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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 532 · 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 11th term of the AP 9, 11, 13, 15, …? (a) 31 (b) 20 (c) 22 (d) 29
  2. 2.What is the 32nd term of the AP 5, 8, 11, 14, …? (a) 96 (b) 98 (c) 93 (d) 101
  3. 3.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 132 (b) 16 (c) 66 (d) 72
  4. 4.What is the 39th term of the AP 9, 15, 21, 27, …? (a) 234 (b) 237 (c) 228 (d) 243
  5. 5.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72
  6. 6.Which term of the AP 15, 19, 23, 27, … is 47? (a) 9th (b) 10th (c) 11th (d) 8th
  7. 7.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 24 (b) 25 (c) 22 (d) 23
  8. 8.What is the 15th term of the AP 2, 6, 10, 14, …? (a) 58 (b) 56 (c) 60 (d) 62
  9. 9.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 30 (c) 25 (d) 9
  10. 10.What is the 37th term of the AP 6, 10, 14, 18, …? (a) 144 (b) 154 (c) 148 (d) 150
  11. 11.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 297 (b) 45 (c) 550 (d) 275
  12. 12.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 16 (b) 22 (c) 18 (d) 17
  13. 13.What is the 12th term of the AP 2, 9, 16, 23, …? (a) 77 (b) 86 (c) 79 (d) 84
  14. 14.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 256 (b) 136 (c) 128 (d) 23
  15. 15.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 126 (b) 135 (c) 22 (d) 252
  16. 16.What is the missing term in the AP 14, 21, ?, 35, 42? (a) 35 (b) 27 (c) 29 (d) 28
  17. 17.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 161 (b) 41 (c) 322 (d) 182
  18. 18.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 13 (b) 98 (c) 56 (d) 49
  19. 19.What is the 31st term of the AP 10, 16, 22, 28, …? (a) 190 (b) 196 (c) 180 (d) 186
  20. 20.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 26 (b) 28 (c) 27 (d) 32
  21. 21.Which term of the AP 11, 15, 19, 23, … is 139? (a) 35th (b) 34th (c) 32nd (d) 33rd
  22. 22.Which term of the AP 18, 20, 22, 24, … is 56? (a) 28th (b) 21st (c) 19th (d) 20th
  23. 23.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2851 (c) 2775 (d) 2850
  24. 24.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 60 (b) 390 (c) 780 (d) 420
  25. 25.What is the 18th term of the AP 12, 21, 30, 39, …? (a) 174 (b) 162 (c) 153 (d) 165
  26. 26.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 21 (b) 90 (c) 81 (d) 162
  27. 27.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 39 (b) 540 (c) 270 (d) 288
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  29. 29.What is the 40th term of the AP 4, 10, 16, 22, …? (a) 238 (b) 244 (c) 234 (d) 240
  30. 30.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 231 (d) 441
  31. 31.What is the 10th term of the AP 13, 20, 27, 34, …? (a) 70 (b) 76 (c) 83 (d) 63
  32. 32.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 1176 (c) 1225 (d) 2450
  33. 33.What is the 23rd term of the AP 1, 3, 5, 7, …? (a) 44 (b) 45 (c) 47 (d) 46
  34. 34.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 108 (c) 198 (d) 19
  35. 35.What is the 33rd term of the AP 15, 21, 27, 33, …? (a) 213 (b) 207 (c) 198 (d) 192
  36. 36.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 20 (b) 19 (c) 21 (d) 29
  37. 37.What is the 12th term of the AP 13, 18, 23, 28, …? (a) 55 (b) 73 (c) 60 (d) 68
  38. 38.What is the 19th term of the AP 3, 11, 19, 27, …? (a) 144 (b) 155 (c) 147 (d) 152
  39. 39.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 38 (b) 70 (c) 35 (d) 13
  40. 40.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 45 (b) 378 (c) 189 (d) 210

Answer key

  1. 29
  2. 98
  3. 66
  4. 237
  5. 64
  6. 9th
  7. 23
  8. 58
  9. 25
  10. 150
  11. 275
  12. 17
  13. 79
  14. 128
  15. 126
  16. 28
  17. 161
  18. 49
  19. 190
  20. 27
  21. 33rd
  22. 20th
  23. 2850
  24. 390
  25. 165
  26. 81
  27. 270
  28. 100
  29. 238
  30. 441
  31. 76
  32. 1225
  33. 45
  34. 99
  35. 207
  36. 20
  37. 68
  38. 147
  39. 35
  40. 189

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