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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 812 · 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 missing term in the AP 14, 16, 18, ?, 22? (a) 21 (b) 20 (c) 22 (d) 19
  2. 2.What is the 16th term of the AP 14, 17, 20, 23, …? (a) 62 (b) 48 (c) 45 (d) 59
  3. 3.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 136 (b) 124 (c) 26 (d) 248
  4. 4.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 54 (c) 27 (d) 7
  5. 5.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 45 (d) 552
  6. 6.What is the 12th term of the AP 4, 10, 16, 22, …? (a) 72 (b) 66 (c) 70 (d) 76
  7. 7.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4232 (c) 4186 (d) 4278
  8. 8.What is the 10th term of the AP 15, 19, 23, 27, …? (a) 36 (b) 40 (c) 55 (d) 51
  9. 9.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 18 (b) 127 (c) 126 (d) 252
  10. 10.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 870 (c) 436 (d) 435
  11. 11.What is the 35th term of the AP 17, 23, 29, 35, …? (a) 204 (b) 227 (c) 210 (d) 221
  12. 12.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 23 (b) 20 (c) 21 (d) 19
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 900 (c) 930 (d) 59
  14. 14.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 270 (b) 43 (c) 250 (d) 500
  15. 15.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 140 (b) 70 (c) 71 (d) 13
  16. 16.What is the 38th term of the AP 13, 21, 29, 37, …? (a) 296 (b) 304 (c) 317 (d) 309
  17. 17.What is the 39th term of the AP 3, 5, 7, 9, …? (a) 79 (b) 81 (c) 78 (d) 76
  18. 18.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 2850 (c) 2775 (d) 5700
  19. 19.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 6 (b) 24 (c) 21 (d) 42
  20. 20.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 562 (c) 528 (d) 561
  21. 21.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 8742 (c) 4372 (d) 4371
  22. 22.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 650 (b) 55 (c) 325 (d) 350
  23. 23.What is the 16th term of the AP 20, 23, 26, 29, …? (a) 45 (b) 68 (c) 65 (d) 48
  24. 24.Which term of the AP 3, 6, 9, 12, … is 99? (a) 34th (b) 32nd (c) 35th (d) 33rd
  25. 25.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 19 (b) 17 (c) 18 (d) 22
  26. 26.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4187 (c) 4095 (d) 4186
  27. 27.Which term of the AP 11, 14, 17, 20, … is 95? (a) 30th (b) 29th (c) 31st (d) 28th
  28. 28.Which term of the AP 7, 16, 25, 34, … is 178? (a) 20th (b) 21st (c) 22nd (d) 19th
  29. 29.What is the 11th term of the AP 18, 23, 28, 33, …? (a) 73 (b) 50 (c) 55 (d) 68
  30. 30.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 400 (d) 39
  31. 31.What is the 33rd term of the AP 9, 12, 15, 18, …? (a) 99 (b) 96 (c) 105 (d) 108
  32. 32.What is the 11th term of the AP 16, 18, 20, 22, …? (a) 36 (b) 22 (c) 20 (d) 38
  33. 33.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 33 (b) 38 (c) 31 (d) 32
  34. 34.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 41 (b) 40 (c) 39 (d) 48
  35. 35.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 37 (b) 44 (c) 35 (d) 36
  36. 36.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 75 (b) 140 (c) 70 (d) 24
  37. 37.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 784 (d) 812
  38. 38.Which term of the AP 19, 28, 37, 46, … is 343? (a) 36th (b) 37th (c) 38th (d) 39th
  39. 39.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  40. 40.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 37 (b) 133 (c) 154 (d) 266

Answer key

  1. 20
  2. 59
  3. 124
  4. 27
  5. 529
  6. 70
  7. 4278
  8. 51
  9. 126
  10. 435
  11. 221
  12. 20
  13. 900
  14. 250
  15. 70
  16. 309
  17. 79
  18. 2850
  19. 21
  20. 561
  21. 4371
  22. 325
  23. 65
  24. 33rd
  25. 18
  26. 4186
  27. 29th
  28. 20th
  29. 68
  30. 400
  31. 105
  32. 36
  33. 32
  34. 40
  35. 36
  36. 70
  37. 784
  38. 37th
  39. 81
  40. 133

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