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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 369 · 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 27th term of the AP 9, 15, 21, 27, …? (a) 156 (b) 165 (c) 162 (d) 171
  2. 2.What is the 29th term of the AP 3, 8, 13, 18, …? (a) 140 (b) 148 (c) 143 (d) 145
  3. 3.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 770 (b) 390 (c) 385 (d) 60
  4. 4.What is the 29th term of the AP 12, 14, 16, 18, …? (a) 70 (b) 68 (c) 56 (d) 58
  5. 5.What is the 32nd term of the AP 5, 14, 23, 32, …? (a) 279 (b) 288 (c) 293 (d) 284
  6. 6.Which term of the AP 8, 15, 22, 29, … is 274? (a) 40th (b) 39th (c) 41st (d) 38th
  7. 7.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 73 (b) 144 (c) 12 (d) 72
  8. 8.What is the 22nd term of the AP 7, 9, 11, 13, …? (a) 49 (b) 51 (c) 42 (d) 44
  9. 9.What is the missing term in the AP 11, 16, 21, ?, 31? (a) 27 (b) 25 (c) 26 (d) 31
  10. 10.What is the 36th term of the AP 18, 21, 24, 27, …? (a) 126 (b) 108 (c) 105 (d) 123
  11. 11.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 18 (b) 176 (c) 88 (d) 96
  12. 12.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 232 (b) 116 (c) 25 (d) 128
  13. 13.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 84 (b) 20 (c) 75 (d) 150
  14. 14.Which term of the AP 5, 12, 19, 26, … is 215? (a) 30th (b) 32nd (c) 33rd (d) 31st
  15. 15.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 253 (c) 242 (d) 231
  16. 16.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 43 (b) 250 (c) 270 (d) 500
  17. 17.Which term of the AP 14, 21, 28, 35, … is 70? (a) 11th (b) 10th (c) 8th (d) 9th
  18. 18.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 506 (d) 484
  19. 19.What is the 21st term of the AP 19, 28, 37, 46, …? (a) 189 (b) 180 (c) 199 (d) 208
  20. 20.What is the 19th term of the AP 9, 11, 13, 15, …? (a) 47 (b) 38 (c) 45 (d) 36
  21. 21.What is the 20th term of the AP 8, 15, 22, 29, …? (a) 133 (b) 148 (c) 141 (d) 140
  22. 22.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 580 (b) 56 (c) 290 (d) 320
  23. 23.Which term of the AP 17, 24, 31, 38, … is 129? (a) 18th (b) 19th (c) 17th (d) 16th
  24. 24.What is the 10th term of the AP 9, 14, 19, 24, …? (a) 54 (b) 50 (c) 45 (d) 59
  25. 25.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 17 (b) 81 (c) 90 (d) 162
  26. 26.What is the 26th term of the AP 13, 20, 27, 34, …? (a) 188 (b) 182 (c) 175 (d) 195
  27. 27.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 63 (b) 390 (c) 720 (d) 360
  28. 28.What is the 14th term of the AP 20, 29, 38, 47, …? (a) 126 (b) 146 (c) 137 (d) 117
  29. 29.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 105 (b) 90 (c) 30 (d) 180
  30. 30.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 529 (d) 276
  31. 31.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 240 (b) 480 (c) 252 (d) 31
  32. 32.What is the 16th term of the AP 13, 15, 17, 19, …? (a) 32 (b) 43 (c) 45 (d) 30
  33. 33.What is the 27th term of the AP 18, 25, 32, 39, …? (a) 189 (b) 207 (c) 182 (d) 200
  34. 34.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3487 (c) 3403 (d) 3486
  35. 35.What is the 16th term of the AP 20, 24, 28, 32, …? (a) 84 (b) 80 (c) 60 (d) 64
  36. 36.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 660 (b) 330 (c) 352 (d) 50
  37. 37.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 319 (b) 638 (c) 49 (d) 341
  38. 38.What is the 34th term of the AP 10, 16, 22, 28, …? (a) 198 (b) 204 (c) 214 (d) 208
  39. 39.What is the 30th term of the AP 7, 13, 19, 25, …? (a) 187 (b) 180 (c) 174 (d) 181
  40. 40.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1431 (c) 1432 (d) 2862

Answer key

  1. 165
  2. 143
  3. 385
  4. 68
  5. 284
  6. 39th
  7. 72
  8. 49
  9. 26
  10. 123
  11. 88
  12. 116
  13. 75
  14. 31st
  15. 253
  16. 250
  17. 9th
  18. 484
  19. 199
  20. 45
  21. 141
  22. 290
  23. 17th
  24. 54
  25. 81
  26. 188
  27. 360
  28. 137
  29. 90
  30. 529
  31. 240
  32. 43
  33. 200
  34. 3486
  35. 80
  36. 330
  37. 319
  38. 208
  39. 181
  40. 1431

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