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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 499 · 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 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 600 (d) 47
  2. 2.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 153 (b) 306 (c) 29 (d) 156
  3. 3.Which term of the AP 3, 5, 7, 9, … is 41? (a) 19th (b) 20th (c) 21st (d) 22nd
  4. 4.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 147 (b) 168 (c) 294 (d) 39
  5. 5.What is the 16th term of the AP 17, 25, 33, 41, …? (a) 120 (b) 145 (c) 128 (d) 137
  6. 6.Which term of the AP 17, 22, 27, 32, … is 177? (a) 34th (b) 35th (c) 32nd (d) 33rd
  7. 7.What is the 17th term of the AP 5, 14, 23, 32, …? (a) 153 (b) 144 (c) 149 (d) 158
  8. 8.What is the 11th term of the AP 2, 4, 6, 8, …? (a) 20 (b) 23 (c) 24 (d) 22
  9. 9.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 90 (d) 45
  10. 10.Which term of the AP 19, 21, 23, 25, … is 75? (a) 29th (b) 30th (c) 28th (d) 31st
  11. 11.What is the 39th term of the AP 15, 24, 33, 42, …? (a) 342 (b) 366 (c) 357 (d) 351
  12. 12.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 900 (d) 59
  13. 13.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 120 (c) 204 (d) 102
  14. 14.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 24 (b) 90 (c) 80 (d) 160
  15. 15.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 41 (b) 33 (c) 31 (d) 32
  16. 16.What is the 21st term of the AP 3, 8, 13, 18, …? (a) 105 (b) 103 (c) 100 (d) 108
  17. 17.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 968 (c) 946 (d) 1980
  18. 18.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 630 (c) 648 (d) 666
  19. 19.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 648 (b) 348 (c) 324 (d) 49
  20. 20.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 203 (b) 42 (c) 198 (d) 396
  21. 21.What is the 18th term of the AP 11, 16, 21, 26, …? (a) 85 (b) 96 (c) 90 (d) 101
  22. 22.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 3306 (c) 1653 (d) 1596
  23. 23.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 230 (b) 210 (c) 420 (d) 39
  24. 24.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 342 (b) 171 (c) 35 (d) 189
  25. 25.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 24 (b) 21 (c) 42 (d) 6
  26. 26.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3362 (c) 3403 (d) 3321
  27. 27.What is the 21st term of the AP 16, 24, 32, 40, …? (a) 168 (b) 184 (c) 160 (d) 176
  28. 28.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 14 (b) 13 (c) 20 (d) 15
  29. 29.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 144 (b) 264 (c) 27 (d) 132
  30. 30.What is the missing term in the AP 13, 21, ?, 37, 45? (a) 28 (b) 29 (c) 30 (d) 37
  31. 31.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 55 (b) 65 (c) 110 (d) 19
  32. 32.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2017 (c) 4032 (d) 2016
  33. 33.What is the 18th term of the AP 9, 12, 15, 18, …? (a) 63 (b) 54 (c) 51 (d) 60
  34. 34.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 550 (b) 278 (c) 275 (d) 40
  35. 35.What is the missing term in the AP 10, 15, 20, ?, 30? (a) 24 (b) 30 (c) 26 (d) 25
  36. 36.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 92 (c) 96 (d) 15
  37. 37.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 12 (c) 75 (d) 150
  38. 38.What is the 23rd term of the AP 12, 15, 18, 21, …? (a) 81 (b) 78 (c) 66 (d) 69
  39. 39.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3042 (d) 3081
  40. 40.What is the 33rd term of the AP 16, 25, 34, 43, …? (a) 297 (b) 313 (c) 288 (d) 304

Answer key

  1. 576
  2. 153
  3. 20th
  4. 147
  5. 137
  6. 33rd
  7. 149
  8. 22
  9. 81
  10. 29th
  11. 357
  12. 900
  13. 102
  14. 80
  15. 32
  16. 103
  17. 990
  18. 666
  19. 324
  20. 198
  21. 96
  22. 1653
  23. 210
  24. 171
  25. 21
  26. 3403
  27. 176
  28. 14
  29. 132
  30. 29
  31. 55
  32. 2016
  33. 60
  34. 275
  35. 25
  36. 92
  37. 75
  38. 78
  39. 3081
  40. 304

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