26, … is 126? (a) 26th (b) 24th (c) 25th (d) 23rd
  16. 16.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 78 (c) 156 (d) 23
  17. 17.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 13 (b) 15 (c) 14 (d) 22
  18. 18.What is the 29th term of the AP 15, 17, 19, 21, …? (a) 58 (b) 71 (c) 56 (d) 73
  19. 19.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  20. 20.What is the 17th term of the AP 18, 22, 26, 30, …? (a) 86 (b) 68 (c) 82 (d) 64
  21. 21.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 187 (b) 27 (c) 374 (d) 198
  22. 22.What is the 36th term of the AP 4, 10, 16, 22, …? (a) 220 (b) 216 (c) 214 (d) 210
  23. 23.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 90 (b) 19 (c) 84 (d) 168
  24. 24.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 30 (b) 21 (c) 23 (d) 22
  25. 25.What is the 10th term of the AP 19, 22, 25, 28, …? (a) 30 (b) 49 (c) 27 (d) 46
  26. 26.What is the 24th term of the AP 16, 19, 22, 25, …? (a) 72 (b) 69 (c) 88 (d) 85
  27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  28. 28.What is the 10th term of the AP 19, 24, 29, 34, …? (a) 64 (b) 50 (c) 45 (d) 69
  29. 29.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 8 (b) 5 (c) 6 (d) 7
  30. 30.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 140 (b) 24 (c) 75 (d) 70
  31. 31.What is the 17th term of the AP 2, 10, 18, 26, …? (a) 136 (b) 130 (c) 138 (d) 128
  32. 32.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 20 (b) 73 (c) 70 (d) 140
  33. 33.What is the 18th term of the AP 20, 22, 24, 26, …? (a) 34 (b) 36 (c) 56 (d) 54
  34. 34.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 392 (c) 812 (d) 406
  35. 35.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 22 (b) 28 (c) 23 (d) 21
  36. 36.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 480 (b) 240 (c) 264 (d) 51
  37. 37.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 200 (d) 190
  38. 38.What is the 16th term of the AP 2, 7, 12, 17, …? (a) 75 (b) 80 (c) 77 (d) 82
  39. 39.What is the 18th term of the AP 9, 18, 27, 36, …? (a) 163 (b) 153 (c) 162 (d) 171
  40. 40.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1129 (c) 1128 (d) 1081

Answer key

  1. 232
  2. 68
  3. 8th
  4. 20
  5. 12th
  6. 105
  7. 136
  8. 57
  9. 25
  10. 109
  11. 990
  12. 211
  13. 841
  14. 2016
  15. 24th
  16. 144
  17. 14
  18. 71
  19. 784
  20. 82
  21. 187
  22. 214
  23. 84
  24. 22
  25. 46
  26. 85
  27. 36
  28. 64
  29. 6
  30. 70
  31. 130
  32. 70
  33. 54
  34. 406
  35. 22
  36. 240
  37. 210
  38. 77
  39. 162
  40. 1128

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