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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 621 · 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 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 132 (c) 66 (d) 78
  2. 2.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 17 (b) 18 (c) 19 (d) 16
  3. 3.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 322 (b) 161 (c) 182 (d) 41
  4. 4.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 20 (b) 96 (c) 180 (d) 90
  5. 5.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3828 (c) 7656 (d) 3829
  6. 6.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 162 (c) 171 (d) 342
  7. 7.What is the 23rd term of the AP 15, 22, 29, 36, …? (a) 154 (b) 161 (c) 176 (d) 169
  8. 8.What is the 23rd term of the AP 15, 17, 19, 21, …? (a) 61 (b) 46 (c) 44 (d) 59
  9. 9.What is the missing term in the AP 19, 23, 27, ?, 35? (a) 31 (b) 35 (c) 32 (d) 30
  10. 10.What is the 17th term of the AP 16, 18, 20, 22, …? (a) 50 (b) 48 (c) 32 (d) 34
  11. 11.What is the 17th term of the AP 12, 15, 18, 21, …? (a) 63 (b) 48 (c) 60 (d) 51
  12. 12.What is the missing term in the AP 13, 21, 29, ?, 45? (a) 37 (b) 38 (c) 45 (d) 36
  13. 13.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 19 (b) 168 (c) 90 (d) 84
  14. 14.What is the 26th term of the AP 9, 11, 13, 15, …? (a) 59 (b) 50 (c) 52 (d) 61
  15. 15.What is the 40th term of the AP 18, 20, 22, 24, …? (a) 78 (b) 98 (c) 96 (d) 80
  16. 16.What is the 28th term of the AP 9, 13, 17, 21, …? (a) 121 (b) 117 (c) 108 (d) 112
  17. 17.What is the missing term in the AP 9, 16, 23, ?, 37? (a) 29 (b) 30 (c) 37 (d) 31
  18. 18.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 5 (c) 3 (d) 4
  19. 19.Which term of the AP 5, 11, 17, 23, … is 143? (a) 26th (b) 24th (c) 23rd (d) 25th
  20. 20.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 408 (b) 204 (c) 216 (d) 28
  21. 21.What is the 17th term of the AP 5, 7, 9, 11, …? (a) 32 (b) 39 (c) 37 (d) 34
  22. 22.What is the 39th term of the AP 6, 12, 18, 24, …? (a) 234 (b) 228 (c) 235 (d) 240
  23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 406 (d) 812
  24. 24.What is the 16th term of the AP 12, 21, 30, 39, …? (a) 135 (b) 144 (c) 147 (d) 156
  25. 25.What is the 18th term of the AP 20, 26, 32, 38, …? (a) 128 (b) 122 (c) 108 (d) 102
  26. 26.What is the missing term in the AP 20, 28, 36, ?, 52? (a) 43 (b) 44 (c) 52 (d) 45
  27. 27.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 34 (b) 26 (c) 25 (d) 27
  28. 28.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1035 (c) 1036 (d) 2070
  29. 29.What is the missing term in the AP 10, 14, 18, ?, 26? (a) 23 (b) 22 (c) 21 (d) 26
  30. 30.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 55 (b) 330 (c) 660 (d) 335
  31. 31.Which term of the AP 11, 18, 25, 32, … is 123? (a) 16th (b) 18th (c) 17th (d) 19th
  32. 32.What is the 37th term of the AP 18, 27, 36, 45, …? (a) 333 (b) 324 (c) 342 (d) 351
  33. 33.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 51 (b) 11 (c) 54 (d) 102
  34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  35. 35.What is the 32nd term of the AP 19, 28, 37, 46, …? (a) 279 (b) 307 (c) 298 (d) 288
  36. 36.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 253 (c) 242 (d) 506
  37. 37.Which term of the AP 20, 27, 34, 41, … is 153? (a) 22nd (b) 19th (c) 21st (d) 20th
  38. 38.What is the 34th term of the AP 3, 10, 17, 24, …? (a) 241 (b) 234 (c) 231 (d) 238
  39. 39.Which term of the AP 6, 9, 12, 15, … is 81? (a) 26th (b) 25th (c) 28th (d) 27th
  40. 40.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 60 (b) 65 (c) 22 (d) 120

Answer key

  1. 66
  2. 17
  3. 161
  4. 90
  5. 3828
  6. 171
  7. 169
  8. 59
  9. 31
  10. 48
  11. 60
  12. 37
  13. 84
  14. 59
  15. 96
  16. 117
  17. 30
  18. 4
  19. 24th
  20. 204
  21. 37
  22. 234
  23. 784
  24. 147
  25. 122
  26. 44
  27. 26
  28. 1035
  29. 22
  30. 330
  31. 17th
  32. 342
  33. 51
  34. 900
  35. 298
  36. 253
  37. 20th
  38. 234
  39. 26th
  40. 60

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