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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 781 · 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 69? (a) 4830 (b) 2346 (c) 2416 (d) 2415
  2. 2.What is the 20th term of the AP 7, 13, 19, 25, …? (a) 114 (b) 121 (c) 120 (d) 127
  3. 3.What is the missing term in the AP 18, 26, ?, 42, 50? (a) 33 (b) 42 (c) 34 (d) 35
  4. 4.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 105 (b) 182 (c) 25 (d) 91
  5. 5.What is the 16th term of the AP 7, 12, 17, 22, …? (a) 75 (b) 80 (c) 87 (d) 82
  6. 6.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 56 (b) 55 (c) 13 (d) 110
  7. 7.What is the 19th term of the AP 3, 5, 7, 9, …? (a) 39 (b) 38 (c) 36 (d) 41
  8. 8.What is the 32nd term of the AP 10, 16, 22, 28, …? (a) 196 (b) 192 (c) 202 (d) 186
  9. 9.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
  10. 10.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 33 (b) 152 (c) 168 (d) 304
  11. 11.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 435 (d) 841
  12. 12.What is the 23rd term of the AP 7, 16, 25, 34, …? (a) 214 (b) 205 (c) 207 (d) 198
  13. 13.What is the 20th term of the AP 5, 11, 17, 23, …? (a) 114 (b) 125 (c) 120 (d) 119
  14. 14.What is the 34th term of the AP 14, 20, 26, 32, …? (a) 218 (b) 204 (c) 198 (d) 212
  15. 15.What is the 35th term of the AP 7, 13, 19, 25, …? (a) 210 (b) 217 (c) 211 (d) 204
  16. 16.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 290 (b) 160 (c) 145 (d) 28
  17. 17.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 20 (b) 17 (c) 15 (d) 16
  18. 18.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5050 (c) 5000 (d) 4950
  19. 19.What is the missing term in the AP 10, 15, ?, 25, 30? (a) 25 (b) 19 (c) 20 (d) 21
  20. 20.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 243 (b) 225 (c) 450 (d) 41
  21. 21.What is the 19th term of the AP 18, 27, 36, 45, …? (a) 180 (b) 171 (c) 189 (d) 162
  22. 22.What is the 22nd term of the AP 6, 13, 20, 27, …? (a) 154 (b) 147 (c) 160 (d) 153
  23. 23.What is the 23rd term of the AP 14, 17, 20, 23, …? (a) 80 (b) 66 (c) 83 (d) 69
  24. 24.What is the 17th term of the AP 6, 9, 12, 15, …? (a) 54 (b) 48 (c) 51 (d) 57
  25. 25.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 380 (c) 37 (d) 190
  26. 26.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 75 (b) 18 (c) 140 (d) 70
  27. 27.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 21 (b) 75 (c) 130 (d) 65
  28. 28.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 38 (b) 46 (c) 36 (d) 37
  29. 29.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 385 (b) 352 (c) 62 (d) 704
  30. 30.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 992 (d) 496
  31. 31.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 200 (b) 40 (c) 180 (d) 360
  32. 32.Which term of the AP 20, 26, 32, 38, … is 152? (a) 25th (b) 24th (c) 23rd (d) 22nd
  33. 33.What is the 16th term of the AP 4, 8, 12, 16, …? (a) 65 (b) 64 (c) 60 (d) 68
  34. 34.What is the 33rd term of the AP 18, 20, 22, 24, …? (a) 82 (b) 84 (c) 66 (d) 64
  35. 35.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 1128 (c) 2352 (d) 1152
  36. 36.What is the 11th term of the AP 8, 14, 20, 26, …? (a) 74 (b) 60 (c) 68 (d) 66
  37. 37.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  38. 38.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 16 (b) 120 (c) 65 (d) 60
  39. 39.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 722 (c) 703 (d) 741
  40. 40.What is the 14th term of the AP 2, 6, 10, 14, …? (a) 58 (b) 54 (c) 52 (d) 56

Answer key

  1. 2415
  2. 121
  3. 34
  4. 91
  5. 82
  6. 55
  7. 39
  8. 196
  9. 529
  10. 152
  11. 841
  12. 205
  13. 119
  14. 212
  15. 211
  16. 145
  17. 16
  18. 5050
  19. 20
  20. 225
  21. 180
  22. 153
  23. 80
  24. 54
  25. 361
  26. 70
  27. 65
  28. 37
  29. 352
  30. 496
  31. 180
  32. 23rd
  33. 64
  34. 82
  35. 1176
  36. 68
  37. 324
  38. 60
  39. 741
  40. 54

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