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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 983 · 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 6 terms of the AP 3, 9, 15, …? (a) 108 (b) 126 (c) 33 (d) 216
  2. 2.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 3 (b) 2 (c) 5 (d) 4
  3. 3.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 1953 (c) 4032 (d) 2017
  4. 4.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 300 (b) 168 (c) 150 (d) 40
  5. 5.What is the missing term in the AP 11, 17, ?, 29, 35? (a) 29 (b) 24 (c) 22 (d) 23
  6. 6.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 26 (b) 29 (c) 24 (d) 25
  7. 7.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 16 (b) 17 (c) 18 (d) 15
  8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 28 (d) 13
  9. 9.What is the 10th term of the AP 17, 23, 29, 35, …? (a) 71 (b) 54 (c) 77 (d) 60
  10. 10.What is the 19th term of the AP 17, 24, 31, 38, …? (a) 150 (b) 133 (c) 126 (d) 143
  11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 33 (c) 306 (d) 153
  12. 12.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 27 (b) 20 (c) 21 (d) 19
  13. 13.Which term of the AP 2, 6, 10, 14, … is 134? (a) 35th (b) 34th (c) 33rd (d) 36th
  14. 14.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 191 (c) 190 (d) 171
  15. 15.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 41 (b) 294 (c) 312 (d) 588
  16. 16.Which term of the AP 16, 25, 34, 43, … is 205? (a) 24th (b) 23rd (c) 22nd (d) 21st
  17. 17.Which term of the AP 3, 12, 21, 30, … is 291? (a) 35th (b) 34th (c) 33rd (d) 32nd
  18. 18.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 420 (d) 210
  19. 19.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 154 (b) 308 (c) 155 (d) 19
  20. 20.Which term of the AP 7, 14, 21, 28, … is 280? (a) 41st (b) 39th (c) 42nd (d) 40th
  21. 21.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 272 (b) 136 (c) 24 (d) 144
  22. 22.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 85 (c) 70 (d) 140
  23. 23.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 180 (b) 324 (c) 34 (d) 162
  24. 24.What is the 19th term of the AP 11, 15, 19, 23, …? (a) 72 (b) 83 (c) 87 (d) 76
  25. 25.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 225 (b) 230 (c) 450 (d) 45
  26. 26.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 946 (c) 1892 (d) 903
  27. 27.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 33 (b) 25 (c) 27 (d) 26
  28. 28.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 31 (b) 8 (c) 60 (d) 30
  29. 29.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 210 (b) 15 (c) 110 (d) 105
  30. 30.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 100 (b) 50 (c) 16 (d) 53
  31. 31.Which term of the AP 5, 8, 11, 14, … is 92? (a) 30th (b) 32nd (c) 31st (d) 29th
  32. 32.What is the 25th term of the AP 20, 26, 32, 38, …? (a) 150 (b) 164 (c) 170 (d) 144
  33. 33.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 288 (b) 24 (c) 144 (d) 153
  34. 34.What is the 17th term of the AP 6, 12, 18, 24, …? (a) 96 (b) 108 (c) 103 (d) 102
  35. 35.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 43 (b) 40 (c) 14 (d) 80
  36. 36.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 248 (b) 496 (c) 52 (d) 272
  37. 37.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 64 (b) 407 (c) 748 (d) 374
  38. 38.What is the 36th term of the AP 8, 14, 20, 26, …? (a) 224 (b) 216 (c) 210 (d) 218
  39. 39.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 42 (b) 336 (c) 189 (d) 168
  40. 40.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 24 (c) 108 (d) 99

Answer key

  1. 108
  2. 3
  3. 2016
  4. 150
  5. 23
  6. 25
  7. 16
  8. 49
  9. 71
  10. 143
  11. 289
  12. 20
  13. 34th
  14. 190
  15. 294
  16. 22nd
  17. 33rd
  18. 400
  19. 154
  20. 40th
  21. 136
  22. 70
  23. 162
  24. 83
  25. 225
  26. 946
  27. 26
  28. 30
  29. 105
  30. 50
  31. 30th
  32. 164
  33. 144
  34. 102
  35. 40
  36. 248
  37. 374
  38. 218
  39. 168
  40. 99

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