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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 437 · 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 21st term of the AP 17, 26, 35, 44, …? (a) 206 (b) 189 (c) 180 (d) 197
  2. 2.What is the 12th term of the AP 15, 20, 25, 30, …? (a) 70 (b) 55 (c) 75 (d) 60
  3. 3.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 325 (c) 326 (d) 300
  4. 4.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 22 (b) 126 (c) 252 (d) 135
  5. 5.What is the 21st term of the AP 6, 8, 10, 12, …? (a) 42 (b) 48 (c) 40 (d) 46
  6. 6.What is the 34th term of the AP 4, 12, 20, 28, …? (a) 264 (b) 276 (c) 272 (d) 268
  7. 7.What is the 13th term of the AP 13, 20, 27, 34, …? (a) 97 (b) 91 (c) 104 (d) 84
  8. 8.What is the missing term in the AP 19, ?, 25, 28, 31? (a) 23 (b) 22 (c) 25 (d) 21
  9. 9.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1431 (c) 2970 (d) 1485
  10. 10.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 50 (b) 12 (c) 51 (d) 100
  11. 11.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 324 (b) 162 (c) 34 (d) 180
  12. 12.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 366 (b) 396 (c) 732 (d) 58
  13. 13.Which term of the AP 1, 8, 15, 22, … is 218? (a) 33rd (b) 34th (c) 32nd (d) 31st
  14. 14.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  15. 15.What is the 23rd term of the AP 3, 11, 19, 27, …? (a) 179 (b) 187 (c) 176 (d) 184
  16. 16.What is the 10th term of the AP 8, 11, 14, 17, …? (a) 35 (b) 30 (c) 27 (d) 38
  17. 17.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 23 (b) 25 (c) 22 (d) 24
  18. 18.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 26 (b) 162 (c) 324 (d) 171
  19. 19.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 729 (d) 378
  20. 20.What is the 30th term of the AP 12, 18, 24, 30, …? (a) 192 (b) 174 (c) 180 (d) 186
  21. 21.What is the 30th term of the AP 16, 18, 20, 22, …? (a) 74 (b) 58 (c) 60 (d) 76
  22. 22.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  23. 23.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 28 (b) 27 (c) 26 (d) 35
  24. 24.Which term of the AP 10, 14, 18, 22, … is 130? (a) 32nd (b) 33rd (c) 31st (d) 30th
  25. 25.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1035 (c) 1036 (d) 2070
  26. 26.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3698 (c) 3655 (d) 3741
  27. 27.What is the 17th term of the AP 2, 7, 12, 17, …? (a) 85 (b) 87 (c) 80 (d) 82
  28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 25 (d) 9
  29. 29.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 10 (b) 12 (c) 16 (d) 11
  30. 30.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 630 (c) 631 (d) 1260
  31. 31.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3828 (c) 7832 (d) 3916
  32. 32.Which term of the AP 6, 15, 24, 33, … is 87? (a) 12th (b) 11th (c) 10th (d) 9th
  33. 33.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 24 (b) 21 (c) 6 (d) 42
  34. 34.What is the 32nd term of the AP 19, 27, 35, 43, …? (a) 248 (b) 275 (c) 256 (d) 267
  35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 153 (d) 289
  36. 36.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 360 (b) 190 (c) 180 (d) 27
  37. 37.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 44 (b) 9 (c) 88 (d) 48
  38. 38.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 224 (b) 25 (c) 115 (d) 112
  39. 39.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 105 (b) 24 (c) 210 (d) 108
  40. 40.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 81 (d) 90

Answer key

  1. 197
  2. 70
  3. 325
  4. 126
  5. 46
  6. 268
  7. 97
  8. 22
  9. 1485
  10. 50
  11. 162
  12. 366
  13. 32nd
  14. 49
  15. 179
  16. 35
  17. 23
  18. 162
  19. 729
  20. 186
  21. 74
  22. 324
  23. 27
  24. 31st
  25. 1035
  26. 3741
  27. 82
  28. 25
  29. 11
  30. 630
  31. 3916
  32. 10th
  33. 21
  34. 267
  35. 289
  36. 180
  37. 44
  38. 112
  39. 105
  40. 81

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