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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 203 · 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 29th term of the AP 3, 12, 21, 30, …? (a) 261 (b) 252 (c) 264 (d) 255
  2. 2.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 21 (b) 20 (c) 24 (d) 22
  3. 3.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 3306 (c) 1654 (d) 1596
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 196 (d) 27
  5. 5.What is the 38th term of the AP 19, 23, 27, 31, …? (a) 152 (b) 148 (c) 167 (d) 171
  6. 6.What is the 37th term of the AP 1, 5, 9, 13, …? (a) 149 (b) 148 (c) 144 (d) 145
  7. 7.What is the 18th term of the AP 19, 21, 23, 25, …? (a) 55 (b) 34 (c) 53 (d) 36
  8. 8.What is the 28th term of the AP 5, 8, 11, 14, …? (a) 81 (b) 84 (c) 86 (d) 89
  9. 9.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 378 (c) 379 (d) 756
  10. 10.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 198 (b) 201 (c) 34 (d) 396
  11. 11.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 104 (b) 10 (c) 52 (d) 56
  12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 361 (d) 380
  13. 13.Which term of the AP 10, 13, 16, 19, … is 58? (a) 18th (b) 17th (c) 19th (d) 16th
  14. 14.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 49 (b) 290 (c) 265 (d) 530
  15. 15.What is the 13th term of the AP 11, 15, 19, 23, …? (a) 63 (b) 48 (c) 52 (d) 59
  16. 16.What is the 18th term of the AP 3, 11, 19, 27, …? (a) 147 (b) 144 (c) 136 (d) 139
  17. 17.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 49 (b) 225 (c) 252 (d) 450
  18. 18.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2628 (c) 2592 (d) 5256
  19. 19.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3240 (c) 6480 (d) 3200
  20. 20.What is the 28th term of the AP 10, 12, 14, 16, …? (a) 54 (b) 64 (c) 56 (d) 66
  21. 21.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 15 (b) 19 (c) 16 (d) 17
  22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  23. 23.Which term of the AP 3, 6, 9, 12, … is 69? (a) 22nd (b) 24th (c) 25th (d) 23rd
  24. 24.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 264 (b) 32 (c) 252 (d) 504
  25. 25.What is the missing term in the AP 16, 24, ?, 40, 48? (a) 40 (b) 32 (c) 33 (d) 31
  26. 26.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 756 (d) 378
  27. 27.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 56 (b) 55 (c) 13 (d) 110
  28. 28.What is the 20th term of the AP 9, 12, 15, 18, …? (a) 69 (b) 60 (c) 57 (d) 66
  29. 29.What is the 12th term of the AP 10, 13, 16, 19, …? (a) 33 (b) 36 (c) 46 (d) 43
  30. 30.What is the 24th term of the AP 4, 7, 10, 13, …? (a) 73 (b) 76 (c) 72 (d) 69
  31. 31.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 21 (b) 22 (c) 23 (d) 28
  32. 32.Which term of the AP 5, 14, 23, 32, … is 158? (a) 19th (b) 20th (c) 17th (d) 18th
  33. 33.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 120 (c) 272 (d) 136
  34. 34.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 465 (c) 450 (d) 435
  35. 35.What is the 13th term of the AP 1, 7, 13, 19, …? (a) 73 (b) 72 (c) 78 (d) 79
  36. 36.What is the 35th term of the AP 15, 17, 19, 21, …? (a) 83 (b) 85 (c) 68 (d) 70
  37. 37.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 9 (b) 8 (c) 7 (d) 13
  38. 38.Which term of the AP 15, 18, 21, 24, … is 126? (a) 39th (b) 38th (c) 42nd (d) 37th
  39. 39.What is the 31st term of the AP 11, 13, 15, 17, …? (a) 60 (b) 62 (c) 71 (d) 73
  40. 40.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78

Answer key

  1. 255
  2. 21
  3. 1653
  4. 196
  5. 167
  6. 145
  7. 53
  8. 86
  9. 378
  10. 198
  11. 52
  12. 361
  13. 17th
  14. 265
  15. 59
  16. 139
  17. 225
  18. 2628
  19. 3240
  20. 64
  21. 16
  22. 81
  23. 23rd
  24. 252
  25. 32
  26. 729
  27. 55
  28. 66
  29. 43
  30. 73
  31. 22
  32. 18th
  33. 136
  34. 465
  35. 73
  36. 83
  37. 8
  38. 38th
  39. 71
  40. 144

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