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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 823 · 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 23rd term of the AP 20, 23, 26, 29, …? (a) 66 (b) 69 (c) 86 (d) 89
  2. 2.What is the 39th term of the AP 19, 24, 29, 34, …? (a) 195 (b) 190 (c) 209 (d) 214
  3. 3.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 30 (b) 105 (c) 200 (d) 100
  4. 4.What is the 10th term of the AP 1, 9, 17, 25, …? (a) 81 (b) 72 (c) 80 (d) 73
  5. 5.What is the missing term in the AP 8, 11, ?, 17, 20? (a) 14 (b) 15 (c) 13 (d) 17
  6. 6.Which term of the AP 5, 8, 11, 14, … is 32? (a) 12th (b) 11th (c) 10th (d) 9th
  7. 7.What is the 31st term of the AP 4, 11, 18, 25, …? (a) 221 (b) 217 (c) 210 (d) 214
  8. 8.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 248 (b) 243 (c) 47 (d) 486
  9. 9.What is the 22nd term of the AP 8, 14, 20, 26, …? (a) 126 (b) 140 (c) 134 (d) 132
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  11. 11.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 224 (b) 408 (c) 43 (d) 204
  12. 12.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 144 (b) 128 (c) 30 (d) 256
  13. 13.What is the 31st term of the AP 4, 12, 20, 28, …? (a) 244 (b) 240 (c) 248 (d) 252
  14. 14.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 100 (b) 18 (c) 60 (d) 50
  15. 15.What is the 17th term of the AP 13, 16, 19, 22, …? (a) 51 (b) 48 (c) 61 (d) 64
  16. 16.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3487 (c) 3403 (d) 3486
  17. 17.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 70 (b) 65 (c) 130 (d) 17
  18. 18.What is the 36th term of the AP 4, 13, 22, 31, …? (a) 319 (b) 315 (c) 324 (d) 328
  19. 19.What is the 36th term of the AP 7, 12, 17, 22, …? (a) 187 (b) 182 (c) 175 (d) 180
  20. 20.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 780 (c) 820 (d) 800
  21. 21.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 110 (d) 100
  22. 22.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 30 (b) 120 (c) 105 (d) 210
  23. 23.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 132 (c) 121 (d) 21
  24. 24.What is the 23rd term of the AP 16, 25, 34, 43, …? (a) 207 (b) 198 (c) 214 (d) 223
  25. 25.What is the 29th term of the AP 7, 16, 25, 34, …? (a) 261 (b) 259 (c) 252 (d) 268
  26. 26.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 17 (b) 15 (c) 14 (d) 13
  27. 27.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 33 (c) 289 (d) 153
  28. 28.What is the sum of all the whole numbers from 1 to 79? (a) 3081 (b) 6320 (c) 3160 (d) 3161
  29. 29.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 147 (b) 28 (c) 144 (d) 288
  30. 30.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 18 (b) 19 (c) 22 (d) 17
  31. 31.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 14 (b) 12 (c) 19 (d) 13
  32. 32.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 130 (b) 75 (c) 21 (d) 65
  33. 33.Which term of the AP 14, 18, 22, 26, … is 74? (a) 17th (b) 16th (c) 15th (d) 18th
  34. 34.What is the 33rd term of the AP 10, 14, 18, 22, …? (a) 132 (b) 128 (c) 138 (d) 142
  35. 35.What is the 15th term of the AP 17, 25, 33, 41, …? (a) 112 (b) 137 (c) 120 (d) 129
  36. 36.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 385 (b) 62 (c) 704 (d) 352
  37. 37.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 722 (c) 741 (d) 703
  38. 38.Which term of the AP 6, 14, 22, 30, … is 206? (a) 25th (b) 26th (c) 27th (d) 28th
  39. 39.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 756 (d) 53
  40. 40.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 22 (b) 25 (c) 21 (d) 20

Answer key

  1. 86
  2. 209
  3. 100
  4. 73
  5. 14
  6. 10th
  7. 214
  8. 243
  9. 134
  10. 256
  11. 204
  12. 128
  13. 244
  14. 50
  15. 61
  16. 3486
  17. 65
  18. 319
  19. 182
  20. 820
  21. 100
  22. 105
  23. 121
  24. 214
  25. 259
  26. 14
  27. 289
  28. 3160
  29. 144
  30. 18
  31. 13
  32. 65
  33. 16th
  34. 138
  35. 129
  36. 352
  37. 741
  38. 26th
  39. 729
  40. 21

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