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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 925 · 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 32nd term of the AP 8, 10, 12, 14, …? (a) 72 (b) 70 (c) 64 (d) 62
  2. 2.What is the 11th term of the AP 8, 10, 12, 14, …? (a) 28 (b) 30 (c) 22 (d) 20
  3. 3.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 46 (b) 49 (c) 45 (d) 42
  4. 4.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1176 (c) 1226 (d) 1225
  5. 5.Which term of the AP 9, 15, 21, 27, … is 111? (a) 17th (b) 19th (c) 20th (d) 18th
  6. 6.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 372 (b) 192 (c) 21 (d) 186
  7. 7.Which term of the AP 8, 13, 18, 23, … is 143? (a) 27th (b) 28th (c) 30th (d) 29th
  8. 8.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 9 (c) 30 (d) 25
  9. 9.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 37 (b) 36 (c) 35 (d) 43
  10. 10.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 33 (b) 34 (c) 35 (d) 41
  11. 11.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 33 (b) 28 (c) 26 (d) 27
  12. 12.Which term of the AP 11, 16, 21, 26, … is 46? (a) 7th (b) 10th (c) 8th (d) 9th
  13. 13.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 29 (b) 228 (c) 126 (d) 114
  14. 14.What is the 39th term of the AP 9, 12, 15, 18, …? (a) 117 (b) 114 (c) 123 (d) 126
  15. 15.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 189 (b) 45 (c) 210 (d) 378
  16. 16.What is the 34th term of the AP 2, 8, 14, 20, …? (a) 204 (b) 198 (c) 206 (d) 200
  17. 17.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 144 (b) 17 (c) 78 (d) 72
  18. 18.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 496 (b) 272 (c) 248 (d) 52
  19. 19.What is the 38th term of the AP 1, 4, 7, 10, …? (a) 114 (b) 112 (c) 115 (d) 111
  20. 20.Which term of the AP 10, 15, 20, 25, … is 130? (a) 27th (b) 25th (c) 26th (d) 24th
  21. 21.What is the 33rd term of the AP 16, 22, 28, 34, …? (a) 214 (b) 198 (c) 192 (d) 208
  22. 22.What is the 21st term of the AP 1, 6, 11, 16, …? (a) 105 (b) 100 (c) 106 (d) 101
  23. 23.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 105 (b) 120 (c) 210 (d) 30
  24. 24.What is the 25th term of the AP 20, 24, 28, 32, …? (a) 96 (b) 116 (c) 100 (d) 120
  25. 25.What is the 10th term of the AP 19, 23, 27, 31, …? (a) 59 (b) 40 (c) 55 (d) 36
  26. 26.What is the missing term in the AP 16, 19, ?, 25, 28? (a) 23 (b) 25 (c) 21 (d) 22
  27. 27.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 6 (b) 5 (c) 4 (d) 3
  28. 28.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 306 (d) 33
  29. 29.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 190 (c) 191 (d) 380
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78
  31. 31.What is the missing term in the AP 6, 9, ?, 15, 18? (a) 11 (b) 12 (c) 15 (d) 13
  32. 32.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 165 (b) 330 (c) 25 (d) 176
  33. 33.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4561 (c) 9120 (d) 4465
  34. 34.What is the 33rd term of the AP 5, 7, 9, 11, …? (a) 71 (b) 69 (c) 66 (d) 64
  35. 35.What is the 20th term of the AP 17, 22, 27, 32, …? (a) 117 (b) 100 (c) 95 (d) 112
  36. 36.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 42 (b) 196 (c) 216 (d) 392
  37. 37.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 65 (b) 23 (c) 130 (d) 70
  38. 38.What is the 32nd term of the AP 5, 11, 17, 23, …? (a) 186 (b) 197 (c) 191 (d) 192
  39. 39.What is the 34th term of the AP 10, 12, 14, 16, …? (a) 68 (b) 78 (c) 76 (d) 66
  40. 40.What is the 23rd term of the AP 3, 5, 7, 9, …? (a) 44 (b) 46 (c) 49 (d) 47

Answer key

  1. 70
  2. 28
  3. 46
  4. 1225
  5. 18th
  6. 186
  7. 28th
  8. 25
  9. 36
  10. 34
  11. 27
  12. 8th
  13. 114
  14. 123
  15. 189
  16. 200
  17. 72
  18. 248
  19. 112
  20. 25th
  21. 208
  22. 101
  23. 105
  24. 116
  25. 55
  26. 22
  27. 4
  28. 289
  29. 190
  30. 144
  31. 12
  32. 165
  33. 4560
  34. 69
  35. 112
  36. 196
  37. 65
  38. 191
  39. 76
  40. 47

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