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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 283 · 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 sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 496 (d) 992
  2. 2.What is the 21st term of the AP 4, 11, 18, 25, …? (a) 144 (b) 147 (c) 140 (d) 151
  3. 3.Which term of the AP 16, 21, 26, 31, … is 111? (a) 21st (b) 20th (c) 19th (d) 22nd
  4. 4.What is the 14th term of the AP 19, 23, 27, 31, …? (a) 52 (b) 71 (c) 75 (d) 56
  5. 5.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 210 (b) 24 (c) 108 (d) 105
  6. 6.Which term of the AP 13, 20, 27, 34, … is 230? (a) 33rd (b) 31st (c) 34th (d) 32nd
  7. 7.What is the 31st term of the AP 17, 26, 35, 44, …? (a) 279 (b) 296 (c) 287 (d) 270
  8. 8.Which term of the AP 9, 13, 17, 21, … is 69? (a) 17th (b) 16th (c) 15th (d) 18th
  9. 9.What is the 25th term of the AP 4, 11, 18, 25, …? (a) 172 (b) 179 (c) 175 (d) 168
  10. 10.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 72 (c) 156 (d) 66
  11. 11.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 379 (c) 351 (d) 378
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 729 (d) 378
  13. 13.What is the 35th term of the AP 4, 9, 14, 19, …? (a) 179 (b) 170 (c) 175 (d) 174
  14. 14.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 506 (d) 253
  15. 15.What is the 25th term of the AP 17, 25, 33, 41, …? (a) 192 (b) 209 (c) 217 (d) 200
  16. 16.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 138 (c) 17 (d) 144
  17. 17.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 147 (b) 294 (c) 161 (d) 33
  18. 18.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 11 (c) 36 (d) 42
  19. 19.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 9 (b) 48 (c) 88 (d) 44
  20. 20.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 15 (b) 21 (c) 17 (d) 16
  21. 21.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 297 (c) 319 (d) 47
  22. 22.What is the 16th term of the AP 1, 4, 7, 10, …? (a) 46 (b) 49 (c) 45 (d) 48
  23. 23.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 13 (c) 90 (d) 180
  24. 24.What is the 36th term of the AP 10, 16, 22, 28, …? (a) 226 (b) 220 (c) 216 (d) 210
  25. 25.What is the sum of all the whole numbers from 1 to 89? (a) 4006 (b) 3916 (c) 4005 (d) 8010
  26. 26.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 816 (c) 408 (d) 444
  27. 27.Which term of the AP 5, 8, 11, 14, … is 77? (a) 24th (b) 26th (c) 27th (d) 25th
  28. 28.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 200 (d) 190
  29. 29.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 162 (b) 324 (c) 26 (d) 171
  30. 30.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 36 (c) 66 (d) 33
  31. 31.Which term of the AP 7, 9, 11, 13, … is 33? (a) 15th (b) 16th (c) 14th (d) 13th
  32. 32.What is the 21st term of the AP 14, 21, 28, 35, …? (a) 147 (b) 161 (c) 140 (d) 154
  33. 33.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 109 (b) 108 (c) 16 (d) 216
  34. 34.What is the 29th term of the AP 4, 12, 20, 28, …? (a) 224 (b) 236 (c) 232 (d) 228
  35. 35.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 35 (c) 36 (d) 9
  36. 36.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 140 (b) 80 (c) 22 (d) 70
  37. 37.What is the 18th term of the AP 6, 15, 24, 33, …? (a) 168 (b) 162 (c) 153 (d) 159
  38. 38.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 91 (c) 210 (d) 98
  39. 39.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 256 (b) 30 (c) 144 (d) 128
  40. 40.What is the 29th term of the AP 11, 20, 29, 38, …? (a) 261 (b) 272 (c) 263 (d) 252

Answer key

  1. 496
  2. 144
  3. 20th
  4. 71
  5. 105
  6. 32nd
  7. 287
  8. 16th
  9. 172
  10. 78
  11. 378
  12. 729
  13. 174
  14. 484
  15. 209
  16. 138
  17. 147
  18. 36
  19. 44
  20. 16
  21. 297
  22. 46
  23. 90
  24. 220
  25. 4005
  26. 408
  27. 25th
  28. 210
  29. 162
  30. 33
  31. 14th
  32. 154
  33. 108
  34. 228
  35. 35
  36. 70
  37. 159
  38. 105
  39. 128
  40. 263

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