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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 305 · 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 10 terms of the AP 6, 11, 16, …? (a) 570 (b) 285 (c) 51 (d) 310
  2. 2.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 46 (b) 45 (c) 54 (d) 44
  3. 3.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 35 (d) 342
  4. 4.What is the 18th term of the AP 16, 21, 26, 31, …? (a) 90 (b) 85 (c) 101 (d) 106
  5. 5.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 19 (b) 15 (c) 17 (d) 16
  6. 6.What is the 10th term of the AP 1, 6, 11, 16, …? (a) 50 (b) 46 (c) 51 (d) 45
  7. 7.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 15 (b) 24 (c) 16 (d) 17
  8. 8.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 13 (b) 90 (c) 45 (d) 50
  9. 9.What is the 40th term of the AP 6, 11, 16, 21, …? (a) 201 (b) 195 (c) 206 (d) 200
  10. 10.What is the 11th term of the AP 15, 19, 23, 27, …? (a) 44 (b) 59 (c) 40 (d) 55
  11. 11.What is the 32nd term of the AP 2, 7, 12, 17, …? (a) 162 (b) 160 (c) 157 (d) 155
  12. 12.What is the 19th term of the AP 3, 12, 21, 30, …? (a) 165 (b) 162 (c) 174 (d) 171
  13. 13.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 15 (d) 64
  14. 14.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 23 (b) 27 (c) 22 (d) 24
  15. 15.What is the 24th term of the AP 12, 19, 26, 33, …? (a) 161 (b) 168 (c) 180 (d) 173
  16. 16.What is the 10th term of the AP 7, 13, 19, 25, …? (a) 60 (b) 67 (c) 54 (d) 61
  17. 17.What is the 10th term of the AP 3, 8, 13, 18, …? (a) 48 (b) 45 (c) 53 (d) 50
  18. 18.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 25 (b) 75 (c) 80 (d) 150
  19. 19.What is the 23rd term of the AP 18, 20, 22, 24, …? (a) 62 (b) 64 (c) 46 (d) 44
  20. 20.What is the 23rd term of the AP 4, 8, 12, 16, …? (a) 96 (b) 88 (c) 93 (d) 92
  21. 21.What is the 14th term of the AP 15, 19, 23, 27, …? (a) 52 (b) 67 (c) 71 (d) 56
  22. 22.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 12 (b) 16 (c) 14 (d) 13
  23. 23.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 253 (d) 484
  24. 24.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3916 (c) 3828 (d) 3872
  25. 25.What is the 28th term of the AP 5, 8, 11, 14, …? (a) 86 (b) 81 (c) 84 (d) 89
  26. 26.Which term of the AP 17, 20, 23, 26, … is 83? (a) 24th (b) 25th (c) 22nd (d) 23rd
  27. 27.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 512 (c) 528 (d) 1056
  28. 28.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 684 (b) 56 (c) 372 (d) 342
  29. 29.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 78 (d) 156
  30. 30.What is the 21st term of the AP 8, 11, 14, 17, …? (a) 63 (b) 71 (c) 60 (d) 68
  31. 31.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 156 (b) 37 (c) 176 (d) 312
  32. 32.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 56 (b) 315 (c) 576 (d) 288
  33. 33.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 51 (b) 12 (c) 100 (d) 50
  34. 34.Which term of the AP 11, 18, 25, 32, … is 172? (a) 24th (b) 26th (c) 23rd (d) 25th
  35. 35.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 27 (b) 36 (c) 28 (d) 29
  36. 36.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 43 (b) 250 (c) 500 (d) 270
  37. 37.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 210 (c) 462 (d) 231
  38. 38.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 465 (d) 497
  39. 39.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  40. 40.What is the 11th term of the AP 11, 16, 21, 26, …? (a) 55 (b) 66 (c) 50 (d) 61

Answer key

  1. 285
  2. 45
  3. 324
  4. 101
  5. 16
  6. 46
  7. 16
  8. 45
  9. 201
  10. 55
  11. 157
  12. 165
  13. 64
  14. 23
  15. 173
  16. 61
  17. 48
  18. 75
  19. 62
  20. 92
  21. 67
  22. 13
  23. 484
  24. 3916
  25. 86
  26. 23rd
  27. 528
  28. 342
  29. 78
  30. 68
  31. 156
  32. 288
  33. 50
  34. 24th
  35. 28
  36. 250
  37. 231
  38. 496
  39. 169
  40. 61

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