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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 228 · 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 24th term of the AP 7, 13, 19, 25, …? (a) 138 (b) 151 (c) 145 (d) 144
  2. 2.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 5112 (c) 2556 (d) 2557
  3. 3.Which term of the AP 10, 12, 14, 16, … is 36? (a) 13th (b) 14th (c) 15th (d) 18th
  4. 4.What is the 35th term of the AP 19, 27, 35, 43, …? (a) 291 (b) 299 (c) 272 (d) 280
  5. 5.Which term of the AP 8, 16, 24, 32, … is 256? (a) 32nd (b) 34th (c) 31st (d) 33rd
  6. 6.What is the 34th term of the AP 18, 27, 36, 45, …? (a) 324 (b) 297 (c) 306 (d) 315
  7. 7.What is the 17th term of the AP 9, 18, 27, 36, …? (a) 154 (b) 153 (c) 162 (d) 144
  8. 8.What is the 38th term of the AP 18, 20, 22, 24, …? (a) 76 (b) 74 (c) 92 (d) 94
  9. 9.What is the 13th term of the AP 11, 13, 15, 17, …? (a) 24 (b) 26 (c) 35 (d) 37
  10. 10.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 6 (b) 8 (c) 7 (d) 9
  11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  12. 12.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 252 (c) 504 (d) 48
  13. 13.What is the 17th term of the AP 20, 28, 36, 44, …? (a) 136 (b) 156 (c) 128 (d) 148
  14. 14.Which term of the AP 14, 20, 26, 32, … is 212? (a) 35th (b) 36th (c) 34th (d) 33rd
  15. 15.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 630 (c) 1332 (d) 648
  16. 16.What is the missing term in the AP 13, 16, ?, 22, 25? (a) 18 (b) 20 (c) 22 (d) 19
  17. 17.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 357 (b) 704 (c) 57 (d) 352
  18. 18.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 45 (b) 48 (c) 90 (d) 15
  19. 19.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 212 (b) 232 (c) 424 (d) 44
  20. 20.Which term of the AP 11, 20, 29, 38, … is 173? (a) 18th (b) 19th (c) 20th (d) 21st
  21. 21.What is the 31st term of the AP 3, 11, 19, 27, …? (a) 243 (b) 251 (c) 248 (d) 240
  22. 22.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 930 (c) 59 (d) 465
  23. 23.Which term of the AP 5, 9, 13, 17, … is 53? (a) 15th (b) 14th (c) 13th (d) 12th
  24. 24.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 61 (b) 682 (c) 374 (d) 341
  25. 25.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 10 (b) 8 (c) 7 (d) 9
  26. 26.What is the 29th term of the AP 6, 15, 24, 33, …? (a) 258 (b) 252 (c) 267 (d) 261
  27. 27.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1891 (c) 1953 (d) 3906
  28. 28.What is the missing term in the AP 4, 12, 20, ?, 36? (a) 27 (b) 28 (c) 29 (d) 36
  29. 29.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 41 (b) 208 (c) 188 (d) 376
  30. 30.What is the 34th term of the AP 9, 12, 15, 18, …? (a) 111 (b) 99 (c) 108 (d) 102
  31. 31.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 3081 (c) 3042 (d) 6162
  32. 32.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 256 (d) 31
  33. 33.What is the missing term in the AP 9, 16, ?, 30, 37? (a) 22 (b) 24 (c) 30 (d) 23
  34. 34.What is the 20th term of the AP 3, 11, 19, 27, …? (a) 160 (b) 152 (c) 155 (d) 163
  35. 35.What is the 23rd term of the AP 12, 14, 16, 18, …? (a) 46 (b) 44 (c) 56 (d) 58
  36. 36.What is the 19th term of the AP 15, 19, 23, 27, …? (a) 87 (b) 91 (c) 72 (d) 76
  37. 37.What is the 29th term of the AP 5, 13, 21, 29, …? (a) 224 (b) 237 (c) 229 (d) 232
  38. 38.What is the 37th term of the AP 10, 12, 14, 16, …? (a) 84 (b) 74 (c) 82 (d) 72
  39. 39.What is the 13th term of the AP 15, 19, 23, 27, …? (a) 48 (b) 63 (c) 52 (d) 67
  40. 40.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 12 (b) 14 (c) 15 (d) 13

Answer key

  1. 145
  2. 2556
  3. 14th
  4. 291
  5. 32nd
  6. 315
  7. 153
  8. 92
  9. 35
  10. 7
  11. 36
  12. 252
  13. 148
  14. 34th
  15. 666
  16. 19
  17. 352
  18. 45
  19. 212
  20. 19th
  21. 243
  22. 900
  23. 13th
  24. 341
  25. 8
  26. 258
  27. 1953
  28. 28
  29. 188
  30. 108
  31. 3081
  32. 256
  33. 23
  34. 155
  35. 56
  36. 87
  37. 229
  38. 82
  39. 63
  40. 13

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