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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 129 · 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 the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 231 (d) 462
  2. 2.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 45 (d) 552
  3. 3.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 65 (b) 900 (c) 480 (d) 450
  4. 4.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 105 (c) 210 (d) 98
  5. 5.What is the 35th term of the AP 19, 25, 31, 37, …? (a) 229 (b) 210 (c) 223 (d) 204
  6. 6.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 3487 (c) 6972 (d) 3486
  7. 7.What is the 17th term of the AP 1, 10, 19, 28, …? (a) 153 (b) 145 (c) 144 (d) 154
  8. 8.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 294 (b) 168 (c) 147 (d) 39
  9. 9.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 153 (b) 306 (c) 156 (d) 29
  10. 10.What is the missing term in the AP 12, 17, ?, 27, 32? (a) 22 (b) 27 (c) 23 (d) 21
  11. 11.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 78 (b) 81 (c) 92 (d) 89
  12. 12.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 231 (c) 242 (d) 506
  13. 13.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 504 (c) 252 (d) 264
  14. 14.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 250 (b) 125 (c) 130 (d) 17
  15. 15.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 814 (b) 67 (c) 440 (d) 407
  16. 16.Which term of the AP 8, 17, 26, 35, … is 134? (a) 17th (b) 15th (c) 14th (d) 16th
  17. 17.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 15 (c) 16 (d) 5
  18. 18.What is the 39th term of the AP 17, 22, 27, 32, …? (a) 207 (b) 190 (c) 212 (d) 195
  19. 19.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 3741 (c) 3829 (d) 7656
  20. 20.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 240 (b) 444 (c) 35 (d) 222
  21. 21.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 480 (b) 260 (c) 42 (d) 240
  22. 22.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 30 (b) 220 (c) 231 (d) 440
  23. 23.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 38 (b) 506 (c) 253 (d) 256
  24. 24.What is the 12th term of the AP 8, 12, 16, 20, …? (a) 56 (b) 52 (c) 48 (d) 44
  25. 25.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2346 (c) 2278 (d) 2312
  26. 26.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 154 (d) 136
  27. 27.Which term of the AP 17, 22, 27, 32, … is 127? (a) 22nd (b) 25th (c) 24th (d) 23rd
  28. 28.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 12 (b) 77 (c) 78 (d) 154
  29. 29.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 11 (b) 15 (c) 12 (d) 13
  30. 30.What is the 33rd term of the AP 17, 24, 31, 38, …? (a) 224 (b) 241 (c) 231 (d) 248
  31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 841 (d) 435
  32. 32.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 480 (c) 31 (d) 240
  33. 33.What is the 33rd term of the AP 18, 21, 24, 27, …? (a) 96 (b) 117 (c) 99 (d) 114
  34. 34.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 600 (c) 288 (d) 276
  35. 35.What is the missing term in the AP 3, 8, 13, ?, 23? (a) 18 (b) 17 (c) 19 (d) 23
  36. 36.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 196 (b) 217 (c) 392 (d) 46
  37. 37.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 17 (b) 22 (c) 18 (d) 16
  38. 38.What is the missing term in the AP 10, 15, 20, ?, 30? (a) 24 (b) 26 (c) 25 (d) 30
  39. 39.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 38 (b) 47 (c) 37 (d) 39
  40. 40.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 19 (b) 17 (c) 22 (d) 18

Answer key

  1. 441
  2. 529
  3. 450
  4. 105
  5. 223
  6. 3486
  7. 145
  8. 147
  9. 153
  10. 22
  11. 89
  12. 253
  13. 252
  14. 125
  15. 407
  16. 15th
  17. 15
  18. 207
  19. 3828
  20. 222
  21. 240
  22. 220
  23. 253
  24. 52
  25. 2346
  26. 153
  27. 23rd
  28. 77
  29. 12
  30. 241
  31. 841
  32. 240
  33. 114
  34. 300
  35. 18
  36. 196
  37. 17
  38. 25
  39. 38
  40. 18

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