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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 632 · 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 12 terms of the AP 7, 11, 15, …? (a) 696 (b) 51 (c) 348 (d) 372
  2. 2.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 18 (b) 120 (c) 60 (d) 63
  3. 3.What is the 39th term of the AP 18, 20, 22, 24, …? (a) 78 (b) 96 (c) 94 (d) 76
  4. 4.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4560 (c) 4608 (d) 4656
  5. 5.Which term of the AP 5, 11, 17, 23, … is 161? (a) 26th (b) 28th (c) 27th (d) 29th
  6. 6.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 70 (c) 15 (d) 63
  7. 7.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 594 (b) 52 (c) 297 (d) 302
  8. 8.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 234 (b) 32 (c) 132 (d) 117
  9. 9.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 25 (b) 26 (c) 23 (d) 24
  10. 10.Which term of the AP 10, 12, 14, 16, … is 48? (a) 21st (b) 19th (c) 24th (d) 20th
  11. 11.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 4371 (c) 8930 (d) 4465
  12. 12.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 192 (c) 26 (d) 108
  13. 13.What is the 27th term of the AP 2, 6, 10, 14, …? (a) 110 (b) 108 (c) 104 (d) 106
  14. 14.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 144 (b) 286 (c) 143 (d) 18
  15. 15.What is the missing term in the AP 19, 26, ?, 40, 47? (a) 40 (b) 33 (c) 34 (d) 32
  16. 16.What is the missing term in the AP 20, 24, ?, 32, 36? (a) 29 (b) 28 (c) 27 (d) 32
  17. 17.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 3160 (c) 3240 (d) 6480
  18. 18.What is the missing term in the AP 14, ?, 32, 41, 50? (a) 22 (b) 23 (c) 24 (d) 32
  19. 19.What is the 14th term of the AP 19, 21, 23, 25, …? (a) 26 (b) 47 (c) 28 (d) 45
  20. 20.What is the 21st term of the AP 18, 21, 24, 27, …? (a) 81 (b) 78 (c) 60 (d) 63
  21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 576 (d) 47
  22. 22.What is the 34th term of the AP 2, 5, 8, 11, …? (a) 99 (b) 104 (c) 102 (d) 101
  23. 23.What is the 17th term of the AP 1, 4, 7, 10, …? (a) 49 (b) 48 (c) 51 (d) 52
  24. 24.What is the 17th term of the AP 6, 13, 20, 27, …? (a) 119 (b) 112 (c) 118 (d) 125
  25. 25.What is the 28th term of the AP 14, 18, 22, 26, …? (a) 112 (b) 122 (c) 108 (d) 126
  26. 26.What is the 37th term of the AP 8, 12, 16, 20, …? (a) 152 (b) 148 (c) 144 (d) 156
  27. 27.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3828 (c) 3872 (d) 3916
  28. 28.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 486 (b) 270 (c) 243 (d) 51
  29. 29.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3362 (c) 3321 (d) 3403
  30. 30.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3655 (c) 3698 (d) 3741
  31. 31.What is the 24th term of the AP 11, 14, 17, 20, …? (a) 72 (b) 83 (c) 69 (d) 80
  32. 32.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 23 (b) 21 (c) 22 (d) 28
  33. 33.What is the 33rd term of the AP 9, 11, 13, 15, …? (a) 73 (b) 66 (c) 64 (d) 75
  34. 34.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 19 (b) 192 (c) 96 (d) 104
  35. 35.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 550 (b) 45 (c) 275 (d) 297
  36. 36.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 522 (b) 53 (c) 288 (d) 261
  37. 37.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 8 (b) 10 (c) 7 (d) 9
  38. 38.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 342 (c) 162 (d) 171
  39. 39.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729
  40. 40.What is the 37th term of the AP 5, 8, 11, 14, …? (a) 108 (b) 111 (c) 116 (d) 113

Answer key

  1. 348
  2. 60
  3. 94
  4. 4656
  5. 27th
  6. 63
  7. 297
  8. 117
  9. 24
  10. 20th
  11. 4465
  12. 96
  13. 106
  14. 143
  15. 33
  16. 28
  17. 3240
  18. 23
  19. 45
  20. 78
  21. 576
  22. 101
  23. 49
  24. 118
  25. 122
  26. 152
  27. 3916
  28. 243
  29. 3403
  30. 3741
  31. 80
  32. 22
  33. 73
  34. 96
  35. 275
  36. 261
  37. 8
  38. 171
  39. 729
  40. 113

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