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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 838 · 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 all the whole numbers from 1 to 33? (a) 528 (b) 1122 (c) 562 (d) 561
  2. 2.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  3. 3.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3655 (c) 3741 (d) 7482
  4. 4.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 28 (b) 133 (c) 136 (d) 266
  5. 5.Which term of the AP 16, 24, 32, 40, … is 320? (a) 41st (b) 39th (c) 38th (d) 40th
  6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  7. 7.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 54 (b) 48 (c) 96 (d) 13
  8. 8.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 18 (b) 17 (c) 20 (d) 16
  9. 9.What is the 30th term of the AP 4, 11, 18, 25, …? (a) 214 (b) 210 (c) 203 (d) 207
  10. 10.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 99 (b) 15 (c) 100 (d) 198
  11. 11.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 22 (b) 26 (c) 21 (d) 20
  12. 12.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 88 (b) 80 (c) 17 (d) 160
  13. 13.Which term of the AP 19, 23, 27, 31, … is 79? (a) 18th (b) 15th (c) 16th (d) 17th
  14. 14.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 18 (b) 20 (c) 19 (d) 27
  15. 15.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 60 (b) 120 (c) 22 (d) 65
  16. 16.What is the 33rd term of the AP 10, 18, 26, 34, …? (a) 266 (b) 264 (c) 274 (d) 256
  17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 9 (d) 30
  18. 18.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  19. 19.Which term of the AP 14, 20, 26, 32, … is 128? (a) 19th (b) 20th (c) 21st (d) 22nd
  20. 20.What is the 39th term of the AP 9, 18, 27, 36, …? (a) 360 (b) 351 (c) 352 (d) 342
  21. 21.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 168 (b) 147 (c) 39 (d) 294
  22. 22.Which term of the AP 14, 23, 32, 41, … is 77? (a) 7th (b) 9th (c) 10th (d) 8th
  23. 23.What is the missing term in the AP 11, 14, ?, 20, 23? (a) 16 (b) 17 (c) 20 (d) 18
  24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
  25. 25.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 60 (b) 8 (c) 30 (d) 31
  26. 26.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 192 (b) 114 (c) 96 (d) 31
  27. 27.What is the 22nd term of the AP 18, 21, 24, 27, …? (a) 84 (b) 63 (c) 66 (d) 81
  28. 28.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 15 (b) 20 (c) 13 (d) 14
  29. 29.What is the 17th term of the AP 16, 24, 32, 40, …? (a) 136 (b) 128 (c) 144 (d) 152
  30. 30.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  31. 31.What is the 16th term of the AP 17, 24, 31, 38, …? (a) 129 (b) 122 (c) 105 (d) 112
  32. 32.What is the 39th term of the AP 3, 6, 9, 12, …? (a) 117 (b) 118 (c) 114 (d) 120
  33. 33.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 81 (b) 82 (c) 13 (d) 162
  34. 34.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 2146 (c) 4290 (d) 2080
  35. 35.Which term of the AP 5, 13, 21, 29, … is 301? (a) 38th (b) 37th (c) 40th (d) 39th
  36. 36.What is the 20th term of the AP 5, 9, 13, 17, …? (a) 80 (b) 85 (c) 76 (d) 81
  37. 37.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 19 (b) 70 (c) 140 (d) 73
  38. 38.What is the 25th term of the AP 20, 28, 36, 44, …? (a) 192 (b) 200 (c) 220 (d) 212
  39. 39.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 289 (d) 306
  40. 40.What is the 19th term of the AP 19, 22, 25, 28, …? (a) 54 (b) 57 (c) 76 (d) 73

Answer key

  1. 561
  2. 784
  3. 3741
  4. 133
  5. 39th
  6. 441
  7. 48
  8. 17
  9. 207
  10. 99
  11. 21
  12. 80
  13. 16th
  14. 19
  15. 60
  16. 266
  17. 25
  18. 144
  19. 20th
  20. 351
  21. 147
  22. 8th
  23. 17
  24. 400
  25. 30
  26. 96
  27. 81
  28. 14
  29. 144
  30. 729
  31. 122
  32. 117
  33. 81
  34. 2145
  35. 38th
  36. 81
  37. 70
  38. 212
  39. 289
  40. 73

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