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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 118 · 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 7 terms of the AP 9, 10, 11, …? (a) 15 (b) 84 (c) 168 (d) 85
  2. 2.What is the 26th term of the AP 13, 17, 21, 25, …? (a) 117 (b) 113 (c) 104 (d) 100
  3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 190 (c) 37 (d) 361
  4. 4.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 46 (b) 45 (c) 11 (d) 90
  5. 5.What is the 20th term of the AP 8, 12, 16, 20, …? (a) 88 (b) 80 (c) 84 (d) 76
  6. 6.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 29 (b) 190 (c) 100 (d) 95
  7. 7.Which term of the AP 1, 3, 5, 7, … is 27? (a) 15th (b) 13th (c) 14th (d) 16th
  8. 8.What is the 21st term of the AP 6, 12, 18, 24, …? (a) 126 (b) 120 (c) 127 (d) 132
  9. 9.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 21 (d) 11
  10. 10.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 33 (b) 25 (c) 24 (d) 23
  11. 11.What is the 39th term of the AP 8, 11, 14, 17, …? (a) 114 (b) 117 (c) 122 (d) 125
  12. 12.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 3741 (c) 7656 (d) 3828
  13. 13.What is the missing term in the AP 15, 24, 33, ?, 51? (a) 41 (b) 42 (c) 43 (d) 51
  14. 14.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 278 (b) 275 (c) 40 (d) 550
  15. 15.What is the 24th term of the AP 8, 12, 16, 20, …? (a) 104 (b) 100 (c) 96 (d) 92
  16. 16.What is the 18th term of the AP 1, 9, 17, 25, …? (a) 144 (b) 136 (c) 145 (d) 137
  17. 17.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4656 (c) 9312 (d) 4560
  18. 18.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 72 (c) 12 (d) 73
  19. 19.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 26 (b) 29 (c) 27 (d) 25
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 784 (d) 406
  21. 21.What is the missing term in the AP 10, ?, 28, 37, 46? (a) 28 (b) 20 (c) 18 (d) 19
  22. 22.What is the 23rd term of the AP 9, 15, 21, 27, …? (a) 138 (b) 132 (c) 141 (d) 147
  23. 23.Which term of the AP 9, 14, 19, 24, … is 129? (a) 24th (b) 25th (c) 27th (d) 26th
  24. 24.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2416 (c) 2415 (d) 2346
  25. 25.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 225 (b) 450 (c) 230 (d) 45
  26. 26.What is the 16th term of the AP 5, 12, 19, 26, …? (a) 110 (b) 117 (c) 112 (d) 105
  27. 27.What is the 24th term of the AP 9, 15, 21, 27, …? (a) 147 (b) 144 (c) 138 (d) 153
  28. 28.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 504 (c) 1008 (d) 540
  29. 29.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 120 (b) 18 (c) 63 (d) 60
  30. 30.What is the 12th term of the AP 6, 12, 18, 24, …? (a) 73 (b) 66 (c) 72 (d) 78
  31. 31.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 25 (b) 29 (c) 23 (d) 24
  32. 32.What is the 17th term of the AP 7, 9, 11, 13, …? (a) 41 (b) 39 (c) 32 (d) 34
  33. 33.What is the 19th term of the AP 2, 10, 18, 26, …? (a) 144 (b) 146 (c) 154 (d) 152
  34. 34.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 297 (b) 594 (c) 57 (d) 324
  35. 35.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 18 (b) 17 (c) 23 (d) 16
  36. 36.What is the 37th term of the AP 17, 22, 27, 32, …? (a) 202 (b) 185 (c) 180 (d) 197
  37. 37.What is the 15th term of the AP 19, 23, 27, 31, …? (a) 56 (b) 79 (c) 60 (d) 75
  38. 38.What is the 40th term of the AP 18, 24, 30, 36, …? (a) 240 (b) 252 (c) 234 (d) 258
  39. 39.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 34 (b) 42 (c) 32 (d) 33
  40. 40.Which term of the AP 9, 17, 25, 33, … is 233? (a) 31st (b) 29th (c) 30th (d) 28th

Answer key

  1. 84
  2. 113
  3. 361
  4. 45
  5. 84
  6. 95
  7. 14th
  8. 126
  9. 36
  10. 24
  11. 122
  12. 3828
  13. 42
  14. 275
  15. 100
  16. 137
  17. 4656
  18. 72
  19. 26
  20. 784
  21. 19
  22. 141
  23. 25th
  24. 2415
  25. 225
  26. 110
  27. 147
  28. 504
  29. 60
  30. 72
  31. 24
  32. 39
  33. 146
  34. 297
  35. 17
  36. 197
  37. 75
  38. 252
  39. 33
  40. 29th

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