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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 212 · 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 30th term of the AP 6, 8, 10, 12, …? (a) 60 (b) 58 (c) 64 (d) 66
  2. 2.Which term of the AP 7, 9, 11, 13, … is 31? (a) 15th (b) 12th (c) 14th (d) 13th
  3. 3.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 192 (b) 384 (c) 38 (d) 208
  4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 17 (d) 45
  5. 5.What is the 30th term of the AP 5, 8, 11, 14, …? (a) 87 (b) 92 (c) 95 (d) 90
  6. 6.What is the 25th term of the AP 17, 19, 21, 23, …? (a) 67 (b) 50 (c) 48 (d) 65
  7. 7.What is the 26th term of the AP 13, 17, 21, 25, …? (a) 113 (b) 100 (c) 117 (d) 104
  8. 8.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3321 (c) 3403 (d) 3362
  9. 9.What is the 34th term of the AP 20, 23, 26, 29, …? (a) 122 (b) 119 (c) 99 (d) 102
  10. 10.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 4006 (c) 3916 (d) 4005
  11. 11.What is the 26th term of the AP 18, 24, 30, 36, …? (a) 174 (b) 168 (c) 156 (d) 150
  12. 12.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  13. 13.Which term of the AP 7, 9, 11, 13, … is 65? (a) 30th (b) 32nd (c) 31st (d) 29th
  14. 14.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 361 (d) 37
  15. 15.What is the 10th term of the AP 12, 17, 22, 27, …? (a) 57 (b) 62 (c) 50 (d) 45
  16. 16.What is the 29th term of the AP 7, 13, 19, 25, …? (a) 174 (b) 175 (c) 168 (d) 181
  17. 17.Which term of the AP 12, 21, 30, 39, … is 174? (a) 18th (b) 20th (c) 21st (d) 19th
  18. 18.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 33 (b) 390 (c) 195 (d) 210
  19. 19.What is the 16th term of the AP 10, 15, 20, 25, …? (a) 85 (b) 75 (c) 80 (d) 90
  20. 20.What is the 12th term of the AP 1, 4, 7, 10, …? (a) 37 (b) 36 (c) 33 (d) 34
  21. 21.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2851 (c) 2850 (d) 2775
  22. 22.What is the 16th term of the AP 15, 18, 21, 24, …? (a) 45 (b) 48 (c) 60 (d) 63
  23. 23.What is the missing term in the AP 15, 20, ?, 30, 35? (a) 25 (b) 30 (c) 24 (d) 26
  24. 24.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 230 (b) 41 (c) 460 (d) 250
  25. 25.What is the 22nd term of the AP 5, 10, 15, 20, …? (a) 115 (b) 111 (c) 105 (d) 110
  26. 26.What is the 29th term of the AP 14, 23, 32, 41, …? (a) 266 (b) 252 (c) 261 (d) 275
  27. 27.What is the 11th term of the AP 18, 22, 26, 30, …? (a) 44 (b) 58 (c) 62 (d) 40
  28. 28.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 20 (b) 19 (c) 18 (d) 17
  29. 29.What is the 39th term of the AP 19, 24, 29, 34, …? (a) 209 (b) 195 (c) 214 (d) 190
  30. 30.What is the 19th term of the AP 6, 9, 12, 15, …? (a) 60 (b) 57 (c) 54 (d) 63
  31. 31.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 85 (b) 26 (c) 140 (d) 70
  32. 32.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  33. 33.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 78 (b) 12 (c) 77 (d) 154
  34. 34.Which term of the AP 12, 18, 24, 30, … is 102? (a) 15th (b) 16th (c) 18th (d) 17th
  35. 35.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 13 (b) 70 (c) 38 (d) 35
  36. 36.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1352 (c) 1378 (d) 2756
  37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  38. 38.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 324 (b) 165 (c) 162 (d) 30
  39. 39.What is the missing term in the AP 10, ?, 18, 22, 26? (a) 18 (b) 14 (c) 15 (d) 13
  40. 40.What is the 23rd term of the AP 20, 26, 32, 38, …? (a) 132 (b) 138 (c) 158 (d) 152

Answer key

  1. 64
  2. 13th
  3. 192
  4. 81
  5. 92
  6. 65
  7. 113
  8. 3403
  9. 119
  10. 4005
  11. 168
  12. 289
  13. 30th
  14. 361
  15. 57
  16. 175
  17. 19th
  18. 195
  19. 85
  20. 34
  21. 2850
  22. 60
  23. 25
  24. 230
  25. 110
  26. 266
  27. 58
  28. 18
  29. 209
  30. 60
  31. 70
  32. 625
  33. 77
  34. 16th
  35. 35
  36. 1378
  37. 144
  38. 162
  39. 14
  40. 152

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